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THE UNIVERSITY OF CALGARY
A Logarithmic Amplifier and Hilbert Transformer
for Optical Single Sideband
by
Christopher Daniel Holdenried
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF ELECTRICAL AND COMPUTER
ENGINEERING
CALGARY, ALBERTA
February, 2005
c© Christopher Daniel Holdenried 2005
THE UNIVERSITY OF CALGARY
FACULTY OF GRADUATE STUDIES
The undersigned certify that they have read, and recommend to the Faculty of Graduate
Studies for acceptance, a thesis entitled “A Logarithmic Amplifier and Hilbert
Transformer for Optical Single Sideband” submitted by Christopher Daniel Holdenried in
partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY.
__________________________________________ Supervisor, Dr. James W. Haslett Department of Electrical and Computer Engineering __________________________________________ Dr. John G. McRory Department of Electrical and Computer Engineering __________________________________________ Dr. Robert J. Davies Department of Electrical and Computer Engineering __________________________________________ Dr. Brent Maundy Department of Electrical and Computer Engineering __________________________________________ Dr. Harvey Yarranton Department of Chemical and Petroleum Engineering __________________________________________ External Examiner, Dr. Calvin Plett Department of Electronics, Carleton University
___________________________ Date
ii
Abstract
Chromatic dispersion is the pulse spreading that occurs during transmission
through optical fiber and is due to the non-constant delay of fiber with wavelength.
Gigabit optical communication systems require some method of dispersion compen-
sation. Optical single sideband (OSSB) is commonly used to transmit narrow-band
signals in order to avoid power fading due to dispersion. However, in the absence
of special optical filters, a broadband Hilbert transformer and logarithmic ampli-
fier are required in order to generate OSSB for baseband gigabit data signals. This
thesis describes the development of unique gigabit logarithmic amplifier and Hilbert
transformer integrated circuits.
The Cherry-Hooper amplifier with emitter follower feedback is introduced as a
gigabit amplifier building block. This circuit is ultimately used to design a broadband
logarithmic amplifier for OSSB. The log amplifier architecture is developed using a
novel design procedure, with proof of a logarithmic response. A Hilbert transformer
integrated circuit is developed based on non-integrated Hilbert transformer designs
by previous researchers. It uses Q-enhanced on-chip LC transmission lines. The log
amplifier and Hilbert transformer designs were fabricated as integrated circuits, and
their performance is verified through measurements of the circuits.
Simulation results of an OSSB system are described and show that the above
mentioned circuits enable an OSSB system with immunity to dispersive power fading.
Actual OSSB transmitters were assembled and measured OSSB optical spectra are
presented for 5 and 10 Gb/s broadband signals and a 1.9 GHz narrow-band signal.
iii
Acknowledgements
I thank Jim Haslett for his superb guidance and sound judgement. I would not
have applied for and won certain awards without his encouragement. Thank you for
helping with designs and the long and productive hours spent writing and editing
articles. He was often able to see core mathematical ideas when I could not. I am
also grateful for his generosity which was demonstrated, for example, by allowing
me to attend conferences very early in my studies. This allowed me to see close up
what was expected of me and how to obtain it.
Thank you to John McRory for teaching me everything I know about microwave
circuits and for help designing the logarithmic amplifier. I thank him for negotiating
access to the NT35 technology at Nortel so that we could fabricate the first loga-
rithmic amplifier. I also gratefully acknowledge the financial support of TRLabs,
including the perks, made possible by John McRory, Roger Pederson, and George
Squires.
Thank you to Bob Davies for guidance with all of the optical communications
aspects of this thesis, and for the idea of this thesis. Thank you to the great minds
who are part of the TRLabs and ATIPS teams for many useful discussions and for
providing a challenging environment. Thank you to Dave Clegg and Chris Haugen
for assistance with experiments and equipment. Thank you to Bogdan Georgescu
for your hard work developing the coupled inductor Q-enhancement principles which
helped me to design the integrated Hilbert transformer. Thank you to Michael Lynch
for many useful discussions, work related and otherwise.
Thank you to A.J. Bergsma and Douglas Beards for their support and design
iv
ideas when designing the first logarithmic amplifier. Thank you to A.J. for teaching
me about IC layout and for working late some nights to finish the IC layout of the
first logarithmic amplifier. Thank you to Nortel for financial support and for allowing
me to work with A.J. and Doug.
Thank you to the Canadian Microelectronics Corporation for paying for the fab-
rication of several ICs that are part of this thesis, for providing access to world class
design software, and for donating test equipment. Without this support I would
never have been able to obtain the results that I did.
I gratefully acknowledge the financial support of NSERC, Alberta iCORE, and
the IEEE. Without this support, my studies would have been cut short. I value the
many friends that I have made through these organizations.
Thank you to Leila Southwood, Pauline Cummings, Simon Arsenault, and Ella
Gee for their administrative support which makes this work possible. Thanks also
to Jonathan Eskritt, Paul Horbal, and Josh Nakaska for keeping the ATIPS system
and web site going when they weren’t busy with their own research. Behind every
strong researcher, there are even stronger administrators.
v
For Regina and Siddhartha.
Thank you for love and support.
vi
Table of Contents
Approval Page ii
Abstract iii
Acknowledgements iv
Dedication vi
Table of Contents vii
List of Tables x
List of Figures xi
List Of Symbols and Abbreviations xvi
1 Introduction 11.1 Research Objective and Scope . . . . . . . . . . . . . . . . . . . . . . 41.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Background 62.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Chromatic Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Types of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Mathematical Definition of Dispersion . . . . . . . . . . . . . 8
2.3 Methods to Compensate for Dispersion . . . . . . . . . . . . . . . . . 92.3.1 Optical Techniques . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Post Detection Compensation . . . . . . . . . . . . . . . . . . 12
2.4 Compatible Optical Single Sideband . . . . . . . . . . . . . . . . . . 142.4.1 Complex Envelope Representation of Bandpass Signals . . . . 142.4.2 COSSB Modulation . . . . . . . . . . . . . . . . . . . . . . . . 172.4.3 COSSB Implementation: The Ideal Minimum Phase Modula-
tor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4.4 Dispersion Effects on Double and Single Sideband Signals . . 212.4.5 Minimum Phase Dispersion Compensation . . . . . . . . . . . 262.4.6 Previous Experiments Using COSSB . . . . . . . . . . . . . . 272.4.7 The Mach-Zehnder Modulator . . . . . . . . . . . . . . . . . . 29
vii
2.4.8 Competing Technologies: Solitons, Coherent Detection Sys-tems, and Duobinary Transmission . . . . . . . . . . . . . . . 31
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Analysis and Design of HBT Cherry-Hooper Amplifiers with Emit-ter Follower Feedback for Optical Communications 36
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Large Signal Performance . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 HBT β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 Small Signal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Design Example . . . . . . . . . . . . . . . . . . . . . . . . . 443.4 Amplifier Noise Performance . . . . . . . . . . . . . . . . . . . . . . 473.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 A Novel Parallel Summation Logarithmic Amplifier 554.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2 Distinction and Comparison of Logarithmic Amplifiers . . . . . . . . 56
4.2.1 The Series Linear-Limit Logarithmic Amplifier . . . . . . . . 574.2.2 Parallel Summation Logarithmic Amplifiers . . . . . . . . . . 59
4.3 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3.1 Logarithmic Slope and Intercept . . . . . . . . . . . . . . . . . 684.3.2 The Delay Matched Progressive Compression Amplifier . . . . 69
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier . . . 704.4.1 Design of Implementation 1 . . . . . . . . . . . . . . . . . . . 704.4.2 Measurements of Implementation 1 . . . . . . . . . . . . . . . 73
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier . 804.5.1 Design of Implementation 2 . . . . . . . . . . . . . . . . . . . 804.5.2 Measurements of Implementation 2 . . . . . . . . . . . . . . . 87
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5 A 10 Gb/s Hilbert Transformer with Q-Enhanced LC TransmissionLines 92
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925.2 HT Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.3 Design of LC Transmission Lines . . . . . . . . . . . . . . . . . . . . 96
5.3.1 Q-Enhanced LC Transmission Lines . . . . . . . . . . . . . . . 975.4 Circuit Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
viii
6 Simulations of COSSB System Implementations 1166.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166.2 Performance of the Logarithmic Amplifier . . . . . . . . . . . . . . . 1166.3 Performance of the HT . . . . . . . . . . . . . . . . . . . . . . . . . 1216.4 Combined Performance of Logarithmic Amplifier and HT Circuits . . 125
6.4.1 Performance at a Mach-Zehnder Modulation Depth of 0.25 . 1256.4.2 Performance at a Mach-Zehnder Modulation Depth of 0.20 . 133
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7 Measurements of COSSB Transmitters 1407.1 10 Gb/s COSSB Experiment Using the HT . . . . . . . . . . . . . . 1407.2 COSSB Experiments Using the HT and the Logarithmic Amplifier . . 145
7.2.1 Experiment Using a 1.9 GHz Sinusoid . . . . . . . . . . . . . 1457.2.2 Experiment Using Filtered 5 Gb/s Data . . . . . . . . . . . . 147
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8 Conclusions 1558.0.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Bibliography 160
A Amplifier DC Transfer Characteristic 167
B Analysis of the Emitter Follower Load 169
C Derivation of Equation (3.11) 171
D Example Calculation of an Amplifier Noise Contribution 172
E Widlar Biasing 174
F Design of the Logarithmic Amplifier Test Fixture 178
G Description of Equipment Used for COSSB Experiments 182
ix
List of Tables
3.1 Differential output noise of the CHEF amplifier at 1 GHz. . . . . . . 49
4.1 Comparison of high frequency true log amplifiers. . . . . . . . . . . . 90
5.1 Noise figure of HT die C with Q-enhancement turned on. . . . . . . . 109
G.1 List of major equipment used in COSSB experiments. . . . . . . . . . 183G.2 Power characteristic of the Sumitomo intensity modulator. . . . . . . 190
x
List of Figures
1.1 Long-haul optical system architectures. . . . . . . . . . . . . . . . . . 2
2.1 Pulse spreading due to chromatic dispersion. . . . . . . . . . . . . . . 72.2 A typical loss and dispersion profile for single mode fiber. . . . . . . . 102.3 Narrow-band bandpass signal. . . . . . . . . . . . . . . . . . . . . . . 152.4 Ideal minimum phase modulator. . . . . . . . . . . . . . . . . . . . . 212.5 Electrical signals at points throughout the COSSB system. . . . . . . 222.6 Filtered 10 Gb/s DSB and SSB signals plotted against frequency nor-
malized to the carrier. . . . . . . . . . . . . . . . . . . . . . . . . . . 232.7 Eye diagram of detected SSB signal. . . . . . . . . . . . . . . . . . . 232.8 Detected 10 Gb/s DSB signal after 200 km of dispersive fiber. . . . . 252.9 Detected 10 Gb/s SSB signal after 200 km of dispersive fiber. . . . . 262.10 Ideal minimum phase dispersion compensator. . . . . . . . . . . . . . 282.11 Dual arm Mach-Zehnder modulator. . . . . . . . . . . . . . . . . . . . 302.12 Transfer function of a Mach-Zehnder with Vπ=1. . . . . . . . . . . . . 31
3.1 Cherry-Hooper amplifier with emitter follower feedback. . . . . . . . . 373.2 Plot of AC β. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3 CHEF amplifier (a) differential mode half circuit and (b) small signal
equivalent including source and load impedances. . . . . . . . . . . . 413.4 Magnitude and group delay responses for a second order system. . . . 443.5 Eye diagrams for a 10 Gb/s signal filtered with second order systems
having (a) Q = 1/√
3 and (b) Q = 1.0. . . . . . . . . . . . . . . . . . 443.6 Plot of Q factor for different values of R1,R2, and R′
f . . . . . . . . . 463.7 Plot of 3 dB bandwidth for different values of R1,R2, and R′
f . . . . . 463.8 Plot of low frequency gain for different values of R1,R2, and R′
f . . . . 463.9 Schematic diagram of the CHEF amplifier test circuit. . . . . . . . . 503.10 CHEF amplifier IC microphotograph. . . . . . . . . . . . . . . . . . . 513.11 Comparison of theoretical gain based on equations (3.9) and (C.2),
simulated gain, and measured gain. . . . . . . . . . . . . . . . . . . . 523.12 Comparison of theoretical group delay based on equations (3.9) and (C.2)
, as well as simulated and measured group delay. . . . . . . . . . . . . 523.13 Measured eye diagrams at 10 Gb/s: (a) Through measurement at
20 mVpp and single-ended CHEF amplifier output for differential in-put signals of amplitude (b) 7 mVpp, (c) 20 mVpp, and (d) 400 mVpp. 54
4.1 Series linear-limit logarithmic amplifier. . . . . . . . . . . . . . . . . . 574.2 Linear-limit logarithmic amplifier response. . . . . . . . . . . . . . . . 58
xi
4.3 High gain limiter and unity gain buffer in parallel. . . . . . . . . . . . 594.4 Progressive compression, parallel summation logarithmic amplifier. . . 604.5 Parallel amplification, parallel summation logarithmic amplifier. . . . 614.6 Parallel summation logarithmic amplifier transfer function. . . . . . . 624.7 An example of a three stage delay matched progressive compression
log amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.8 Parallel summation logarithmic amplifier implementation. . . . . . . . 714.9 Amplifier used as a gain or delay cell. . . . . . . . . . . . . . . . . . . 724.10 Summing/limiting amplifier. . . . . . . . . . . . . . . . . . . . . . . . 724.11 Input matching circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . 724.12 Microphotograph of the Si logarithmic amplifier integrated circuit. . . 734.13 Measured return loss and gain. . . . . . . . . . . . . . . . . . . . . . . 744.14 Measured group delay response. . . . . . . . . . . . . . . . . . . . . . 754.15 Measured logarithmic responses, peak voltages shown. . . . . . . . . 774.16 Logarithmic error for separate and broadband line fits. . . . . . . . . 784.17 Measured and ideal logarithmic amplifier output spectrum for a 1.8 GHz
input tone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.18 Real time oscilloscope plot of single ended output voltage. . . . . . . 794.19 Simulated log amplifier differential responses to sinusoidal inputs with
and without capacitive delay tuning. . . . . . . . . . . . . . . . . . . 814.20 Logarithmic amplifier block diagram. . . . . . . . . . . . . . . . . . . 824.21 Schematic diagram of the input impedance match circuit and first
high gain stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.22 Schematic diagram of the DC offset error reduction circuit. . . . . . . 844.23 Schematic diagram of the output summation circuit. . . . . . . . . . . 844.24 Simulated DC transfer characteristic of logarithmic amplifier over one
hundred Monte Carlo iterations. . . . . . . . . . . . . . . . . . . . . . 864.25 Simulated logarithmic response of SiGe logarithmic amplifier at 4 GHz
for three different temperatures. . . . . . . . . . . . . . . . . . . . . . 864.26 Microphotograph of the SiGe logarithmic amplifier integrated circuit. 874.27 Measured single ended logarithmic response from 100 MHz to 6 GHz. 884.28 Measured real time logarithmic amplifier single ended output waveforms. 89
5.1 Response of filter with an infinite number of taps. . . . . . . . . . . . 935.2 Tapped delay implementation of an HT. . . . . . . . . . . . . . . . . 935.3 Magnitude responses of four tap HTs for three different values of Υ. . 955.4 Spectrum of a COSSB signal generated with a four tap HT. . . . . . 955.5 Schematic diagram of the LC transmission line used in the HT. . . . 975.6 Layout and loss of passive LC transmission line. . . . . . . . . . . . . 985.7 Transformer based Q-enhanced floating inductor. . . . . . . . . . . . 99
xii
5.8 Delay line with emitter follower tap buffers. . . . . . . . . . . . . . . 1005.9 Efficient Q-enhancement circuit using both signal currents. . . . . . . 1015.10 A floating inductor which is Q-enhanced using a simple cross coupled
pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.11 HT summing amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.12 Integrated HT microphotograph. . . . . . . . . . . . . . . . . . . . . 1045.13 Supply independent current source. . . . . . . . . . . . . . . . . . . . 1045.14 Measured S11 and S22 of three dice with Q-enhancement on. . . . . . 1065.15 Plot of (a) S21 and (b) group delay simulated with resistive and ca-
pacitive layout parasitics. . . . . . . . . . . . . . . . . . . . . . . . . . 1075.16 Plot of (a) measured S21 and normalized theoretical S21 and (b) group
delay for three die with Q-enhancement on and off. . . . . . . . . . . 1085.17 Measured phase of three die with a phase shift corresponding to 120 ps
of delay subtracted, and theoretical four tap HT phase response witha phase shift corresponding to 90 ps of delay subtracted. . . . . . . . 108
5.18 Responses of four tap HTs to the repeated binary pattern 01001000. . 1115.19 Output of transmission line to a sequence of pulses. . . . . . . . . . . 1125.20 Responses of four tap HTs to the repeated binary pattern 10. . . . . 1135.21 Responses of four tap HTs to the repeated binary pattern 1000. . . . 1145.22 Responses of four tap HTs to the repeated binary pattern 0111. . . . 115
6.1 Minimum phase COSSB transmitter. . . . . . . . . . . . . . . . . . . 1176.2 5 Gb/s COSSB signals obtained through transient simulation of vari-
ous HTs and of the logarithmic amplifier IC. . . . . . . . . . . . . . . 1206.3 Transmitted 10 Gb/s COSSB spectrum and eye diagram with tran-
sient simulation of HT IC without logarithmic amplifier. . . . . . . . 1226.4 Eye diagrams of COSSB system using only the HT and using only
self-homodyning post detection equalization. . . . . . . . . . . . . . . 1236.5 Eye diagrams of COSSB system using only the HT and using only
minimum phase post detection equalization. . . . . . . . . . . . . . . 1246.6 Scaled optical signal envelope and its logarithm for a modulation
depth of 0.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.7 Spectra and eye diagram of 5 Gb/s COSSB signals filtered at 2.75 GHz
for a modulation depth of 0.25. . . . . . . . . . . . . . . . . . . . . . 1286.8 Eye diagram of 5 Gb/s signal recovered from a DSB system after
400 km of uncompensated dispersive fiber for a modulation depth of0.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
xiii
6.9 Eye diagram of 5 Gb/s signal recovered from COSSB system with HTIC, without logarithmic amplifier, and using only self-homodyningpost detection equalization after 400 km. The modulation depth is0.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.10 Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and with logarithmic amplifier and using only self-homodyningpost detection equalization. The modulation depth is 0.25. . . . . . . 130
6.11 Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and with logarithmic amplifier and using only minimum phasepost detection equalization. The modulation depth is 0.25. . . . . . . 131
6.12 Spectra recovered from OSSB systems after 400 km with and withoutlogarithmic amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.13 Scaled optical signal envelope and its logarithm for a modulationdepth of 0.20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.14 Spectra and eye diagram of 5 Gb/s COSSB signals filtered at 2.75 GHzfor a modulation depth of 0.20. . . . . . . . . . . . . . . . . . . . . . 134
6.15 Eye diagram of 5 Gb/s signal recovered from a DSB system after400 km of uncompensated dispersive fiber for a modulation depth of0.20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.16 Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and without logarithmic amplifier and using only self-homodyningpost detection equalization. The modulation depth is 0.20. . . . . . . 136
6.17 Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and without the logarithmic amplifier and using only minimumphase post detection equalization. The modulation depth is 0.20. . . 137
6.18 Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and with logarithmic amplifier and using only self-homodyningpost detection equalization. The modulation depth is 0.20. . . . . . . 138
6.19 Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and with logarithmic amplifier and using only minimum phasepost detection equalization. The modulation depth is 0.20. . . . . . . 139
7.1 COSSB 10 Gb/s measurement system. . . . . . . . . . . . . . . . . . 1427.2 Spectrum and eye diagram of 10 Gb/s COSSB signal for 16 dBm of
intensity modulation power. . . . . . . . . . . . . . . . . . . . . . . . 1447.3 Spectrum and eye diagram of 10 Gb/s COSSB signal for 20 dBm of
intensity modulation power. . . . . . . . . . . . . . . . . . . . . . . . 1457.4 Spectrum of 1.9 GHz COSSB signal for 23 dBm of intensity modula-
tion power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1477.5 COSSB measurement system including the logarithmic amplifier. . . . 148
xiv
7.6 Logarithmic amplifier waveforms. . . . . . . . . . . . . . . . . . . . . 1507.7 Spectrum of 5 Gb/s COSSB signal for 17 dBm of intensity modulation
power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1517.8 Spectrum of 5 Gb/s COSSB signal and eye diagrams of 5 Gb/s COSSB
and DSB signals for 20 dBm of intensity modulation power. . . . . . 153
B.1 Schematic diagram of (a) emitter follower output buffers and differen-tial pair load and (b) high frequency small signal circuit of one emitterfollower and a differential mode half circuit of the differential pair. . 170
D.1 Half of the amplifier small signal circuit including dominant noisesources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
E.1 Differential pair. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175E.2 Differential pair with Widlar current biasing. . . . . . . . . . . . . . . 176
F.1 Logarithmic amplifier circuit boards. . . . . . . . . . . . . . . . . . . 179F.2 Logarithmic amplifier test fixture. . . . . . . . . . . . . . . . . . . . . 180
G.1 10 Gb/s optical experiment setup using only HT, Part 1 of 3. . . . . 186G.2 10 Gb/s optical experiment setup using only HT, Part 2 of 3. . . . . 186G.3 10 Gb/s optical experiment setup using only HT, Part 3 of 3. . . . . 187G.4 5 Gb/s optical experiment setup using HT and logarithmic amplifier,
Part 1 of 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187G.5 Logarithmic amplifier DC offset tuning circuit. . . . . . . . . . . . . . 191
xv
List Of Symbols and Abbreviations
5AM Five Analog Metal, an IBM SiGe technology
5HP Five High Performance, an IBM SiGe technology
A Amperes, the unit of current
A Factor difference between the input voltages which causetwo logarithmic amplifier gain paths to limit
A1 Gain across Cµ1 in CHEF amplifier
A2 Gain across Cµ2 in CHEF amplifier
AE Cross sectional area of the base-emitter junction
A(f) Frequency domain bandpass signal containing only positive frequencies
AC Alternating current
AGC Automatic gain control
a(t) Time domain bandpass signal containing only positive frequencies
aL(t) Time domain low pass signal
aLSSB(t) Time domain low pass signal containing only positive or negative
frequencies
a′LSSB(t) Detectable time domain low pass signal containing only positive or
negative frequencies
B Material parameter =5.4 ×1031 for silicon
BER Bit error rate or ratio
BJT Bipolar junction transistor
C Capacitance
C Constant number
C Coulombs, the unit of charge
C12 Noise voltage correlation coefficient
CL Capacitance which loads a CHEF amplifier output terminal
Csubk Collector-substrate parasitic capacitance, k = 1, 2, 3, ...
Cµk Base-collector parasitic capacitance, k = 1, 2, 3, ...
xvi
Cπk Base-emitter parasitic capacitance, k = 1, 2, 3, ...
CHEF Cherry-Hooper amplifier with emitter follower feedback
CMOS Complimentary metal oxide semiconductor
COSSB Compatible optical single sideband
c Speed of light in a vacuum
D Dispersion parameter
Dn Concentration of ‘donor’ or phosphorous atoms
D(s) Laplace domain transfer function denominator
DC Direct current
DCF Dispersion compensating fiber
DP Differential pair
DR Dynamic range
DSB Double sideband
d(t) Detected signal in an optical receiver (generic)
dB Decibels, a logarithmic ratio of power
dBv Logarithmic ratio of voltage referenced to one volt
dBm Logarithmic ratio of power referenced to one milliwatt
EG Bandgap energy =1.12 electron volts for silicon
Ein Mach-Zehnder input signal envelope electric field
Eout Mach-Zehnder output signal envelope electric field
EF Emitter follower
e2R Mean square noise voltage due to resistor R
F Fourier transform operator
F Farads, the unit of capacitance
FFP Fiber Fabry-Perot
f Frequency in hertz
fc Carrier frequency of a bandpass electrical signal
fo Carrier frequency in an optical system
xvii
fT Frequency where bipolar transistor common emittercurrent gain becomes unity
fβ Frequency at which β decreases to 3 dB below βo
fF Femtofarads
GA Gain of an amplifier within a logarithmic amplifier
Gb/s Gigabits per second
Ge Germanium
GN Sum of logarithmic amplifier path gains one to N
Gpk Gain of kth logarithmic amplifier path, k = 1, 2, 3, ...
GHz Gigahertz
GVD Group velocity dispersion
GS/s Gigasamples per second
gm Transconductance (general)
H(f) Frequency domain transfer function (generic)
HDn(f) Transfer function of nth Hilbert transformer delay element , n = 1, 2, 3, ...
HL[ ] Indicates the Hilbert transform of the logarithm of a variable
H Henrys, the unit of inductance
HBT Heterojunction bipolar transistor
HP Hewlett Packard
HSPICE A brand name of SPICE
HT Hilbert transformer
hfe Common emitter current gain of a bipolar transistor
Ik Current (generic) , k = 1, 2, 3, ...
IBk DC base current, k = 1, 2, 3, ...
ICk DC collector current, k = 1, 2, 3, ...
IEk DC emitter current, k = 1, 2, 3, ...
IEEk DC bias current (generic), k = 1, 2, 3, ...
IESk Scaling current proportional to base-emitter junction area, k = 1, 2, 3, ...
IL Limiting current of transconductance element
xviii
IS Output current step for a parallel summation logarithmic amplifier
Ihigh Bias current of a high gain amplifier
Ilow Bias current of a low gain amplifier
Iout Logarithmic amplifier output current
IBM International Business Machines
IC Integrated circuit
IF Intermediate frequency
ISI Inter-symbol interference
IV Current voltage
In Indium
ib AC base current
i2c Mean square collector shot noise current
ip Signal current of transformer primary
is Signal current of transformer secondary
J Joules, the unit of energy
j Imaginary number
K Kelvin, the unit of absolute temperature
k Counting index
k Coupling coefficient between the coils of a transformer
kb Boltzmann’s constant (=1.38 ×10−23J/K)
km Kilometers
L Length of fiber
L Inductance
LE Emitter length
Lp Inductance of transformer primary
Ls Inductance of transformer secondary
LED Light emitting diode
LO Local oscillator
xix
Li Lithium
logA Logarithm with base A
M Scaling factor
M12 Mutual inductance of two transformer coils
MHz Megahertz
MPC Minimum phase compensator
m Meters, the unit of distance
m(t) Optical signal complex envelope, also referred to as simply m
mA Milliamperes
mHz Millihertz
mV Millivolts
mW Milliwatt
N Counting index
NA Concentration of ‘acceptor’ or boron atoms
Nb Niobate
NF Noise figure
NPN P-type silicon between two sections of n-type silicon
NRZ Non-return-to-zero
n Counting index
ni Concentration of holes or electrons in silicon at a given temperature
nr Fiber refractive index
nm Nanometers
ns Nanoseconds
nV Nanovolts
O Oxygen
OC Optical communications
OH Oxygen hydrogen
OSSB Optical single sideband
xx
P Phosphide
PD Detected power
PLL Phase locked loop
PN Junction of p-type and n-type silicon
PNP N-type silicon between two sections of p-type silicon
PRBS Pseudo random bit sequence
PSPL Picosecond Pulse Labs
PTAT Proportional to absolute temperature
pL A pole in the CHEF amplifier transfer function
ps Picoseconds
Q Pole quality factor
Qk kth bipolar transistor; k = 1, 2, 3, ...
QAM Quadrature amplitude modulation
q Electron charge (=1.60 ×10−19C)
< Real operator
R Resistor (generic)
RC Resistor connected to a transistor collector
RE Resistor connected to a transistor emitter
Rf Feedback resistor in the CHEF amplifier
R′
f Rf + re5 in the CHEF amplifier
Rmk Current mirror resistor, k = 1, 2, 3, ...
Ro Output impedance of the CHEF amplifier
Rp Resistance of transformer primary
RS Resistor connected to a voltage source
R′
S Rs + rb1 where rb1 is part of the CHEF amplifier
RF Radio frequency
RMS Root mean square
RSSI Receive strength signal indicator
xxi
RZ Return-to-zero
rbk Parasitic base resistance of kth transistor, k = 1, 2, 3, ...
rc Parasitic collector resistance
rce Collector-emitter resistance
rdk Inverse of transconductance of kth transistor, k = 1, 2, 3, ...
r′dk Equal to 1gmk
+ rek, k = 1, 2, 3, ...
rek Parasitic emitter resistance of kth transistor, k = 1, 2, 3, ...
rπk Intrinsic base-emitter resistance of kth transistor, k = 1, 2, 3, ...
SB(f) Frequency domain bandpass signal
S11 Input reflection coefficient s-parameter
S21 Forward transmission coefficient s-parameter
S22 Output reflection coefficient s-parameter
SICS Supply voltage independent current source
Si Silicon
SMA Subminiature Version A
SNR Signal to noise ratio
SONET Synchronous optical network
SPICE Simulation Program with Integrated Circuit Emphasis
SPM Self-phase modulation
SSB Single sideband
s Laplace domain variable
s(t) Information signal
s(t) Hilbert transform of information signal
sB(t) Time domain bandpass signal
sBSSB(t) Time domain bandpass single sideband signal
T Temperature in kelvins
THz Terahertz
Tb/s Terabits per second
xxii
t Time
U(f) Frequency domain unit step frequency
V Volts, the unit of voltage
VBE DC base-emitter voltage
VCC Positive DC supply voltage
VCE DC collector-emitter voltage
VDC DC offset voltage
VEE Negative DC supply voltage
VL Limiting amplifier maximum output voltage
VT Thermal voltage
Va Mach-Zehnder contact voltage
Vb Mach-Zehnder contact voltage
Vg Propagation velocity of an optical signal
Vin Input DC voltage (generic)
Vintercept Logarithmic transfer function intercept voltage
Vmin Lowest input voltage in logarithmic amplifiertheoretical dynamic range
Vout Output DC voltage (generic)
Vπ Mach-Zehnder modulator bias parameter
V BCE Collector-emitter breakdown voltage
VBIC Vertical Bipolar Intercompany Model
vbe AC voltage across rπ
vin AC input voltage (generic)
vo AC output voltage (generic)
vp Voltage across transformer primary
vπ AC voltage across rπ, the same as vbe
W Effective width of the base
WDM Wavelength division multiplexing
ZinEF Input impedance of an emitter follower
xxiii
ZL Impedance which loads a CHEF amplifier output terminal
Zo Characteristic impedance
z1 A zero in the CHEF amplifier transfer function
α Ratio of collector to emitter DC current
β AC common emitter current gain of a bipolar transistor
βDC DC common emitter current gain of a bipolar transistor
βo Low frequency common emitter current gain of a bipolar transistor
∆ Change operator
δ Partial derivative operator
δ(t) Impulse response function
λ Wavelength (generic)
λo Optical system carrier wavelength
µV Microvolts
Ξ(f) Frequency domain dispersive fiber transfer function
Π Propagation constant
Π2 Group velocity dispersion parameter
ρ Wave number
τ Time variable
Υ Hilbert transformer tap delay
Φ Phase of an optical signal envelope
χ Discrete time index
ψ(f) Phase response of a system as a function of frequency (generic)
Ω Ohms, the unit of resistance
ω Frequency in radians/s
ωo Pole frequency
xxiv
Chapter 1
Introduction
The development of low loss silica fiber in the 1960s and 70s enabled fiber-optic
communications to become commercially viable. When it was first developed, the
bandwidth-distance product of fiber was so enormous compared to copper wire, that
scientists were compelled to pour effort into improving the other two components
required in a fiber optic link, light emitting elements and photo-diodes. As of 2004,
fiber-optic systems span the entire earth, both across land and under the oceans.
Commercial fiber-optic systems operate at a data rate of over 1 Tb/s, and 10 Tb/s
systems have been demonstrated in the laboratory [1].
These data rates are possible because of a number of important technologies,
including Wavelength Division Multiplexing (WDM) and optical amplifiers. WDM
is the technique whereby information is modulated onto several wavelengths of light
simultaneously and is transmitted over a single fiber. The development of commercial
WDM systems with as many as 120 channels in the last decade has increased the
capacity of fiber-optic systems by a similar factor. The impact of optical amplifiers on
long-haul fiber-optic systems may be seen using Figure 1.1. Figure 1.1(a) shows the
architecture of long-haul fiber-optic systems which was used before the proliferation
of fiber-optic amplifiers. An intensity modulated laser or light emitting diode (LED)
inside the transmitter sends information on a fiber-optic cable. After the optical
signal is transmitted approximately 50 km, the loss and the non-linearities in the
fiber distort the signal and a regenerator is used. The regenerator receives the
1.0 Introduction 2
Tx
Transmitter
TxRx TxRx Rx
Regenerator Regenerator
...
Receiver
(a) System using regeneration.
Rx
ReceiverTransmitter
Tx
Amplifier Amplifier
...
(b) System using optical amplification.
Figure 1.1: Long-haul optical system architectures.
information using a photodiode, the output current of which is processed into ones
and zeros in the electrical domain. The data is then re-timed and is again modulated
onto a light emitting element and transmitted to the next regenerator. This process
of reception and transmission occurs at each regeneration node until the data is
received at the final destination.
The regeneration nodes in Figure 1.1(a) become quite complex and expensive in
the case of WDM systems. In fact, WDM was not widely used until the proliferation
of optical amplifier technology around 1995 [2]. Optical amplifiers are devices which
may amplify an entire range of light wavelengths at once. This makes it possible to
amplify a WDM signal without having to regenerate the data. Figure 1.1(b) shows
a system which uses this technology. As the optical signal propagates and loses
power due to losses in the fiber, it may be repeatedly amplified as long as system
performance is not limited by amplifier noise, nonlinearities in the fiber and the
amplifiers, and a problem known as chromatic dispersion, which will be described
1.0 Introduction 3
shortly. Most modern long-haul commercial fiber systems use a combination of the
two techniques shown in Figure 1.1, with optical amplifiers used approximately every
50 km and regeneration used after several optical amplifiers [2].
One of the most significant challenges in designing WDM systems is overcom-
ing the effects of chromatic dispersion. Chromatic dispersion is characterized by a
wavelength dependent propagation velocity in the fiber. When a light signal with
information contained on a range of wavelengths is transmitted on fiber, different
wavelengths propagate at different speeds, and so they arrive at the detector at
different times. One particularly harmful form of distortion caused by chromatic
dispersion is the power penalty incurred by transmission of double sideband signals.
When a double sideband signal, which is the usual form of a signal, is transmitted,
the upper and lower sidebands of information arrive at the receiver at different times.
These sidebands may interfere destructively, causing loss of power.
Unless it is compensated, dispersion severely limits system performance above
2 Gb/s [2]. Cascading optical amplifiers as in Figure 1.1(b) solves the loss problem.
However, since an amplifier does not restore the signal to its original state, dispersion
induced degradation of the signal is allowed to accumulate over several amplifiers.
For this reason, all commercial long-haul fiber systems operating at 10 Gb/s or
higher use some form of dispersion compensation. The dispersion is compensated
by adding a device in series with the fiber optic cable which has a frequency de-
pendent delay profile opposite to that of the fiber, so that the overall system delay
becomes approximately wavelength independent. However, it is difficult to attain
full compensation for all channels in a WDM system. A small amount of residual
dispersion usually remains and may become a problem for transmission distances of
a few hundred kilometers or more. Further complicating the problem is that the
approximate amount of dispersion in a WDM system must be known before it can
1.1 Research Objective and Scope 4
be compensated. However, in reconfigurable networks, where entire spans of fiber
may be added or dropped from the network during operation, the amount of over-
all dispersion may vary significantly. Furthermore, at bit rates of 40 Gb/s, even
temperature induced changes in the fiber delay characteristics become of concern.
The goal of this work is to help overcome the negative effects of chromatic dis-
persion using optical single sideband (OSSB). It is widely known that by only trans-
mitting one sideband of the electrical information on the fiber, the problem of two
sidebands interfering with each other is overcome. OSSB could be used with either
no optical dispersion compensation or with a reduced amount of optical compensa-
tion. OSSB is already widely used for bandpass electrical signals, such as a 1 Gb/s
signal centered at 20 GHz [3, 4]. However, a limited number of experiments have
been performed using OSSB with baseband signals.
1.1 Research Objective and Scope
The objectives of this thesis are to develop an integrated circuit logarithmic ampli-
fier and Hilbert transformer for the Compatible Optical Single Sideband (COSSB)
system. A further objective is to quantify the performance of these circuits in the
COSSB system.
1.2 Thesis Outline
In Chapter 2, chromatic dispersion is examined along with a discussion of its undesir-
able effects on system performance and methods of compensating for it. One of these
methods is COSSB transmission, and the COSSB system architecture is introduced.
Chapter 3 describes a novel design procedure for a necessary logarithmic amplifier
building block, the Cherry-Hooper amplifier with emitter follower feedback. An em-
1.2 Thesis Outline 5
phasis is placed on low distortion magnitude and group delay frequency responses,
which are important for broadband operation. Chapter 4 describes the development
of a novel DC-4 GHz Si BJT logarithmic amplifier, and of a DC-6 GHz SiGe HBT
logarithmic amplifier. The latter implementation uses the same parallel summation
architecture as the first, but makes use of the Cherry-Hooper amplifiers developed
in Chapter 3. Chapter 5 describes the implementation of the first fully integrated
10 Gb/s Hilbert transformer. In Chapter 6, simulations of the SiGe HBT log ampli-
fier and the Hilbert transformer in the COSSB system are described. This chapter
lays the foundation for Chapter 7, where a COSSB transmitter is constructed, and
the sideband suppression is quantified. Finally, Chapter 8 concludes the thesis and
provides recommendations.
Chapter 2
Background
2.1 Introduction
The target application of the circuits in this work is COSSB, which is described in
Section 2.4. However, in order to understand why COSSB is desirable, it is essential
to understand chromatic dispersion. Section 2.2 describes chromatic dispersion, and
Section 2.3 describes methods of compensating for it.
2.2 Chromatic Dispersion
To understand chromatic dispersion, the distinction should be made between single
mode and multi-mode fiber. When an optical signal is launched into fiber, the exact
mode in which the optical wave propagates depends on the dimensions of the fiber.
Silica fiber has a core surrounded by cladding in order to form a waveguide. As
with any waveguide, if the diameter of the core is large compared to the wavelength
of the signal, the signal may move down the fiber using multiple modes of wave
propagation. The core diameter may be reduced until only a single mode may
propagate, in which case the fiber is called ‘single mode’. Commercial long-haul
systems with an information capacity of 10 Gb/s or higher use single mode fiber
almost exclusively. For this reason, single mode fiber will be assumed throughout
this work.
If a short pulse of light, such as a ‘one’ signal in a digital system, is launched
into the fiber and allowed to propagate many tens of kilometers, that pulse will
2.2 Chromatic Dispersion 7
Time
Distance
Time
Figure 2.1: Pulse spreading due to chromatic dispersion.
spread out in time. Chromatic dispersion is the pulse spreading that occurs within
a single mode [5]. Figure 2.1 shows how two pulses may begin to overlap each other
as they propagate down the fiber. This phenomenon is detrimental to the operation
of high data rate communication systems because overlapping pulses cause inter-
symbol interference and bit errors at the receiver. Chromatic dispersion may also be
explained in terms of group delay, defined as
group delay = −dψ(f)
df
1
2π(2.1)
where ψ(f) is the phase response of that system, and f is frequency. Chromatic
dispersion is also known as Group Velocity Dispersion (GVD), because it may be
characterized by a wavelength dependence of group delay.
2.2.1 Types of Dispersion
Three different types of dispersion are waveguide dispersion, nonlinear dispersion,
and material dispersion. Waveguide dispersion occurs because only about 80 percent
of the optical power is confined to the core of the fiber, and about 20 percent of the
power propagates in the cladding. The optical signal in the cladding travels faster
than the signal in the core, causing dispersion [5]. Nonlinear dispersion is caused
by the dependence of the fiber refractive index on the optical signal intensity. The
physical origin of this effect may be traced to the nonlinear response of electrons
to optical fields [2]. Nonlinear dispersion may be mitigated by avoiding high power
2.2 Chromatic Dispersion 8
levels in optical systems. Material dispersion is due to the wavelength dependence of
the refractive index of fiber, which causes a wavelength dependence of propagation
velocity. The material and waveguide dispersion may be added together to obtain an
estimate of the dispersion for low to medium power pulses [2]. In the next section,
a mathematical description of dispersion is developed.
2.2.2 Mathematical Definition of Dispersion
As a signal propagates down a fiber, each wavelength requires a certain amount of
time or group delay per unit length of travel. This delay τ is given by [5]
τ =L
Vg
(2.2)
where L is the distance traveled, and the group velocity Vg is given by
Vg =
(
dΠ
dω
)
−1
(2.3)
where Π is the propagation constant, λ is wavelength, and c is the speed of light in
a vacuum. Furthermore, the propagation constant is given by
Π =2πnr
λ(2.4)
where nr is the fiber refractive index. For a signal with spectral width ∆λ the amount
of pulse broadening over a distance L is given by [2]
∆τ =d
dλτ∆λ. (2.5)
In terms of angular frequency this is given by [5]
∆τ =d
dωτ∆ω =
d
dω
(
L
Vg
)
∆ω = L
(
d2Π
dω2
)
∆ω. (2.6)
2.3 Methods to Compensate for Dispersion 9
The factor d2Π/dω2(= Π2) is the group velocity dispersion (GVD) parameter. By
using ω = 2πc/λ and ∆ω = (−2πc/λ2)∆λ, equation (2.6) may then be rewritten as
∆τ =d
dλ
(
L
Vg
)
∆λ = DL∆λ (2.7)
where
D =d
dλ
(
1
Vg
)
= −2πc
λ2Π2. (2.8)
In this case, D is the dispersion parameter and is typically expressed in units of
ps/(nm · km). The meaning of D is best understood by equation (2.7), in relation
to the amount of pulse broadening that it causes. If D is slightly negative, then the
pulse may actually compress, which is the principle of dispersion compensating fiber
to be discussed in Section 2.3.1.
Figure 2.2 shows a plot of typical values for the parameter D and the fiber loss,
also called attenuation, versus wavelength for single mode fiber. The relatively high
loss at 1390 nm is due to signal absorption by small concentrations of the OH ion in
fiber [2]. The wavelength which experiences the least amount of loss is at approx-
imately 1550 nm. Unfortunately, the dispersion at this wavelength is significant,
typically 15-20 ps/(nm · km). The dispersion is zero near 1350 nm, however, the loss
is prohibitively high at this wavelength for systems spanning many tens of kilometers
or more. For this reason, it is common practice for long-haul fiber systems to oper-
ate at 1550 nm, and the dispersion is compensated for. The next section describes
dispersion compensation techniques.
2.3 Methods to Compensate for Dispersion
Chromatic dispersion is a major problem in optical systems, and several techniques
exist to deal with it. For a dispersion compensation technique to be useful in com-
2.3 Methods to Compensate for Dispersion 10
1.2
0.3
0.9
0.6
0
10
0
−10
20
1250 1300 1350 1400 1450 1500 1550 1600
Wavelength (nm)
Dis
pers
ion
para
met
er D
Atte
nuat
ion
(dB
/km
)
(ps/
(nm
−km
))
Figure 2.2: A typical loss and dispersion profile for single mode fiber.Adapted from [2].
mercial systems, it should be capable of compensating the dispersion in all channels
of a WDM system simultaneously. In this section, three techniques which meet
this criteria are described. One of the techniques, post detection compensation, is
uniquely suited to the COSSB system described in Section 2.4.
2.3.1 Optical Techniques
Dispersion Compensating Fiber
One broadband dispersion compensation technique involves the use of Dispersion
Compensating Fiber (DCF). In Figure 2.2, it was shown that the dispersion param-
eter of standard single mode fiber increases with wavelength. If it were possible to
design another type of fiber that had a large negative dispersion parameter, then
adding this fiber to a system would compensate for the dispersion in standard fiber.
Single mode fiber with a negative dispersion parameter may be fabricated, how-
ever it may only support relatively low levels of optical power with acceptable linear-
ity. Single mode fiber has a relatively small core diameter, and if the core diameter
is increased just enough to allow a second mode to propagate, the second mode will
exhibit a negative dispersion parameter and the fiber can support higher power levels
2.3 Methods to Compensate for Dispersion 11
with less nonlinearity [2]. The dispersion of the second mode can be as large as -770
ps/(nm · km).
Dispersion compensation is achieved by using approximately 2-5 km of DCF fiber
for every 50 km of standard single mode fiber. Furthermore, a mode coupling device
is required at each interface of the DCF fiber and the standard fiber, in order to
convert between the standard propagation mode to the second order mode with the
negative dispersion.
Dispersion management using DCF is practical and effective in dense WDM
systems, and it is used in virtually all systems with a spectral width of 30 nm or
more. In one of the highest capacity experiments to date, DCF was used to transmit
40 Gb/s on each of 273 channels over 117 km, resulting in a total bandwidth of
11 Tb/s and a spectral width of more than 100 nm [1]. The disadvantage of DCF
is its high loss, which can be 5 dB for a 5 km length. This can be compensated
for by increased optical amplifier gain, however the resulting amplifier noise may
corrupt the signal to an unacceptable level. For this reason, other optical dispersion
compensation schemes have been developed. One of the more successful technologies
is described in the next section.
Fiber Bragg Gratings
Fiber Bragg gratings are optical filters approximately 10 cm in length that may
compensate for the dispersion of approximately 100 km of fiber. As its name implies,
a grating is a periodic change in the material inside an optical transmission medium.
The medium commonly used is simply optical fiber. Its refractive index may be
changed at small spacings through a photo-imprinting process [5]. The result is that
certain wavelengths of light are transmitted, whereas others are reflected. At the
Bragg wavelength, the light is almost completely reflected, and so there is a type of
2.3 Methods to Compensate for Dispersion 12
stop-band at this frequency. At this wavelength, the phase response of the grating is
almost linear, and so it could not be used to compensate for dispersion. However, at
wavelengths slightly above the Bragg wavelength, most of the light is allowed to pass
and it undergoes a negative dispersion. The mathematics behind Bragg gratings
are somewhat involved, and will not be shown here. They involve an analysis of
the coupling between forward and backward waves. The situation becomes more
complicated for gratings whose refractive index is linearly increased over the length
of the grating in order to achieve an even larger negative dispersion parameter [2].
Fiber Bragg gratings are advantageous because they are physically small. Fur-
thermore, they only pass signals at periodic, narrow regions of spectrum, and so
they filter out some optical amplifier noise. However, in order to compensate the
dispersion of more than one channel in a WDM system, gratings which are centered
at different wavelengths must be cascaded with optical isolators between each grat-
ing. As the number of channels increases to 10 or more, it becomes very difficult to
compensate the dispersion of all of the channels at once. For this reason, DCFs are
preferred over Bragg gratings in dense WDM systems.
2.3.2 Post Detection Compensation
Another general dispersion compensation technique is electrical compensation used
after the signal is detected. The type of detection most widely used in optical systems
is square law detection with a photodiode, also known as direct detection. The output
current of the photodiode is proportional to the optical power or intensity. As part
of this process, the information on the optical signal is converted directly down to
baseband. This is known as homodyne detection, as opposed to heterodyne detection
where an intermediate frequency is used. Furthermore, since no local oscillator (LO)
is used, direct detection is also referred to as self-homodyning detection in this thesis
2.3 Methods to Compensate for Dispersion 13
and in [6, 7]. The dispersion incurred by the optical signal during transmission
imposes a different delay on the upper and lower sidebands of the signal. Once the
signal is detected using self-homodyning detection, the upper and lower sidebands
fold onto each other and the dispersion may no longer be compensated [6, 8]. There
are two ways that the dispersion information may remain intact so that it may be
compensated post detection; heterodyne detection and optical single sideband. Each
of these will be discussed in turn.
In heterodyne detection, the main optical signal must be combined with an LO
optical signal at a slightly different wavelength prior to detection. The photodiode
output then contains an intermediate frequency (IF) containing the data. The dis-
persion distortion inherent in the data may then be electrically equalized at the IF,
and the resulting signal may then be converted down to baseband using a mixer [7].
Furthermore, since the propagation delay of fiber increases with wavelength, it de-
creases with increasing frequency since c = λf . As a result, all that is required to
equalize the dispersion in the IF signal is an electrical structure whose delay increases
with frequency. Microstrip line is most commonly used for this purpose [2, 7, 8, 9, 10].
The disadvantage of heterodyne systems is that for 10 or 40 Gb/s signals, the re-
quired mixers, which would have minimum RF frequencies at approximately 20 and
80 GHz respectively, would be expensive if not impractical.
If optical single sideband (OSSB) is used, the dispersion characteristic in the
signal remains intact during self-homodyning detection. Hence, the signal may be
detected using a photodiode and the requirement for broadband mixers is elimi-
nated, and the signal may be equalized post detection. In 1998, Sieben demon-
strated 10 Gb/s transmission over 320 km using OSSB transmission and post detec-
tion compensation using microstrip [7]. Furthermore, Winters described a tunable
analog tapped delay line for dispersion compensation [11]. It had fractionally spaced
2.4 Compatible Optical Single Sideband 14
weights that could be tuned based on the amount of dispersion. The disadvantage of
these methods is that long lengths of microstrip are needed in order to compensate
long lengths of fiber, such as 32 cm for 320 km of fiber. The loss of microstrip typi-
cally increases with frequency, and this may become problematic. Nevertheless, this
problem may be mitigated through the use of low loss microstrip substrates. As well,
if OSSB is used along with a reduced amount of optical dispersion compensation, the
lengths of the required microstrip and optical compensators are reduced compared
to the case where only OSSB or optical compensation is used.
2.4 Compatible Optical Single Sideband
In this section, the COSSB system is introduced as a spectrally efficient and generally
desirable system architecture. It is described how chromatic dispersion causes power
fading in double sideband (DSB) signals, and how OSSB signals are immune to this
problem. Before describing the COSSB system, it is worthwhile to introduce the
idea of complex envelope representation of signals. This will greatly simplify the
mathematics in the rest of this section. Some of the mathematical development in
this section is paraphrased from [6], and it is reprinted with permission.
2.4.1 Complex Envelope Representation of Bandpass Signals
We begin by defining a low pass, also called a baseband, information signal s(t),
such as a 10 Gb/s signal. In an optical system, this information is modulated onto
a light signal or carrier. Since c = fλ, the typical carrier wavelength of 1550 nm
corresponds to a carrier frequency of 200 THz. As a result, the 10 Gb/s information
becomes a narrow-band bandpass signal on the fiber. The resulting optical signal
sB(t) has the frequency spectrum SB(f) as shown in Figure 2.3, where fo is the
2.4 Compatible Optical Single Sideband 15
fo fof
+−
SB
Figure 2.3: Narrow-band bandpass signal.
optical carrier frequency.
The bandpass signal SB(f) has two copies of the same information at −fo and
+fo. In order to obtain the complex envelope of SB(f), we first construct a signal
that has only the positive frequencies of SB(f) according to [6, 12]
A(f) = 2U(f)SB(f) (2.9)
where U(f) is the frequency domain unit step function. Since multiplication in
the frequency domain involves convolution in the time domain, the time domain
expression for (2.9) is given by
a(t) = 2F−1[U(f)] ∗ sB(t) (2.10)
where F−1 denotes the inverse Fourier transform. The inverse Fourier transform of
U(f) is given by
F−1[U(f)] =1
2δ(t) +
j
2πt(2.11)
where δ(t) is the impulse function. a(t) may then be expressed as [12]
a(t) = 2sB(t) ∗ 1
2δ(t) + 2sB(t) ∗ j
2πt
= sB(t) +j
π
∫
∞
−∞
sB(τ)
t− τdτ. (2.12)
2.4 Compatible Optical Single Sideband 16
The integral on the right hand side of (2.12) is defined as
sB(t) =1
π
∫
∞
−∞
sB(τ)
t− τdτ (2.13)
where sB(t) is called the Hilbert transform of the signal sB(t). A Hilbert transformer
may be represented as a filter with frequency response [12]
H(f) = −j · sgn(f). (2.14)
where sgn indicates the signum function. The signal A(f) in (2.9) is still bandpass
in nature, and a low-pass equivalent may be created as
AL(f) = A(f + fo). (2.15)
In the time domain this amounts to multiplication of a(t) with a complex sinusoid
as in:
aL(t) = a(t)exp(−j2πfot). (2.16)
The low pass equivalent signal aL(t) is also called the complex envelope of sB(t).
Conversely, the bandpass signal sB(t) is related to aL(t) by
sB(t) + jsB(t) = aL(t)exp(j2πfot). (2.17)
The left hand side of this equation contains what is known as a Hilbert transform
pair.
Before moving on to the description of the COSSB system, it will be shown how
a single sideband signal may be generated. A single sideband signal is a bandpass
signal with either the upper or lower half of its spectrum removed. An upper single
sideband signal has zero magnitude for 0 < f < fo and a lower single sideband
2.4 Compatible Optical Single Sideband 17
signal has zero magnitude for f > fo. The complex envelope of a SSB signal, defined
as aLSSB(t), may be acquired starting with the baseband information signal s(t)
according to
aLSSB(t) = s(t) ± js(t). (2.18)
The real bandpass signal associated with aLSSB(t) is given by
sBSSB(t) = < [aLSSB
(t)exp(±j2πfot)]
= s(t)cos(2πfot) ± s(t)sin(2πfot) (2.19)
with the lower single sideband signal corresponding to the plus sign and the upper
single sideband signal corresponding to the negative sign.
2.4.2 COSSB Modulation
We now consider the process of optical detection as it relates to optical single side-
band. The output current of a photodiode is proportional to the optical power or
intensity, which, in turn, is proportional to the information envelope squared. As
a result, any phase information in the optical signal is discarded during detection.
What is of interest in this thesis is what happens when square law detection is ap-
plied to a single sided bandpass signal. The answer to this question may be found
more readily by applying square law detection to the complex envelope of a SSB
signal, aLSSB(t). With aLSSB
(t) being complex, its real and imaginary parts may be
expressed as
aLSSB(t) = s(t) ± js(t). (2.20)
Furthermore, the polar form of aLSSB(t) is defined as
2.4 Compatible Optical Single Sideband 18
aLSSB(t) = m(t)exp (jφ(t)) (2.21)
where m(t) is given by
m(t) =√
s2(t) + s2(t) (2.22)
and
φ(t) = tan−1
(
s(t)
s(t)
)
. (2.23)
Using these definitions, square law detection may be applied to the complex envelope
aLSSB(t) according to
d(t) = |aLSSB(t)|2
= s2(t) + s2(t). (2.24)
Unfortunately this result is not proportional to the original information s(t), and
so the data will not be recovered. We now derive the complex envelope of a SSB
signal that may be square law detected without loss of information, which we will
denote as a′LSSB(t). We begin by making the important observation that since the
information obtained after square law detection is the square of the magnitude of the
signal, the magnitude of the signal must be equal to the data s(t). In addition, the
information should always be greater than zero, meaning that a DC offset should be
added if needed. However, the phase of the signal, which is discarded during square
law detection, may be modulated in a way so that the signal is single sideband.
Expressing a′LSSB(t) in polar form with the magnitude equal to s(t),
a′LSSB(t) = s(t)exp (jφ(t)) . (2.25)
2.4 Compatible Optical Single Sideband 19
Taking the natural logarithm of both sides of this equation gives
lna′LSSB(t) = lns(t) + jφ(t). (2.26)
Let us force this signal to consist of a Hilbert transform pair. In this case, φ(t) is
found to be
φ(t) = ±HL [s(t)] (2.27)
where HL [s(t)] indicates the Hilbert transform of the logarithm of s(t). This will
ensure that lna′LSSB(t) contains only positive or negative frequencies, as is required
of the complex envelope of a single sideband signal. However, if lna′LSSB(t) meets
this condition, then a′LSSB(t) does as well [6]. Hence, a′LSSB
(t) may be expressed as
a′LSSB(t) = s(t) · exp (jHL [s(t)]) . (2.28)
It is now possible to use square law detection to recover s(t) as in
d(t) = |s(t) · exp (jHL [s(t)])|2
= s2(t). (2.29)
Thus, compatibility with direct detection is achieved in theory [13]. In practice,
the type of modulation suggested by (2.28) is difficult to perform. It is difficult to
take the logarithm of s(t), especially if it is at a data rate of 10 Gb/s or higher.
Furthermore, designing a Hilbert transformer is difficult because of the abrupt tran-
sition in its phase response at DC, as indicated by its −j · sgn(f) phase response.
Building suitable approximations to a broadband logarithmic converter and Hilbert
transformer in integrated circuit form is the main goal of this thesis.
2.4 Compatible Optical Single Sideband 20
2.4.3 COSSB Implementation: The Ideal Minimum Phase Modulator
The structure of the modulator suggested by (2.28) is shown in Figure 2.4. The
term ‘minimum phase’ relates to the trajectory of the analytic signal in the complex
plane, and the reader is referred to Reference [6] for further details on minimum
phase signals. In Figure 2.4, M is a scaling factor applied to s(t) and a DC offset
VDC is added to ensure that the resulting signal is strictly greater than zero. It is
instructive to view the electrical waveform before and after applying the logarithm,
and after it has been Hilbert transformed. These waveforms are shown in Figure 2.5
for a 10 Gb/s 211−1 length pseudo random bit sequence (PRBS) scaled with M=0.6
and VDC=1. The PRBS sequence is filtered with a fifth order Butterworth filter with
a cutoff frequency of 5 GHz immediately after it is scaled in order to avoid aliasing.
Furthermore, filtering at 5 GHz removes higher frequency components that would
be the most distorted by dispersion.
It is seen in Figure 2.5(b) that the effect of the logarithm is to stretch out the
parts of the waveform that are closest to zero amplitude. If a signal consists of two
perfect digital levels, and if it is scaled by M and VDC and then logged, the logarithm
of this waveform also consists of two perfect signal levels. Hence, for perfect binary
signals that are strictly positive, a level shifter and an amplifier may act in place
of a logarithmic converter. The waveform at the output of the Hilbert transformer,
on the other hand, is very different, and appears to be a series of amplitude spikes
corresponding to each bit transition. This demonstrates the unique response of the
Hilbert transformer. The −j · sgn(f) frequency response indicates that all positive
frequencies undergo a constant -90 phase shift, resulting in the unusual waveform
in Figure 2.5(c). This is in contrast to the phase shift imposed on a sinusoid passing
through a wire, for example, which increases with increasing frequency.
2.4 Compatible Optical Single Sideband 21
AmplitudeModulator
PhaseModulator
To Fiber
exp(j t)ω
+
VDC
HilbertTransformer
Laser
ConverterLogarithmic
.M s(t)
Figure 2.4: Ideal minimum phase modulator.Adapted from [6].
Figure 2.6 shows the optical spectra of the original DSB information and of the
COSSB signal created using ideal amplitude and phase modulation. Note that the
mild distortion in the OSSB signal spectrum is due to the choice of filter used on
the data, and is also effected by the length of the PRBS sequence. However, the eye
diagram of the detected COSSB signal in Figure 2.7 shows that the information is
recovered without error. It is noted that optical USB, which is LSB in the frequency
domain, must be transmitted if microstrip post detection equalization is to be used.
This ensures that the microstrip will equalize the phase distortion caused by fiber
dispersion [7]. If optical LSB is transmitted and microstrip equalization is attempted,
the phase distortion due to fiber dispersion will be made worse, and the equalization
will fail.
2.4.4 Dispersion Effects on Double and Single Sideband Signals
In this section, the distortion of DSB signals caused by dispersion is demonstrated,
and it is shown how single sideband signals defeat the distortion mechanism. To be-
2.4 Compatible Optical Single Sideband 22
5 6 7 8 9 10 11 12 13 14 150
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Li
near
Am
plitu
de
Time (ns)
(a) Raw waveform.
5 6 7 8 9 10 11 12 13 14 15−2
−1.5
−1
−0.5
0
0.5
1
Line
ar A
mpl
itude
Time (ns)
(b) Logged waveform.
5 6 7 8 9 10 11 12 13 14 15−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Line
ar A
mpl
itude
Time (ns)
(c) Hilbert transformed waveform.
Figure 2.5: Electrical signals at points throughout the COSSB system.
gin, a mathematical representation is needed of the way in which dispersion increases
with wavelength, as in Figure 2.2. This characteristic may be represented by defining
the complex envelope of the frequency domain transfer function of dispersive fiber,
given by
Ξ(f) = exp
(
jπDλ2of
2L
c
)
(2.30)
2.4 Compatible Optical Single Sideband 23
−10 −8 −6 −4 −2 0 2 4 6 8 10−80
−70
−60
−50
−40
−30
−20
−10
0
Normalized Frequency (GHz)
Det
ecte
d P
ower
(dB
)
(a) Filtered 10 Gb/s DSB signal.
−10 −8 −6 −4 −2 0 2 4 6 8 10−80
−70
−60
−50
−40
−30
−20
−10
0
Normalized Frequency (GHz)
Det
ecte
d P
ower
(dB
)
(b) Filtered 10 Gb/s SSB signal.
Figure 2.6: Filtered 10 Gb/s DSB and SSB signals plotted against frequency nor-malized to the carrier.
−100 −50 0 50 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (ps)
Am
plitu
de
Figure 2.7: Eye diagram of detected SSB signal.
where, as before, D is the dispersion parameter, λo is the optical wavelength, and L
is the length of fiber [6]. The group delay of Ξ(f) is proportional to the derivative of
its phase with respect to frequency. The phase of Ξ(f) is contained in the argument
of the exponential, whose derivative is proportional to f . Hence, the group delay of
Ξ(f) is linearly proportional to frequency, and so it models first order dispersion.
2.4 Compatible Optical Single Sideband 24
Consider the case where a sinusoid defined by
r(t) = cos(2πfct) (2.31)
propagates in dispersive optical fiber. The upper and lower sidebands of that signal
will experience different group delays. Assume that the signal is then recovered
using direct detection. It was mentioned in Section 2.3.2 that the information on
the upper sideband is combined with the information in the lower sideband during
direct detection. It is easy to imagine that if two corresponding frequencies in each
sideband were out of phase due to dispersion, they may cancel each other out. In
fact, using (2.30) it may be shown that dispersion causes fading in the detected
power PD as a function of frequency and fiber length according to [6, 14]
PD ∝ cos2
(
jπDλ2of
2c L
c
)
. (2.32)
From this equation, it is seen that the detected power reduces to zero for arguments
corresponding to ±π/2± kπ, k = 1, 2, 3, ... . Hence, for a given frequency, the power
will fade to zero at certain lengths of fiber. Alternatively, for a given length of
fiber, the power at certain frequencies will fade to zero. Although this equation
is for the case of a sinusoid at frequency fc, the same fading mechanism will be
present for broadband signals, such as 10 Gb/s signals. Intuitively, we would expect
a frequency selective nulling of broadband signals at certain lengths of fiber. This
hypothesis may be verified through the simulation of a DSB 10 Gb/s signal through
dispersive fiber. Figure 2.8(a) shows the detected spectrum of the 10 Gb/s DSB
from Section 2.4.3 after transmission on 200 km of fiber with a dispersion parameter
of D = 18 ps/(nm · km). The detected signal shows significant power fading in the
4 GHz region of the spectrum.
2.4 Compatible Optical Single Sideband 25
−10 −8 −6 −4 −2 0 2 4 6 8 10−80
−70
−60
−50
−40
−30
−20
−10
0
Normalized Frequency (GHz)
Det
ecte
d P
ower
(dB
)
(a) Spectrum of recovered DSB signal.
−100 −50 0 50 1000
0.2
0.4
0.6
0.8
1
Time (ps)
Am
plitu
de
(b) Eye diagram of recovered DSB signal.
Figure 2.8: Detected 10 Gb/s DSB signal after 200 km of dispersive fiber.
Based on the above discussion, it may be realized that if one of the sidebands in a
signal is removed, then there is no second sideband to cause destructive interference
upon detection, and power fading is avoided. In fact, the immunity of OSSB signals
to chromatic dispersion induced power fading is well established in the optical com-
munity [3, 4, 8, 15]. This notion may readily be verified through a simulation of the
10 Gb/s COSSB signal from Section 2.4.3 over 200 km of dispersive fiber and using
self-homodyning post detection dispersion compensation. Figure 2.9(a) shows the
detected spectrum of the COSSB signal where it is observed that the power fading
problem is gone. The small ripples that are present in the spectrum do not cause
a serious degradation in the signal. This fact makes post detection dispersion com-
pensation possible in COSSB systems. If the detected power had nulls in it, then
there would be no way to compensate its distorted phase. This also explains why
the dispersion in DSB signals must be compensated prior to direct detection.
2.4 Compatible Optical Single Sideband 26
−10 −8 −6 −4 −2 0 2 4 6 8 10−80
−70
−60
−50
−40
−30
−20
−10
0
Normalized Frequency (GHz)
Det
ecte
d P
ower
(dB
)
(a) Spectrum of recovered SSB signal.
−100 −50 0 50 100−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Time (ps)
Am
plitu
de
(b) Eye diagram of recovered SSB signal.
Figure 2.9: Detected 10 Gb/s SSB signal after 200 km of dispersive fiber.
2.4.5 Minimum Phase Dispersion Compensation
In Section 2.3.2, it was described how microstrip line may be used to equalize a SSB
signal post detection. At least one other post detection compensation scheme has
been developed for OSSB systems [6]. Davies showed that the optimal post detection
dispersion compensator is of the form shown in Figure 2.10. The compensator is best
described by Davies as follows [6]:
The minimum phase compensator (MPC) structure could be thought of
as a ‘mirror’ of the minimum phase modulator in which the optical elec-
tric field linear envelope (m) is recovered and preserved as the envelope
portion of the detected signal. Under the minimum phase assumption the
phase of the optical electric field is recovered by the successive operation
of the natural log and Hilbert Transform of the linear envelope (Φ). The
phase and amplitude signal are then combined in a polar representation
2.4 Compatible Optical Single Sideband 27
of the complex predetection electric field, given by
a(t) = m(t) · exp jΦ(t) . (2.33)
The complex signal is then passed through a complex anti-dispersive filter
to remove the fiber induced distortion. The resulting signal, which is still
complex, will be the corrected signal in which the original information
is contained in the envelope. Since the recovered signal in this case is
single sideband, the anti-dispersive filter transfer function is simply the
inversion of the fiber transfer function:
Cmp(f) = exp
(
−jπDλ2f 2L
c
)
; f ≥ 0. (2.34)
Simulations by Davies and in Chapter 6 of this thesis show that this type of
compensation, while requiring more processing steps, may double the transmission
distance in a fiber optic system. The most significant challenge to implementing
this compensator for a 10 Gb/s system remains the design of the amplitude and
phase combiner. The minimum phase compensator in Figure 2.10 also requires a
logarithmic function and Hilbert transformer, similar to the minimum phase OSSB
modulator. This provides a further motivation for the development of the logarithmic
amplifiers and the Hilbert transformer in this thesis.
2.4.6 Previous Experiments Using COSSB
OSSB transmission is popular for systems where the electrical information is a radio
signal above 15 GHz [3, 4]. The reason is that since these signals are at such high
frequencies, the dispersion induced power fading described in the last section occurs
even with short lengths of fiber, such as 10 km. For these signals, single sideband may
be generated using a narrow-band -90 phase shift and a baseband gigabit per second
2.4 Compatible Optical Single Sideband 28
2
CompensatedSignal
Φ
Combiner
Complex Anti−dispersiveFilter
Phase (Φ)
.m exp(j )
Amplitude (m)
Converter TransformerHilbertLogarithmic
AbsoluteValue
Photodiode RootSquare
Fiber
Figure 2.10: Ideal minimum phase dispersion compensator.Adapted from [6].
Hilbert transformer is not required [3, 4]. Previous OSSB experiments where the
signal was a baseband, multi-gigabit per second data signal include Yonenaga’s work
where he demonstrated 6 Gb/s OSSB transmission of a 27−1 length PRBS sequence
over 270 km of fiber in 1993 [8]. In his work, an optical filter was used to remove
the unwanted sideband. In contrast, Sieben implemented OSSB using the method
described in Section 2.4.3 in 1997. He demonstrated transmission of a 10 Gb/s PRBS
sequence up to pattern lengths of 214−4 over 320 km of fiber and achieved a bit error
ratio (BER) of 10−9 [7, 16, 17]. He used post detection dispersion compensation
consisting of a 32 cm length of microstrip. In that experiment, the logarithmic
converter required to implement the system in Figure 2.4 was not included, because
no such converter existed. It was described in Section 2.4.3 how the logarithm
of digital waveforms with only two levels is also a waveform with only two levels.
Hence, by providing the proper scaling and DC offset, the logarithm function was
approximated in Sieben’s experiment.
As part of Sieben’s research, he investigated ways to generate the Hilbert trans-
form of a 10 Gb/s signal [7]. One of the methods that he discussed was to implement
2.4 Compatible Optical Single Sideband 29
a Hilbert transformer using a tapped delay filter. This technique will be described
further in Section 5.1, when the fully integrated Hilbert transformer in this thesis is
presented.
2.4.7 The Mach-Zehnder Modulator
For the simulations in Section 2.4.3, an ideal amplitude and phase modulator were
used. This section describes a realistic amplitude modulation device. It is not
advisable in optical systems to amplitude modulate optical lasers directly. This
is because amplitude modulation in lasers is accompanied by an inherent phase
modulation process, known as chirp. Instead of modulating the laser, an external
modulator is used, such as the Mach-Zehnder modulator. This type of modulator
will be used for the experimental work in this thesis, so it is introduced here.
The Mach-Zehnder modulator is a type of interferometer, where two signals inter-
fere constructively or destructively. Figure 2.11 shows a diagram of a Mach- Zehnder
modulator. It consists of two waveguides which are, for example, formed by diffusing
titanium on a LiNbO3 substrate [2]. The refractive index of LiNbO3 may be changed
by applying an electric field. There is an electrical contact on each waveguide path
of the modulator for applying an electrical signal, Va or Vb. With no applied signals,
the refractive index and hence the phase shift through each path is the same and
the output signals of each path simply add. If a voltage is applied to the contact on
one arm, the phase shifts will differ and the optical signals in each arm will interfere
when they combine at the output. A phase difference of π between the two arms
occurs at a voltage difference Vπ between Va and Vb. Simply stated, Vπ is the voltage
change that causes the modulator to go from full optical output power to minimum
optical output power. Some Mach-Zehnder modulators have electrical bandwidths in
excess of 40 GHz, making them suitable for amplitude modulation of optical signals
2.4 Compatible Optical Single Sideband 30
Waveguide
Substrate
Contact
Figure 2.11: Dual arm Mach-Zehnder modulator.
with 10 or 40 Gb/s data streams.
The electric field of the data contained in the output signal of the Mach-Zehnder,
Eout, may be represented in terms of the electric field of the data on the input signal,
Ein, according to
Eout =Ein
2exp
(
jπVa
Vπ
)
+Ein
2exp
(
jπVb
Vπ
)
. (2.35)
The power in the electrical signal is found by taking the square of (2.35). Figure 2.12
shows the output signal power characteristic for a modulator with Vπ=1. In order to
obtain the most linear modulation possible, the modulator is typically biased with
Va − Vb=3Vπ/2 ± k · 2Vπ, k = ...,−2,−1, 0, 1, 2, ... . Even at this bias point, the
amplitude modulation will induce some nonlinearity. The modulator may also be
biased at Va − Vb=Vπ/2 ± k · 2Vπ, k = ...,−2,−1, 0, 1, 2, ..., but then any applied
amplitude modulation is inverted when changed into optical intensity.
When the external bias voltages Va and Vb are applied to the modulator, the
change in the material refractive index may result in there being some amplitude
dependent phase shift or chirp in Eout. However, the total chirp may be eliminated
by having Va = −Vb, and this is usually done in practice [6, 7, 18].
The above discussion describes that a Mach-Zehnder modulator contains two
phase modulation paths whose outputs are combined. The minimum phase COSSB
2.4 Compatible Optical Single Sideband 31
0 0.5 1 1.5 2 2.5 3 3.5 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a
out
E
(
V)
2
(V −V ) x V (V)πb
Figure 2.12: Transfer function of a Mach-Zehnder with Vπ=1.
modulator structure described in Section 2.4.3 consists of an intensity modulator,
usually implemented with a Mach-Zehnder, followed by a phase modulator. It is
possible to perform the amplitude modulation and phase modulation using only one
Mach-Zehnder by superimposing a common mode signal onto both Mach-Zehnder
control voltages [7]. This common mode voltage would be the Hilbert transform of
the logarithm of the information. Although this reduces the amount of hardware
required, the Mach-Zehnder control voltages become prohibitively large, and so this
method was not explored further in this thesis.
2.4.8 Competing Technologies: Solitons, Coherent Detection Systems,
and Duobinary Transmission
Some time has passed since Sieben and Davies conducted their experiments on
COSSB. In that time, significant research has taken place worldwide on different
fiber system architectures. It is important to establish whether COSSB is still rel-
evant. Two areas which are a current topic of fiber systems research are soliton
transmission and coherent detection. Each of these will be discussed in turn.
2.4 Compatible Optical Single Sideband 32
Solitons
Solitons are pulses that propagate in a nonlinear medium. In the case of fiber sys-
tems, soliton transmission occurs when dispersion is canceled by self-phase modula-
tion (SPM) of the optical pulse. SPM occurs as the result of the nonlinear refractive
index of optical fiber. Hence, soliton propagation relies on the balancing of two
effects which, on their own, are detrimental to fiber systems.
Since solitons rely on dispersion to propagate, their advantage is that they elim-
inate the need for exact dispersion compensation. One disadvantage of soliton com-
munications is that the optical power must return to zero after each pulse, known
as return-to-zero (RZ) transmission, or else the solitons will interact with each other
and they will no longer propagate undistorted [2]. This occupies considerably more
bandwidth than the non-RZ (NRZ) transmission format that is typically used. Fur-
thermore, optical amplifiers must be still be used for long-haul systems, and these
amplifiers introduce considerable noise. This noise results in frequency fluctuations
in the solitons, and this results in timing jitter which limits the transmission distance
in a soliton link [2]. Due to these and other issues, soliton systems operate at lower
data rates than non-soliton systems. For this reason, improvements to non-soliton
systems such as COSSB are still needed.
Coherent Detection Systems
A different set of system architectures that are growing in popularity are coherent
detection systems. As an analogy, consider that many radio systems modulate the
data onto an RF signal using the phase and amplitude of that data. This requires
that a local oscillator be present at the receiver so that the LO may be mixed or
multiplied with the received signal. Coherent optical systems operate the same way.
A laser must be present at the receiver so that it is combined with the received signal
2.4 Compatible Optical Single Sideband 33
prior to detection. If homodyne detection is used, the laser at the receiver must be
locked in phase to the optical carrier in the received signal using an optical phase-
locked loop (PLL), the design of which is not trivial and which remains a new area
of research. The need for an optical PLL may be eliminated if heterodyne detection
is used. In a heterodyne system the receive laser is at a slightly different frequency
than the main frequency of the received signal, so that the output current of the
photodiode is at an IF. It was also mentioned in Section 2.3.2 that dispersion may
be compensated post detection at an IF frequency, eliminating the need for optical
compensation techniques. Another advantage of coherent detection has to do with
the fact that the received signal in direct detection fiber systems contains a lot of
carrier power compared to the signal power. During coherent detection, the carrier
power is effectively stripped away leaving only the signal. This can increase the signal
to noise (SNR) ratio at the receiver by up to 20 dB compared to self-homodyning
transmission [2]. Furthermore, coherent detection allows for the use of modulation
techniques that use the phase and amplitude of the optical signal, allowing for the
use of more spectrally efficient modulation techniques. This is important in dense
WDM systems.
Research continues on the development of coherent detection optical systems,
particularly on ways of integrating coherent optical receivers. They have yet to be
adopted in commercial systems, partly because of the success of WDM technology
using optical amplifiers [2]. So, although research will continue on coherent detection
systems, direct detection systems, to which the work in this thesis belongs, will be
around for a long time.
2.5 Conclusion 34
Duobinary Transmission
In a typical NRZ system, an optical intensity modulator, such as a Mach-Zehnder,
is biased in its linear range and is used to modulate the optical signal with the data.
The disadvantage of this technique is that the bias voltage used on the intensity
modulator causes a large DC content in the electrical data. This DC offset increases
the quiescent optical power and reduces the linearity, and decreases the SNR ratio.
The SNR may be improved using duobinary transmission, where the electrical signal
swings positive and negative. In order to perform duobinary modulation and main-
tain linearity, the conventional NRZ signal is encoded into two signals, one positive
and one negative. These encoded signals are used to separately modulate two optical
streams, which are then combined and transmitted. Lee et al. recently demonstrated
that duobinary signals are somewhat more tolerant to chromatic dispersion than bi-
nary signals [19]. However, Davies recently patented a technique for performing
single sideband modulation of duobinary signals [20]. A duobinary single sideband
signal, even with modest 15 dB sideband cancellation, would have extremely high
tolerance to dispersion, and a high SNR. Davies’ method still requires an integrated
Hilbert transformer in the case of digital signals, providing still further motivation
for the development of the Hilbert transformer in this thesis. The only disadvantage
of duobinary transmission is its complexity, such as the requirement for a duobinary
encoder.
2.5 Conclusion
The problem of chromatic dispersion was introduced in this chapter along with com-
monly used techniques used to solve it. COSSB transmission was described and
it was shown that COSSB signals are immune to dispersive power fading, and so
2.5 Conclusion 35
the dispersion in these systems may be compensated post detection. The challenges
of how to generate the logarithm of a broadband signal, and how to integrate a
broadband Hilbert transformer for the COSSB system have been posed.
Chapter 3
Analysis and Design of HBT Cherry-Hooper
Amplifiers with Emitter Follower Feedback for
Optical Communications
In this chapter, the design of Cherry-Hooper amplifiers with emitter follower feedback
(CHEF) is described. This amplifier is required in order to design the SiGe HBT
logarithmic amplifier in the next chapter.
3.1 Introduction
The CHEF amplifier, shown in Figure 3.1, is widely used in limiting amplifiers and
decision circuits in fiber-optic receivers [21, 22, 23, 24, 25, 26]. The use of these ampli-
fiers operating at 40 Gb/s in InP technology has recently been demonstrated [27, 28].
The amplifier shown includes resistor R2, an addition suggested by Greshishchev and
Schvan in order to raise the gain [29]. Although this circuit is useful as a high per-
formance broadband amplifier, it can have excessive gain and group delay peaking
for certain choices of the component values. Designing the gain to peak with fre-
quency may give the highest bandwidth, but this results in the group delay peaking
with frequency as well and leads to a distorted eye pattern [24]. For this reason, it
is necessary to strike a balance between gain and delay flatness and bandwidth in
transceiver amplifiers.
Ohhata et al. presented an analysis of the CHEF amplifier for an implemen-
tation using selective-epitaxial SiGe HBTs for which the parasitic capacitances are
3.1 Introduction 37
R1
R2
Rf
Q5
Q3
Q1
Q4
R2
R1
Rf
Q2
Q6
IEE2
IEE1
Vo1,
gm1vin2
gm3(v1-v2)V1,v1
VEE
Vin
vin2
2
-Vin
-vin2
2
V2,v2
vo1
Vo2,vo2
2
Figure 3.1: Cherry-Hooper amplifier with emitter follower feedback.
relatively small and the base resistance is relatively large [24]. In that work, the base
resistance of the small feature size HBTs had a significant effect on the small signal
transfer function of the amplifier. In this chapter, amplifiers that are designed with
SiGe HBTs having base resistances less than 100 Ω are examined [30]. To the au-
thor’s knowledge, the small signal behavior of the CHEF amplifier using such devices
and using R2 has not been characterized in a way that would allow designers to op-
timize group delay and bandwidth. Also in this chapter, equations for the frequency
response, DC transfer characteristic, and output noise of the amplifier are given and
are used to develop design guidelines. Using these guidelines, the amplifier may be
designed as a second order all pole system to have a Bessel transfer function.
This chapter is arranged as follows. In Section 3.2 the large signal performance
of the amplifier is considered. In Section 3.3, a small signal high frequency model of
the amplifier is presented. Suggestions for low noise design are given in Section 3.4.
Section 3.5 uses the equations that are presented to design a 13.7 GHz bandwidth,
19.7 dB gain implementation of the amplifier in a 47 GHz fT SiGe HBT technology.
Measurement results are presented to confirm the theory.
3.2 Large Signal Performance 38
3.2 Large Signal Performance
The large signal performance of the amplifier may be understood by first consider-
ing the DC transfer characteristic. In Figure 3.1, uppercase variables are used to
represent DC voltages and currents. In Appendix A, equations (3.1) and (3.2) are
derived for the amplifier in Figure 3.1. In these equations, βDC is the DC common
emitter current gain of the transistors and VT is the thermal voltage of approximately
26 mV at room temperature. These expressions show that the DC voltage difference
V1 − V2 for a given Vin may be calculated through iteration, and then Vo1 − Vo2 may
be calculated.
V1 − V2∼= R1IEE2 · tanh
(
V2 − V1
2VT
)
+RfIEE1 · tanh(−Vin
2VT
)
+VT · ln(
IEE1
1 + eVin/VT+
IEE2
βDC(1 + e(V1−V2)/VT )
)
(3.1)
−VT · ln(
IEE1
1 + e−Vin/VT+
IEE2
βDC(1 + e(V2−V1)/VT )
)
Vo1 − Vo2∼= (R1 +R2)IEE2 · tanh
(
V2 − V1
2VT
)
(3.2)
A first observation from equations (3.1) and (3.2) is that R2 will only scale the
output voltage, without affecting its basic shape. Hence, increasing R2 is an ef-
fective means of increasing the output voltage swing of the amplifier. However,
equation (3.2) also shows that in order for Vo1 − Vo2 to reach the maximum output
swing of (R1 + R2)IEE2, tanh must reach its full value of ±1. This occurs when
|V1 − V2| >> VT . Having Vo1 − Vo2 reach its approximate full output swing is desir-
able in the presence of large high frequency signals, because the resulting voltage will
then be ±(R1 + R2)IEE2, which is known and well defined. In contrast, the voltage
V1 − V2 will not be well defined, since it depends on the emitter voltages of Q5 and
3.2 Large Signal Performance 39
Q6, which will suffer from amplitude overshoot due to capacitive feed through at the
emitters of Q5 and Q6.
As a further consideration, IEE1 and IEE2 should be large enough to achieve a
high fT for the HBTs in the amplifier. However, there is a range of bias current
for certain SiGe HBT technologies where the current may be changed, for example
by a factor of two, without significantly affecting fT [31]. This gives the designer
the freedom to choose the bias currents at or somewhat lower than that required for
peak fT , and near peak fT may still be achieved.
3.2.1 HBT β
It is instructive to note that if the CHEF amplifier bandwidth reaches nearly one
quarter of fT , then β will be significantly lower at this frequency than its low fre-
quency value. The AC β is frequency dependent, and is given by [32]
β =βo
1 + j ffβ
. (3.3)
The frequency at which β is 3 dB down from βo is called fβ and is given by
fβ∼= 1
2πrπ(Cπ + Cµ). (3.4)
The frequency at which β becomes unity, which is fT , is approximately expressed as
fT∼= gm
2π(Cπ + Cµ). (3.5)
From these relations, it is observed that fT = βofβ. Figure 3.2 shows a rough plot
of β versus frequency and is marked with βo, fβ, and fT .
3.3 Small Signal Analysis 40
fβ T
βo
f
−20 dB/decade
Figure 3.2: Plot of AC β.
3.3 Small Signal Analysis
Figure 3.3(a) shows the differential mode half circuit of the amplifier and Fig-
ure 3.3(b) shows the small signal equivalent with only the dominant parasitics. It
is assumed that the circuit is symmetrical, so that the small signal parameters of
Q1 and Q2, for example, are equal. Capacitance C1 represents the sum of Csub1,
and Cµ1 and Cµ3 reflected to node v1 using Miller’s theorem. The fact that Cπ3
connects to ground through re3 will be neglected and Cπ3 will simply be added to
C1. Specifically,
C1 = Cπ3 + (1 − 1/A1)Cµ1 + Csub1 + Cµ3(1 − A2) (3.6)
where A1 and A2 are the gains across Cµ1 and Cµ3 respectively and are given by
A1∼= −
r′d3(R′
f + rd5)
r′d1(r′
d3 +R1)(3.7)
A2∼= −R1 +R2
r′d3
(3.8)
where rdk = 1/gmk, r′
dk = 1/gmk + rek, gmk is the transconductance of transistor
k, rek is the parasitic emitter resistance of transistor k, and R′
f = Rf + re5. It is
noted that Cπ3 is shown explicitly in Figure 3.3(b) but was added to C1 during for
3.3 Small Signal Analysis 41
vin
2
vo1
R1
R2
RfQ3
Q1
Q5
Rs
Vin
2
ZinEF
(a)
R1
C1vin
rd5
vo1
β
rd3β
R2
ZLrd1β
Cπ1
rb1Rs
Rs
re1
vbe5rd5
vbe5
rd3
vbe1
vbe1
Rf’
2rd1
ic5
ic1=
=
rb5
re3
Cπ3
Cπ5
vbe3vbe3
ic3 =
’
v1
(b)
Figure 3.3: CHEF amplifier (a) differential mode half circuit and (b) small signalequivalent including source and load impedances.
the computations in this chapter. The component of Cµ1 reflected to the base of
Q1 through Miller effect has been ignored, since the gain across Q1 is usually small
and so the Miller capacitance will be much less than Cπ1. Also in Figure 3.3(b), the
base-emitter resistance rπk for a transistor k has been rewritten using the identity
rπk = βrdk. These approximations facilitate analysis without introducing significant
error, as will be shown.
The small signal transfer function may be broken into two parts, vo1/vin =
vbe1/vin × vo1/vbe1. The transfer function vbe1/vin is calculated to be
vbe1
vin
∼= rd1
2r′d1 + rd1sCπ1(R′
s + re1). (3.9)
This expression has a single pole resulting from Cπ1 and mainly from R′
s, which is
the resistance of the input signal source plus the base resistance of the input HBT.
In practice, the amplifier is usually driven by an emitter follower, which has a very
low output impedance, making R′
s small. As a result, this pole will be at a frequency
significantly higher than the bandwidth of the overall amplifier.
3.3 Small Signal Analysis 42
The stage following the amplifier is usually an emitter follower output buffer, and
the amplifier is loaded by the input impedance of this emitter follower, ZinEF . This
impedance, along with Csub3 and the Miller capacitance of Cµ3 reflected to node Vo1,
form the load impedance ZL, according to
1
ZL
=1
ZinEF
+ sCsub3 + sCµ3(1 − 1/A2). (3.10)
The magnitude of the impedance ZinEF decreases with frequency, and so ZL may be
modeled to first order by a capacitor CL. A more accurate prediction of the amplifier
response may be obtained with a more detailed formulation of ZinEF , as described
in Appendix B.
Nodal analysis was used to find the transfer function vo1/vbe1, which is derived in
Appendix C. With the assumption that ZL∼= 1/sCL, vo1/vbe1 may be approximately
expressed as
vo1
vbe1
∼= 1
rd1r′
d3C1CL
[
s2 +ωo
Qs+ ω2
o
] (3.11)
where Q and ωo are the pole quality factor and pole frequency given by
Q ∼=[
C1CL(R1 +R2)(R′
f + rd5)(R1 + r′d3)
r′d3
C1(R′
f + rd5) + CL(R1 +R2)2
]1/2
(3.12)
ωo∼=
[
R1 + r′d3
r′d3C1CL(R1 +R2)(R′
f + rd5)
]1/2
. (3.13)
Equations (3.12) and (3.13) are valid for R′
f/R1 > 2, which approximately corre-
sponds to the bandwidth where the equations are reasonably accurate. The lat-
ter equation indicates that the pole frequency ωo, which is one indication of am-
plifier bandwidth, is inversely proportional to the square root of C1, CL, and R′
f
3.3 Small Signal Analysis 43
if R′
f >> rd5. This indicates that although increasing R′
f raises the amplifier
gain, it decreases the bandwidth. Equation (3.12) may be further simplified if
C1(R′
f + rd5) >> CL(R1 +R2) to
Q ∼=[
CL(R1 +R2)(R1 + r′d3)
r′d3C1(R′
f + rd5)
]1/2
. (3.14)
This shows that increasing R1 raises Q, and increasing R′
f or C1 lowers Q. Further-
more, increasing R2 will result in modest increases in Q, and a comparable decrease
in ωo, two effects which may be expected to leave the bandwidth roughly unchanged.
This is consistent with the observation of Greshishchev and Schvan, who noted that
increasing R2 in the range 0 < R2/R1 < 2.5 had little effect on the bandwidth but
increased the gain significantly [29].
The two poles in (3.11) located at ωo are a complex conjugate pair for Q > 0.5
and they dominate the frequency response of the CHEF amplifier. Figure 3.4 shows
the magnitude and group delay responses for such a system for different values of Q
and for ωo = 1 rad/s. The case where Q = 1/√
2 ∼= 0.707 corresponds to a second
order Butterworth response, where the magnitude response is maximally flat. The
case where Q = 1/√
3 ∼= 0.58 corresponds to a second order Bessel response, where
the group delay is maximally flat [33]. Figure 3.5 shows eye diagrams of 10 Gb/s
signals which have passed through second order systems with Q values of 1/√
3 and
1.0 respectively, and with ωo = 2π · 15 × 109 rad/s. The eye diagram for the system
with Q = 1.0 is distorted due to the gain peaking and group delay distortion of that
system. To avoid this type of distortion, it is always desirable to have a Q factor of
approximately 1/√
3 for broadband optical applications. The disadvantage of such a
design is that it has less bandwidth than a design with a higher Q factor. It should
be noted that when this amplifier is viewed as a lowpass system, a higher Q increases
3.3 Small Signal Analysis 44
100
101
0
10
20
30
40
50
60
70
80
90
Frequency (rad/s)
Gro
up D
elay
(s)
100
101
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (rad/s)
Mag
nitu
de
Q=0.5
Q=0.85
Q=1/ 3
Q=1/ 2
Q=1
Q=0.5
Q=1
Q=0.85
Q=1/ 3
Q=1/ 2
Figure 3.4: Magnitude and group delay responses for a second order system.
−150 −100 −50 0 50 100 150−0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time (ps)
Am
plitu
de
(a)
−150 −100 −50 0 50 100 150−0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time (ps)
Am
plitu
de
(b)
Figure 3.5: Eye diagrams for a 10 Gb/s signal filtered with second order systemshaving (a) Q = 1/
√3 and (b) Q = 1.0.
the bandwidth. However, if this amplifier is viewed as a bandpass system, a higher
Q decreases the bandwidth.
3.3.1 Design Example
The method in which the amplifier may be designed to have Q = 1/√
3 can be
illustrated through an example. Bias currents are first chosen based, for instance,
on the desired amount of power dissipation. The value of IEE2 will also partially
determine the output voltage swing. For the purpose of illustration, one amplifier
with two different current bias levels will be considered here. One bias level is
3.3 Small Signal Analysis 45
IEE1 = IEE2 = 1.0 mA, and the other bias level is IEE1 = 3.0 mA and IEE2 = 3.2 mA,
chosen based on output swing. Higher currents than these may cause a biasing
problem when a 3.3 V or lower supply voltage is used.
When designing the amplifier, the emitter length LE of the HBTs should be
chosen to provide peak or near peak fT , assuming that such an LE is large enough
to safely handle the desired amount of bias current. The emitter length of Q1 and
Q2 in the first stage of a limiting amplifier chain should be chosen based on noise
considerations as well, as will be shown in Section 3.4. For the present circuit, dual
stripe emitters are used for all transistors, each emitter stripe width is 0.5 µm, and
the emitter length of each stripe is 5.0 µm for Q1, Q2, Q5, and Q6; and 2.5 µm for Q3
and Q4. Once the bias currents and LE of the HBTs are chosen, the only unknowns
in equation (3.11) are R1, R2, R′
f , and ZL. ZL may be calculated by equation (3.10)
with a capacitance chosen to model ZinEF . The choice of the resistors R1, R2,
and R′
f will determine the gain and bandwidth of the amplifier, and the Q factor
of the two dominant poles. R1 may be chosen based on the desired amount of
output swing, and is chosen as 55 Ω for this example. The values of R′
f and R2
may then be varied in order to observe the obtainable performance. Figs. 3.6, 3.7,
and 3.8 show plots of Q, 3 dB bandwidth, and low frequency gain respectively versus
R′
f/R1 for different values of R2. At the lower current bias level, the circuit has
reduced bandwidth because the fT of the HBTs is reduced to 50-75% of the peak
value. These plots were generated using the complete expression for vo1/vbe1 in
Appendix C, equation (C.2), with ZL = 1/sCL and CL = 40 fF. Of this capacitance,
approximately 15 fF represents Cµ3 reflected to node vo1 and Csub3, and 25 fF was
used to model ZinEF .
Using these plots, consider the amplifier when biased with IEE1 = 3.0 mA and
IEE2 = 3.2 mA. From Figure 3.6, it is seen that in order to have Q ∼= 1/√
3,
3.3 Small Signal Analysis 46
100
101
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Q
Rf /R
1
R2=2*R1R2=R1R2=R1/2R2=0
1/ 3
LC =40 fF
I =1.0mAEE1
I =1.0mAEE2
I =3.0mA, I =3.2mAEE2EE1
’
Figure 3.6: Plot of Q factor for different values of R1,R2, and R′
f .
100
101
0
5
10
15
20
25
30
35
Rf /R
1
Ban
dwdi
th (
GH
z)
R2=2*R1R2=R1R2=R1/2R2=0
C =40 fFL
I =1.0mAI =1.0mAEE1
EE2
I =3.0mA, I =3.2mAEE2EE1
’
Figure 3.7: Plot of 3 dB bandwidth for different values of R1,R2, and R′
f .
100
101
0
5
10
15
20
25
30
35
Rf /R
1
Gai
n (d
B)
R2=2*R1R2=R1R2=R1/2R2=0
I =3.0mA, I =3.2mA EE2EE1
I =1.0mAI =1.0mA
EE1
EE2
C =40 fFL
’
Figure 3.8: Plot of low frequency gain for different values of R1,R2, and R′
f .
3.4 Amplifier Noise Performance 47
R′
f/R1 should be in the range from 2.3 to 2.7. This shows that the ratio R′
f/R1 is
highly constrained for a fixed set of bias currents. For this example, Rf = 160 Ω
gives Rf/R1 = 2.9. This gives a Q factor slightly lower than 1/√
3 and will allow
for some variation in the load impedance ZL without introducing significant group
delay peaking. From Figs. 3.7 and 3.8, it may be seen that for R′
f/R1∼= 2.9 the
bandwidth ranges from 11.5 GHz to 14.5 GHz and the gain ranges from 14.4 dB to
24.0 dB for different values of R2. Choosing R2 = R1 = 55 Ω gives a reasonable
compromise, leading to a theoretical bandwidth of 12.9 GHz and a gain of 20.5 dB.
It should be noted that IEE1 and IEE2 need not be equal. However, with LE of
Q1 and Q2 chosen to be 5 µm to lower rb, IEE1 must be 3.0 mA to obtain near peak
fT . With IEE2 = 3.2 mA chosen to obtain the desired output swing and peak fT ,
the currents end up being nearly equal.
3.4 Amplifier Noise Performance
The CHEF amplifier often follows the transimpedance amplifier (TIA) in a fiber-
optic receiver. Hence, in addition to having a good frequency response, low noise
operation is desired in the first amplifier following the TIA. In this section, a simple
expression is given for the output noise power spectral density (PSD) of the amplifier.
In the following analysis, the mean square thermal noise voltage due to a given
resistor R will be expressed as e2R, where e2
R = 4kTR∆f and where k is Boltzmann’s
constant, T is temperature in Kelvins, and ∆f is equivalent noise bandwidth. For
a DC collector current IC , the mean square collector shot noise current will be
expressed as i2ck for the kth transistor, where i2ck = 2qICk∆f and where q is the
electron charge.
Using the above notation, an example calculation of the differential output noise
3.4 Amplifier Noise Performance 48
due to i2c1 is given in Appendix D. In the same way, the differential noise PSD
between vo1(t) and vo2(t) due to all noise sources in the amplifier is calculated as
v2o
∆f∼= 2(R1 +R2)
2
(R1 + r′d3)2
[
e2R′
f
∆f+
(R′
f + rd5)2
r′ 2d1
×(
e2rb1,2
∆f+e2re1,2
∆f+ r 2
d1
i2c1,2
∆f
)]
(3.15)
where, for example, e2rb1,2
is the noise of either rb1 or rb2. The input referred differential
noise PSD may be obtained if desired by dividing this equation by the square of the
low frequency differential amplifier gain, given by the product of (3.7) and (3.8).
From equation (3.15), it is seen that if (R′
f + rd5)2/r′ 2
d1 >> 1 and rb1 >> re1, then
the most important amplifier noise sources will be the collector current shot noise and
base resistance thermal noise of Q1 or Q2, i2c1,2 and e2rb1,2respectively. As an example,
consider the amplifier with IEE1 = 3.0 mA, IEE2 = 3.2 mA, R1 = R2 = 55 Ω, and
Rf = 160 Ω. Table 3.1 gives the values predicted by the terms in equation (3.15)
with the values simulated at 1 GHz using 47 GHz fT SiGe HBTs. This table shows
only the noise of the amplifier. The noise equations assume zero source impedance
because the amplifier is usually driven by emitter followers. In Table 3.1, it is clear
that the parasitic base resistance and collector shot noise of Q1,2 are the dominant
noise sources. The collector current shot noise of Q1,2 is difficult to reduce, since
a certain amount of current is required for high fT and gain. However, the base
resistance may be minimized by increasing the emitter length at a fixed emitter
width while keeping the bias current constant. The effective emitter length may
also be increased by using multiple transistors in parallel. This will result in some
decrease in fT , but a greater decrease in noise than in bandwidth. Using multiple
transistors also reduces self heating in these HBTs [29].
3.5 Experimental Results 49
Table 3.1: Differential output noise of the CHEF amplifier at 1 GHz.
Simulated Simulated Calculated
Noise Noise % of Noise % Error
Source (V 2/Hz × 10−17) Total (V 2/Hz × 10−17)
Q1,2 : rb 13.6 65.1% 15.4 13.2%Q1,2 : Ic 3.83 18.3% 4.11 7.3%Q1,2 : re 1.23 5.9% 1.39 13.0%Rf × 2 0.89 4.3% 1.01 13.5%Totals 19.6 93.6% 21.9 11.7%
3.5 Experimental Results
The design described in Section 3.3.1 was fabricated in IBM’s 5HP (Five High Perfor-
mance) SiGe process with 47 GHz fT HBTs and 0.5 µm feature sizes. This technology
was made available to the author through the Canadian Microelectronics Corpora-
tion. The schematic diagram of the amplifier is shown in Figure 3.9. The tail current
sources of the amplifier are provided by a modified Widlar biasing scheme, described
in Appendix E. The input of the circuit is an emitter follower input buffer, with
resistors and a capacitor arranged to maintain an impedance match up to 10 GHz
when the input leads are wire bonded. It was found that if a simple 50 Ω resistor was
used, the parasitic capacitance at the input node of the HBTs and approximately
1 nH of bond wire inductance would unacceptably degrade the input match if the
chip was wire bonded, as is typically required for packaging. By having the approx-
imate 70 Ω input impedance at low frequencies, it was found that the effects of the
300 fF capacitor and the bond wire inductance combine to achieve a better 50 Ω
match above 5 GHz [29]. However, for the measurements presented in this section,
wafer probing of RF signals was used to provide a characterization of the amplifier
that is unobscured by bond wire parasitics. Wafer probing is the technique whereby
microscopic metal probes directly contact the square metal pads on the unpackaged
3.5 Experimental Results 50
300fF
300fF
45Ω
34Ω
550Ω
45Ω
34Ω
550Ω
55Ω
55Ω 55Ω
55Ω
160Ω 160Ω
45Ω
34Ω 34Ω
45Ω300fF 300fF
3.0mA 3.2mA
-3.3V
Vchip_in1
Vchip_in2
Vchip_out1
Vchip_out1
3.2mA3.2mA 1.5mA 1.5mA 11.3mA
300fF
Input Buffer Output Buffer
0.5µm10.0µm
x
0.5µm10.0µm
x
0.5µm15.0µm
x
each
0.5µm5.0µm
x
each
0.5µm10.0µm
x 0.5µm10.0µm
x
0.5µm10.0µm
x 0.5µm10.0µm
x
0.5µm8.0µm
x
0.8mA/µm2
0.7mA/µm2
0.7mA/µm2
0.3mA/µm2
0.3mA/µm2
0.3mA/µm2 0.3mA/µm2
0.4mA/µm2
each
0.7mA/µm2
1.0mA
Figure 3.9: Schematic diagram of the CHEF amplifier test circuit.
integrated circuit. Furthermore, the power supply and ground were wire bonded
to the chip. All of the measurements were obtained by wafer probing the amplifier
with ground-signal-ground probes on Cascade Microtech REL 4800 and Summit 11K
probe stations.
The output buffer is a differential pair with an impedance match similar to that
used in the input buffer. The important component values of the amplifier are
shown in the schematic diagram. The 300 fF capacitor in the biasing reference was
restricted in size by the available chip area, or else it would have been increased in
value. Furthermore, it was suggested this capacitor could be connected from the
base of the β helper transistor to VEE in the current mirror reference for improved
stability [34]. The amplifier core draws 10.2 mA from a -3.3 V supply. A micro-
photograph of the integrated circuit is shown in Figure 3.10.
Figure 3.11 shows the theoretical transfer function of the amplifier predicted by
equations (3.9) and (C.2), the simulated transfer function with and without resistive
3.5 Experimental Results 51
700 µm
µm700
CHEF Amplifier
Input Buffer
Output Buffer
Figure 3.10: CHEF amplifier IC microphotograph.
and capacitive layout parasitics, and the deembedded measured transfer function.
The measured gain was deembedded from a measurement of S21 taken with a -
20 dBm input signal using a Hewlett Packard (HP) 8510C network analyzer. The
accuracy of the calibrated network analyzer measurement is estimated to be better
than 0.1 dB. For the theoretical transfer function calculation, the load impedance was
modeled using equations (3.10) and (B.1). All of the simulated curves in this section
were generated using Cadence Spectre software. The error between the theoretical
and deembedded measurement is less than 1.2 dB between 0-5 GHz, and is less than
0.8 dB between 5-15 GHz, which is sufficiently small for design purposes. In the
layout, multiple resistors in parallel were used to implement R1 and R2, leading
to increased metalization area connecting to these resistors. The difference in the
simulated response with parasitics is partially attributed to the capacitance of this
metalization to the substrate and to surrounding nodes.
3.5 Experimental Results 52
108
109
1010
1011
5
10
15
20
25
Frequency (Hz)
AC
Gai
n (d
B)
TheoreticalDeembedded MeasurementSimulation − Without Layout ParasiticsSimulation − With Layout Parasitics
Figure 3.11: Comparison of theoretical gain based on equations (3.9) and (C.2),simulated gain, and measured gain.
2 4 6 8 10 12 140
10
20
30
40
50
60
70
80
90
100
Frequency (GHz)
Gro
up D
elay
(ps
)
TheoreticalDeembedded MeasurementSimulation − Without Layout ParasiticsSimulation − With Layout Parasitics
Figure 3.12: Comparison of theoretical group delay based on equa-tions (3.9) and (C.2) , as well as simulated and measured group delay.
Figure 3.12 shows a comparison of the theoretical group delay, the simulated
group delay with and without resistive and capacitive layout parasitics, and the
measured group delay. Note that the measured phase response was closely fit to a
seventh order polynomial and the group delay was obtained using the derivative of
this polynomial curve. It is estimated that the accuracy of the group delay obtained
with this technique is better than ±5 ps. Since the phase response is roughly a
straight line up to the frequencies of interest, using a polynomial results in negligible
3.5 Experimental Results 53
error in representing the phase response, but removes the 50 ps of noise which would
be present if the raw measured phase response were used to obtain group delay.
This is true even if averaging is turned on in the network analyzer. The group delay
distortion up to 10 GHz is approximately ±10 ps theoretical, ±6 ps simulated without
layout parasitics, ±12 ps simulated with layout parasitics, and ±10 ps measured.
In this case, the theory provides a reasonable prediction of group delay for design
purposes.
The noise figure (NF) was measured at one output terminal with the signal
applied to one input terminal, and the other input and output terminals were
terminated in 50 Ω. The noise figure was measured using a HP8970B noise fig-
ure meter with a HP346B noise source. The measured NF is 14.7 dB at 1 GHz.
The equivalent deembedded differential noise at the output of the amplifier core is
2.36 × 10−16 V 2/Hz. Comparing this with the theoretical output noise from Ta-
ble 3.1, it is observed that equation (3.15) predicts the measured noise with −8%
error.
Figure 3.13 shows measured eye diagrams for a data rate of 10 GB/s. A PRBS
signal with a pattern length of 231 − 1 was used for all measurements. The PRBS
signal was generated using the Anritsu MP1763B pattern generator and the eye
diagram was measured on a HP 54750A oscilloscope with a 54754A 18 GHz sampling
module. Figure 3.13(a) shows the signal at the output of the pattern generator, and
Figs. 3.13(b),(c), and (d) show the single ended amplifier output eye for a differential
input signal with amplitudes of 7 mVpp, 20 mVpp, and 400 mVpp respectively. The
data eye has good opening and low overshoot for all cases. In order to have a more
square eye, which is desirable, the required bandwidth is approximately 1.5 times
the clock rate, or 15 GHz for 10 Gb/s. Although the bandwidth of the amplifier is
13.7 GHz, the inclusion of the input and output buffers reduces the bandwidth to
3.6 Conclusion 54
20 mV
100 ps
(a)
100 ps
30 mV
(b)
80 mV
100 ps
(c)
100 ps
220 mV
(d)
Figure 3.13: Measured eye diagrams at 10 Gb/s: (a) Through measurement at20 mVpp and single-ended CHEF amplifier output for differential input signals ofamplitude (b) 7 mVpp, (c) 20 mVpp, and (d) 400 mVpp.
11.2 GHz. A bandwidth of 15 GHz could be achieved in this technology by sacrificing
some core amplifier gain, and by reducing the gain of the output buffer.
3.6 Conclusion
When used for optical transceiver applications, the CHEF amplifier must have high
gain and bandwidth, low noise, and high output swing. Design techniques for achiev-
ing all of these goals simultaneously were given in this chapter. A pair of complex
poles was found to dominate the amplifier frequency response. The relative values
of resistors which result in optimum pole quality factor were described. Further-
more, the dominant noise sources in the amplifier were identified. A 19.7 dB gain,
13.7 GHz bandwidth implementation of the circuit verified the small and large signal
behavior. The CHEF amplifier from this chapter is used in the DC-6 GHz SiGe HBT
logarithmic amplifier in the next chapter.
Chapter 4
A Novel Parallel Summation Logarithmic
Amplifier
4.1 Introduction
In Section 2.4.3, it was shown how the implementation of a COSSB modulator re-
quires a logarithmic conversion of data. In this chapter, logarithmic amplifiers suit-
able for the OSSB application are described. The parallel summation logarithmic
amplifier is described in Section 4.3 in a way that allows logarithmic converters with
or without gain to be designed.
Logarithmic amplifiers which are suitable for use in fiber optic applications should
meet a unique set of requirements. In the COSSB application, the input signal is
a baseband signal which is strictly positive, and so it has DC and low frequency
components. Hence, the logarithmic amplifier should be DC-coupled throughout. As
well, maximizing the bandwidth of the logarithmic amplifier is critical, because of
the high data rates. However, low group delay distortion is important for broadband
operation. This chapter presents logarithmic amplifiers that feature low group delay
distortion.
In Section 4.2, the various types of logarithmic amplifiers are considered. A band-
width limitation of the series linear-limit logarithmic amplifier topology is considered,
and parallel summation logarithmic amplifiers, which overcome this limitation, are
described. In Section 4.3, a unified design procedure for parallel summation logarith-
mic amplifiers is given. In Section 4.4, the design and operation of a novel DC-4 GHz
4.2 Distinction and Comparison of Logarithmic Amplifiers 56
Si bipolar logarithmic amplifier are described. In Section 4.5, a DC-6 GHz SiGe HBT
logarithmic amplifier that uses the CHEF amplifier from the last chapter is described.
4.2 Distinction and Comparison of Logarithmic Amplifiers
There are two basic types of logarithmic amplifiers, the true and the demodulating
types. True logarithmic amplifiers, also known as ‘baseband’ or ‘video’ logarithmic
amplifiers, provide the logarithm of the signal without detecting or demodulating
the signal. In contrast, demodulating logarithmic amplifiers provide the logarithm
of the envelope of a signal. Exceptions are those circuits that may operate in the true
and demodulating modes through the use of Gilbert cell multipliers [35]. Demodu-
lating logarithmic amplifiers are widely used in radar and radio receivers as received
strength signal indicators (RSSI). However, for the COSSB application, demodula-
tion is not wanted, and implementations of true logarithmic amplifiers are described.
A list of prior publications describing demodulating logarithmic amplifiers that are
not related to this thesis was compiled by the author, and is listed in [36].
Logarithmic amplifiers may be further subdivided into single stage and piece-
wise approximate types. Transconductance feedback log converters are based on
an amplifier with a PN junction or a MOSFET device in subthreshold in feedback
around the amplifier [37]. These converters provide an excellent logarithmic response
in low frequency applications. A technique that has been more successful at high
frequencies is the piecewise approximation of a logarithm and this is the technique
considered in this work.
4.2 Distinction and Comparison of Logarithmic Amplifiers 57
1
1x
2 k N
Vin Vout
1x1x1x
GgainVin
Vout
VL
Σ Σ Σ Σ
Figure 4.1: Series linear-limit logarithmic amplifier.
4.2.1 The Series Linear-Limit Logarithmic Amplifier
Figure 4.1 shows the most widely used high frequency, true logarithmic amplifier
topology. The amplifier consists of a cascade of dual gain cells, with each cell having
a high gain, limiting amplifier in parallel with a unity gain buffer. For small signals,
this structure will simply amplify. However, as the signal becomes larger a point
will be reached at which the limiting amplifier in the last stage ceases to amplify
and provides a constant voltage VL. As the input signal becomes larger, the limiting
amplifiers will successively reach their upper bound, starting with the second last
stage and progressing toward the input. Meanwhile, the buffer amplifiers in all stages
will continue to pass the signal. This response, shown in Figure 4.2, approximates a
straight line when plotted on a semilogarithmic axis. A mathematical description of
this amplifier’s operation is given in [38].
The series linear-limit topology is attractive because process variations, such as a
low current gain for the transistors on a given wafer, will likely affect all stages more
or less equally. If the gain of all of the stages is lower than expected, the only result
is a scaling of the overall response, without affecting the logarithmic characteristic.
The linear-limit topology is also simple, since more stages may be added in cascade
if increased dynamic range is required, provided that the low gain path in each stage
4.2 Distinction and Comparison of Logarithmic Amplifiers 58
10−5
10−4
10−3
10−2
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Ou
tpu
t V
olta
ge
(V
)
Input Voltage (V)
Ideal Logarithm Linear−Limit Log Amp
0−1−2−310 10 1010
Out
put V
olta
ge (
mV
)
Input Voltage (V)
log error
300
100
0
200
−20−40−60 0Input Voltage (dBv)
Figure 4.2: Linear-limit logarithmic amplifier response.
does not saturate.
The requirement that the low gain buffer amplifiers not saturate presents a chal-
lenge in designing the twin-gain stages. A common implementation consists of two
differential pairs in parallel with shared collector nodes, as shown in Figure 4.3
[38, 39, 40]. One differential pair uses emitter degeneration to provide low gain and
the other differential pair is undegenerated to provide high gain.
Since the buffer amplifier in the N th stage must buffer the signal generated by
stages 1 to N − 1, the requirement on Ilow with respect to Igain may be found to
be [38]
Ilow
Igain> N. (4.1)
However, Igain needs to be somewhat large in order to achieve the desired gain.
Therefore, (4.1) indicates that Ilow will be large, necessitating large devices with high
parasitic capacitance. These capacitances, in turn, will place bandwidth limitations
4.2 Distinction and Comparison of Logarithmic Amplifiers 59
Ilow
Igain
in1V in2V
out2Vout1VRcRc
ReRe
Figure 4.3: High gain limiter and unity gain buffer in parallel.
on the series linear-limit logarithmic amplifier. One way to mitigate this difficulty is
to lower the gain of the buffer amplifiers below unity so that they require a higher
input voltage in order to limit, and so their current may be reduced. The gain may
be lowered using increased emitter degeneration or a series resistor connected to the
base of the buffering transistors [39].
Even if the size of the transistors in the buffer amplifier is reduced, the parasitic
capacitance of the buffer amplifier will still load the gain amplifier in parallel with
it. There is another class of log amplifiers where the high and low gain paths are
separate. These are known as parallel summation log amplifiers, which are described
in the next section.
4.2.2 Parallel Summation Logarithmic Amplifiers
The second class of log amplifiers is the parallel summation type. Parallel summation
log amplifiers may be divided into the progressive compression type and the parallel
amplification type. Each of these will be discussed in turn.
Figure 4.4 shows a progressive compression log amplifier [41]. Functionally it is
exactly the same as the series linear-limit amplifier, except that instead of sequen-
4.2 Distinction and Comparison of Logarithmic Amplifiers 60
Σ Σ ΣΣ
gm
gm1 gm gm gm gm
gmgm1
gm
outI
Vin
p1G p2G pkG pNGp3G
A1G A2G Ak-1G AN-1G
Vin
Iout
IL
Vin
Iout
IL1
Figure 4.4: Progressive compression, parallel summation logarithmic amplifier.
tially summing and buffering the clipped outputs of each stage, the stage outputs
are summed in parallel. In the progressive compression amplifier, each component
amplifier output voltage is converted to a current using a transconductance element.
The transconductance elements provide current up to a maximum level, at which
point their output current limits. Another type of parallel summation log amplifier
is shown in Figure 4.5, where it is seen that the component signals are generated in
parallel. This topology exhibits high symmetry among the different paths. Hence, al-
though the logarithmic dynamic range is lower, the phase and group delay matching
are inherently improved compared to the progressive compression topology.
Comparing the two parallel summation topologies, it is seen that the progressive
compression structure has the advantage of using multiple cascaded amplifiers to
achieve high logarithmic dynamic range. As a result, the progressive compression
structure is widely used in log amplifier designs, for example in [35] and [42]. The
parallel amplification scheme is efficient in low dynamic range applications, and has
been used in works such as [43] and [44]. However a mathematical design procedure
has yet to be presented for parallel summation logarithmic amplifiers. Such a design
procedure is given in the next section, with proof of a logarithmic result. Some
4.3 Design Procedure 61
IoutΣ Σ Σ
gm gm gmgm1
Vin
p1G p2G pkG pNG
Figure 4.5: Parallel amplification, parallel summation logarithmic amplifier.
unique and efficient delay matching structures are then given for these circuits to
allow for ultra broadband operation.
4.3 Design Procedure
A mathematical model of parallel summation logarithmic amplifiers is now presented
which may be used for design purposes. It will be proven that this method yields an
exact logarithmic relationship between the output current and the input voltage of
the amplifier at the breakpoints of the approximation.
Considering the parallel summation logarithmic amplifiers in Figs. 4.4 and 4.5,
the desired transfer function is shown in Figure 4.6. The constant A is defined
as the factor increase in the input voltage between the cusps of the logarithmic
approximation. The current IS is defined as the step in output current between the
cusps of the approximation. The dynamic range of the logarithmic amplifier will be
defined as AN , so for a dynamic range DR the constant A is chosen as DR1N .
The gains through the kth paths in Figs. 4.4 and 4.5 are labeled as Gpk, where
k = 1, 2, ...N . This is because the same signals are being generated in two different
ways, using series and parallel amplifiers. For either topology there are N discrete
states corresponding to the cases where N, N-1, ... 1 paths are contributing linearly
4.3 Design Procedure 62
Vin
C
TotalCircuitGains
GN
GN-1
Iout
G1
Gk
A VminN-1
A VminNAVmin
A Vmin2Vmin
SI +C
S2I +C
(N-k)I +CS
S(N-1)I +C
NI +CS
A VminN-k
GN-2
Figure 4.6: Parallel summation logarithmic amplifier transfer function.
to the output current. A path ceases to contribute linearly once its output current
limits at IL. As the input voltage increases, the logarithmic structure passes through
the N states where gain decreases and follows the series
GN = Gp1 +Gp2 + ...GpN
GN−1 = Gp1 +Gp2 + ...Gp(N−1)
...
Gk = Gp1 +Gp2 + ...+Gpk
...
G1 = Gp1. (4.2)
These state gains are labeled on the right side of Figure 4.6 at the signal levels at
4.3 Design Procedure 63
which they occur.
In any given state, the output current of the overall amplifier consists of two
parts; the current that is proportional to the input voltage, and the fixed current
supplied by the gain paths which have already limited. The output currents shown
on the y-axis of Figure 4.6 may be expressed as a sum of these two components, as
in
C = VminGN
IS + C = AVminGN−1 + IL
2IS + C = A2VminGN−2 + 2IL
...
(N − k)IS + C = AN−kVminGk + (N − k)IL
...
(N − 2)IS + C = AN−2VminG2 + (N − 2)IL
(N − 1)IS + C = AN−1VminG1 + (N − 1)IL
NIS + C = VminGN +NIL. (4.3)
A straightforward solution to these equations may be found by allowing IS = IL.
As well, since G1 = Gp1 from (4.2), the overall amplifier gains, Gk, may be found
from (4.3) by assuming that the gain of the lowest gain path Gp1 is simply gm, the
gain of the first transconductance element. This yields the logarithmic amplifier
gains
4.3 Design Procedure 64
G1 = gm
G2 = gmA
...
Gk = gmAk−1
...
GN−1 = gmAN−2
GN = gmAN−1. (4.4)
Using this knowledge of the gains in each state of the overall parallel summation
amplifier, the gains of the component amplifiers in both the progressive compression
and parallel amplification structures may be derived.
Solving (4.2) and (4.4) yields the gains of the paths through the parallel summa-
tion amplifiers
Gp1 = gm
Gp2 = gm(A− 1)
Gp3 = gmA(A− 1)
...
Gpk = gmAk−2(A− 1)
...
GpN = gmAN−2(A− 1). (4.5)
The path gains in equation (4.5) correspond directly to the amplifier gains in the
parallel amplification, parallel summation topology in Figure 4.5, multiplied by the
4.3 Design Procedure 65
gm of the transconductance elements. Note that these gains may be increased or
decreased by any factor as long as their respective ratios stay the same.
Applying equation (4.4) to the progressive compression topology, the gain of the
first path is just gm from the first transconductance element. The amplifier gains in
Figure 4.4 are
GA1 = A− 1
GA2 = A
...
GAk−1 = A
...
GAN−1 = A. (4.6)
In practice, it is more convenient in the progressive compression structure to make
the gain of amplifier GA1 equal to A so that all of the amplifiers are the same. This
may be done provided that the first transconductance element is also scaled from
gain gm to gmA/(A− 1).
Although a logarithmic amplifier with loss in some paths could be constructed,
the limiting transconductance elements would still be required. The input signal of
the amplifier would have to be large enough to cause the transconductance elements
to limit even after the signal is attenuated. It is impractical to use attenuation larger
than 20 dB in the paths, because the input signal voltage would have to be more
than ten times IL/gm. Hence, in a logarithmic converter with 40 dB of dynamic
range or more, some paths must use gain.
Having chosen the gains, it may be shown that the breakpoints are logarithmically
related to the input voltage. The proof bears some resemblance to the description
4.3 Design Procedure 66
of the linear-limit amplifier given in [38]. Assuming that the kth path in Figure 4.4
or 4.5 is just on the point of limiting, then the input is
Vink= Vin =
ILGpk
. (4.7)
However, Gpk is known from (4.5) to be Gpk = gmAk−2(A− 1), so that
Vin =IL
gmAk−2(A− 1)k ≥ 2. (4.8)
Additionally, if the kth path is limiting, then there are N −k paths with higher gains
which are also limiting, and k − 1 more paths which are still amplifying linearly.
Thus, the output current is
Iout = (N − k)IL + [Gp1 +Gp2...+Gpk]Vin. (4.9)
Using (4.2) and then (4.4),
Gk = Gp1 +Gp2 + ... +Gpk
= gmAk−1. (4.10)
Substituting (4.8) and (4.10) into (4.9) yields
Iout = (N − k)IL +AILA− 1
. (4.11)
Additionally, (4.8) is rewritten as
k = logA
[
A2ILgmVin(A− 1)
]
. (4.12)
Finally, substituting (4.12) into (4.11) gives
4.3 Design Procedure 67
Iout = IL
[
N +A
A− 1+ logA
[
gmVin(A− 1)
A2IL
]]
(4.13)
which is the desired logarithmic relationship between Iout and Vin.
A check of (4.13) may be made by substituting values for Vin and verifying that
the output current behaves as shown in Figure 4.6. Consider the case where the kth
amplifier path is just on the point of limiting. The input voltage for this case is given
in equation (4.8). Substituting this into (4.13) for Vin and simplifying gives
Iout = IL
[
N − k +A
A− 1
]
. (4.14)
For different values of k, this equation evaluates to
k = N Io = IL
[
A
A− 1
]
= IL
[
1 +1
A− 1
]
k = N − 1 Io = IL
[
1 +A
A− 1
]
= IL
[
2 +1
A− 1
]
...
k = 2 Io = IL
[
N − 1 +1
A− 1
]
(4.15)
which confirms that as each gain path limits, the output current increases by a fixed
step as shown in Figure 4.6. The constant C in Figure 4.6 is identified from (4.15)
to be IL/(A− 1). As well, Vmin from Figure 4.6 is identified from equation (4.3) as
Vmin =C
GN=
IL(A− 1)gmAN−1
. (4.16)
There is one final consideration regarding the case of k = 1 not considered in (4.8),
which is the case where the lowest gain path limits. The highest output current
4.3 Design Procedure 68
considered in (4.15) is the case where the second lowest gain path, whose gain is
Gp2 = gm(A−1), limits and provides a current of IL. The input voltage at this point
is
Vin =ILGp2
=IL
gm(A− 1). (4.17)
At this input voltage, the current provided by the lowest gain path is
I = gmVin =IL
A− 1. (4.18)
This point occurs at the total system output current of (N − 1)IS +C in Figure 4.6,
and in order for the logarithmic slope of the output to continue, the lowest gain path
must provide another IS of current before it limits. However, IS = IL, and so adding
this to (4.18) yields
IL1 =IL
A− 1+ IL =
A
A− 1IL, (4.19)
which represents the value of the limiting current required in the lowest gain path.
Thus, the lowest gain path provides a maximum current that is A/(A − 1) times
higher than the other paths.
4.3.1 Logarithmic Slope and Intercept
The response of logarithmic amplifiers may also be characterized in terms of the
logarithmic slope and intercept of the transfer characteristic, as in the equation
Iout = Islope 20 log10
(
Vin
Vintercept
)
. (4.20)
The amplifier transfer function in equation (4.13) may be used to calculate these
parameters for the given model. Solving (4.13) for the intercept yields
4.3 Design Procedure 69
Vintercept =A2−N−A/(A−1)ILgm(A− 1)
. (4.21)
The logarithmic slope may be found from (4.13) to be
Islope =dIout
d [20 log10(Vin)]=
IL20 log10(A)
Amperes/dBv. (4.22)
Hence, the logarithmic slope is directly proportional to IL and is inversely propor-
tional to the logarithm of A.
4.3.2 The Delay Matched Progressive Compression Amplifier
Having described a model of parallel summation amplifiers, it is worth considering
a disadvantage of the progressive compression amplifier at high frequencies. In the
progressive compression circuit, the phase delays of each signal undergoing parallel
summation will be different. This is because the first component signal in Figure 4.4
does not pass through any amplifiers and has zero phase shift, and this signal must
be added to the Nth parallel signal, which will have significantly higher phase shift
from having propagated through N amplifiers. A method proposed by the author of
extending the bandwidth is shown in Figure 4.7, where the group delay and phase
shift of each gain path are matched using delay amplifiers. It has been recognized
that the signals in the lowest gain paths may share delay amplifiers after they have
been limited and summed. Any number of paths may be combined and delayed using
this method, provided that the output voltage swing requirement of the shared delay
amplifiers does not lower their bandwidth below that of the highest gain path.
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 70
Σ Σ
∆
∆∆
Σ
gm1 gm gmgm
∆Delay
Amplifiers
outI
Vin
gm
A1G A2G A3G
Figure 4.7: An example of a three stage delay matched progressive compression logamplifier.
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic
Amplifier
4.4.1 Design of Implementation 1
In the present design a novel hybrid series/parallel topology, as shown in Figure 4.8,
was chosen for implementation [36]. A logarithmic voltage dynamic range of 50 dB
was targeted, corresponding to a factor A of 32014 = 4.23 in a four branch amplifier.
The scaled gains of the four paths are thus 1.00, 3.23, 13.7, and 57.8. However
in practice, some logarithmic dynamic range will be lost when DC-coupling is used
because the DC offsets in the component amplifiers will be amplified and will reduce
the available signal swing.
The cascode long-tail differential pair circuit, which is shown in Figure 4.9, was
chosen for both the gain and delay amplifiers. Using the CHEF amplifier as a building
block in the logarithmic amplifier would have resulted in more bandwidth. However,
the first logarithmic amplifier was designed long before the CHEF amplifier was fully
understood by the author and before the integrated circuit in the previous chapter
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 71
I log1
Vin1 Vin2
I log2
ΣΣ
ΣΣ
ΣΣ
∆
∆
gm1 gm gm gm
p1G p2G p4Gp3G
Figure 4.8: Parallel summation logarithmic amplifier implementation.
was designed. The second logarithmic amplifier implementation will be described in
Section 4.5, and it makes use of CHEF amplifiers.
The voltage outputs of the four amplification paths were each converted to cur-
rents and summed using the amplifier shown in Figure 4.10. This summing/limiting
circuit consists of four differential pairs in parallel. The circuit will sum an input
signal up to the point where that signal is large enough to steer all of the current in
one of the differential pairs to one side, at which point it limits that input’s contri-
bution. The bias current in each amplifier in Figure 4.10 is chosen as IL, except the
current in the lowest gain path, which is chosen as IL1 = ILA/(A − 1). This also
increases the gain of that differential pair, however, the gain of the delay amplifiers
in the lowest gain path may be lowered to compensate.
In addition to summing and limiting, the summing amplifier has a collector
impedance of 50 Ω, so as to allow for direct DC coupling of the output to a 50 Ω
system. The inputs of the chip are matched to 50 Ω using the circuit shown in
Figure 4.11.
For the first implementation, the best available technology was a silicon bipolar
process with fT values of 35 GHz and a 0.35 µm minimum feature size. This fabri-
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 72
Vee
+
-Vin Re Re
Rc Rc
+
-Vout
Q1 Q2
Q3 Q4
Figure 4.9: Amplifier used as a gain or delay cell.
in3
out1 out2
in3in4 in4 in1in2in2in1
5050
Vee
IL
IL
IL
IL1
Figure 4.10: Summing/limiting amplifier.
50
in1
out1in2
out2
50
Vee
Vee
Figure 4.11: Input matching circuit.
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 73
Output
Summer1 Gain
Stages
st
2 Gain
Stages
nd
Input
Buffer
2 mm
2 mm
Figure 4.12: Microphotograph of the Si logarithmic amplifier integrated circuit.
cation process was made available to the author through TRLabs’ association with
Nortel. Simulations consisted of transient, AC, and s-parameter analysis using the
Cadence Spectre and Avanti HSPICE simulators within the Cadence design software,
made available to the author by the Canadian Microelectronics Corporation. A die
microphotograph of the 2×2 mm2 parallel logarithmic amplifier chip is shown in
Figure 4.12. It has a single supply voltage of -5 Volts and draws 150 mA of current.
A negative supply voltage was used so that the circuit’s input and output common
mode voltage would be close to zero.
4.4.2 Measurements of Implementation 1
The small signal gain and reflection coefficients of the chip, obtained using using
an HP 8510C network analyzer, are shown in Figure 4.13. Similar to in the last
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 74
100
101
−30
−20
−10
0
10
20
30
40
dB
f (GHz)
S11S22S21
27
4 GHz
Figure 4.13: Measured return loss and gain.
chapter, measurements or RF signals were obtained using wafer probing, and the
power supply and ground connections were wire bonded. The small signal gain is
30 dB with a 3 dB bandwidth of 4.0 GHz. The circuit is impedance matched at its
input and output terminals below -10 dB for S11 and S22 up to 5 GHz.
Variations in the group delay versus frequency are also of prime importance in the
COSSB application. Figure 4.14 shows the measured small signal group delay of the
amplifier versus frequency. The maximum deviation of the group delay within the
4 GHz passband is 35 ps, which represents approximately one tenth of the period of a
2.5 Gb/s signal. The low group delay distortion is a direct consequence of the parallel
summation topology used, which achieves low delay by using only two amplifiers in
series to generate a four segment logarithmic response.
The measured one-tone response of the chip is shown in Figure 4.15 (a) for fre-
quencies from DC to 4 GHz. To make this measurement, a microwave signal source
was ramped in power, and a HP8563A spectrum analyzer was used to measure the
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 75
0 1 2 3 4 5150
160
170
180
190
200
210
220
dela
y (S
21)
(pic
osec
onds
)
f (GHz)
Group Delay
Figure 4.14: Measured group delay response.
logarithmic amplifier output signal. The loss in the measurement system has been
calibrated out of the measurements that are shown here. The single-ended loga-
rithmic slope is approximately 1.2 mV/dB and the logarithmic intercept is 167 µV.
Regarding the effect of process variations on the logarithmic response, Figure 4.15 (b)
shows the measured amplitude response of eight die samples at 1 GHz. The loga-
rithmic slope is quite constant among the samples, indicating that the logarithmic
response of the chosen topology may be designed to be robust. As a metric of
logarithmic linearity, the logarithmic error was calculated for the responses in Fig-
ure 4.15 (a) at each frequency and also for a broadband logarithmic fit. The definition
of the log error is shown graphically in Figure 4.2, where the definition of logarithmic
error indicated in [37] and [45] has been used. This log error was computed at each
1 GHz interval, and is plotted in Figure 4.16 (a). It is seen that the log conformity
is ± 2dB over the 4 GHz interval. The broadband log error of the data fit to a single
logarithmic line for a DC-3 GHz bandwidth is shown in Figure 4.16 (b), where the
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 76
error is kept to a maximum of ±5dB.
Figure 4.17 shows the normalized measured and ideal frequency domain spectrum
of the logarithmic amplifier output to a 1.8 GHz, -10 dBm signal with a 90 mV DC
offset added in order to make the input signal greater than zero. The measured
waveform was obtained with the HP 54750A oscilloscope with a HP 54751A 20 GHz
sampling module, and was Fourier transformed in Matlab. The amplitude of the
first three measured harmonics matches the ideal response well. The errors at the
fundamental and first two harmonics are 0.5, 0.1, and 2.5 dB respectively.
A real time oscilloscope plot of the log amplifier’s response to a 40 dB range of
input power at 1.8 GHz is shown in Figure 4.18. The HP 54750A oscilloscope with
a HP 54751A 20 GHz sampling module was also used to measure this signal. The
rise and fall times of this circuit are 100 ps each.
In Figure 4.18, it is apparent that the circuit contributes substantial noise for
small signals, with the amount of noise decreasing as the higher gain amplification
paths begin to limit. The noise figure of the amplifier was measured to be 20 dB
using a HP 8970B noise figure meter with a HP 346B noise source. This corresponds
to a maximum input referred noise density of 9 nV/√Hz, which is undesirably high.
Included in this version of the design was a unity gain buffer at the input of the chip,
which was removed in the second implementation described in Section 4.5. Another
significant noise component in the logarithmic amplifier is the thermal noise arising
from the parasitic base resistance of the transistors in the input matching circuit, and
from Q1 and Q2 in the first amplifier (see Figure 4.9) in the highest gain path only.
In the implementation to be presented in the next section, this noise was reduced by
using transistors with larger emitter areas.
In the real time oscilloscope plot of Figure 4.18 the log signal is also observed
to peak or overshoot in response to the input sinusoid. In designing this chip, the
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 77
10−3
10−2
10−1
0
0.01
0.02
0.03
0.04
0.05
0.06DC1 GHz2 GHz3 GHz4 GHz
10 10 10−3 −2 −1
0
10
20
30
40
50
60
Input Voltage (V)
|Out
put V
olta
ge| (
mV
)
Input Voltage (dBv)40 20− −−60
(a) Measured one tone response at different frequen-cies.
10−3
10−2
10−1
0
10
20
30
40
50
60
70
10−3 10−2 10−1
|Out
put V
olta
ge| (
mV
)
10
20
30
40
50
60
70
Input Voltage (V)
0
Input Voltage (dBv)60− 40− 20−
(b) Measured one tone response at 1 GHz of eight diesamples.
Figure 4.15: Measured logarithmic responses, peak voltages shown.
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 78
10−3
10−2
10−1
−5
−4
−3
−2
−1
0
1
2
3
4
5DC1 GHz2 GHz3 GHz4 GHz
− −−
10 10 10−3 −2 −1
1
−1
−5
−4
0
5
4
3
2
−3
−2
Log
Err
or (
dB)
Input Voltage (V)
Input Voltage (dBv)
60 40 20
(a) Separate fit error.
10−3
10−2
10−1
−8
−6
−4
−2
0
2
4
6
8DC1 GHz2 GHz3 GHz
10 10 10−3 −2 −1
−8
4
−4
2
−2
−6
6
8
0
− −−
Input Voltage (V)
Log
Err
or (
dB)
Input Voltage (dBv)60 40 20
(b) Broadband fit error.
Figure 4.16: Logarithmic error for separate and broadband line fits.
4.4 Implementation 1: A DC-4 GHz Si BJT Logarithmic Amplifier 79
−1 0 1 2 3 4 5 6−60
−50
−40
−30
−20
−10
0
f (GHz)
dB
Ideal Logarithm of InputMeasured
Figure 4.17: Measured and ideal logarithmic amplifier output spectrum for a 1.8 GHzinput tone.
−45 dBm
−32 dBm
−19 dBm
−5 dBm
Input Power
Figure 4.18: Real time oscilloscope plot of single ended output voltage.
delay through the two lower gain paths was set using delay amplifiers of the topology
shown in Figure 4.9. However, it was later determined that the delay of the buffer
amplifiers could be increased to better match the high gain path. The resistive loads
Rc interact with the parasitic capacitance of transistors Q3 and Q4 in the amplifier
in Figure 4.9 and form the dominant pole that limits the amplifier’s bandwidth.
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 80
The phase response of the delay amplifiers is approximately −45 degrees near the
pole frequency. The lower the dominant pole frequency, the more phase shift the
amplifier contributes at lower frequencies. The derivative of the phase with respect
to frequency defines the group delay, and so a lower 3 dB bandwidth corresponds to a
higher group delay. Hence, amplifiers with increased group delay may be constructed
by using differential amplifiers with sufficient capacitive loading to increase the delay
as needed. The error in the phase shift through each gain path may be as high
as approximately 20 at the log amplifier’s highest frequency of operation without
introducing significant distortion. Figs. 4.19 (a) and (b) show the simulated response
of the amplifier with and without capacitive loading respectively. It is seen that by
including enough capacitance in the load of the delay amplifiers, the response appears
more like a compressed sinusoid as desired. Care must be taken, however, not to
lower the bandwidth of the delay amplifiers below that of the highest gain path.
In the next section, an improved SiGe HBT implementation is described.
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic
Amplifier
4.5.1 Design of Implementation 2
For the second implementation of the logarithmic amplifier, IBM’s 5HP SiGe process
was used, similar to Chapter 3. Using this technology, a logarithmic amplifier was
fabricated which has 50% higher bandwidth, 5.5× higher logarithmic slope, 10 dB
higher logarithmic dynamic range, significantly lower noise figure, half of the chip
area, and consumes 43% less power than the amplifier in the last section.
Figure 4.20 shows a block diagram of the second logarithmic amplifier implemen-
tation. This architecture is the same as for the first implementation. The logarithmic
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 81
(a) Without capacitance.
(b) With capacitance.
Figure 4.19: Simulated log amplifier differential responses to sinusoidal inputs withand without capacitive delay tuning.
amplifier was again designed using DC coupled amplifier stages, as required by the
optical application. However, in order to improve the dynamic range, it is critical
that some form of DC offset cancellation be used. In the circuit in Figure 4.20, only
the DC offset errors in the highest gain path Gp4 are large enough to cause significant
performance degradation. For this reason, an amplifier and a low pass filter network
were used in negative feedback around path Gp4 in order to reduce the DC offset
error.
Figure 4.21 shows the schematic diagram of the input buffer, as well as the
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 82
gm1
gm
gm
gm Vout1Vout2
RLRL
gm
DC offset reductionamplifier
Vin1Vin2
bufferInput
Gp2
Gp1
Gp3
Gp4
Linear amplifier
Limiting transconductance element
Figure 4.20: Logarithmic amplifier block diagram.
first stage in the highest gain path Gp4. The input match uses resistors as well
as a capacitor to lower the input impedance at high frequencies. This capacitor
counteracts the effect of bond wire inductances and so the input remains impedance
matched to 50 Ω within 10 dB up to approximately 9 GHz. Large emitter lengths
were used in the emitter follower input buffers in order to achieve low base resistance
and low noise. As well, the bias currents of these buffers were optimized for low
noise. Following the input buffer in Figure 4.21 is the first stage of the highest gain
path Gp4. The noise figure of the logarithmic amplifier is completely dominated by
the input buffer and this stage. This stage is a CHEF amplifier, and it uses the
component values from the design example in Section 3.3.1. The emitter lengths of
the two input transistors to this stage were also chosen relatively large in order to
achieve low noise. All of the amplifier gain stages use CHEF amplifiers. Both of
the gain stages in path Gp4 are the same and were designed with a voltage gain of
approximately 10. Furthermore, it should be noted that by using the Cherry-Hooper
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 83
First Stage of Gp4
300fF300fF
45Ω
34Ω
550Ω
45Ω
34Ω
550Ω
55Ω
55Ω 55Ω
55Ω
160Ω 160Ω
3.0mA3.2mA
-3.3V
Vin1
Vin2
Vout_high1
Vout_high22.9mA
1.5mA2.9mA
1.5mA
To Gp1
Input Buffer
Figure 4.21: Schematic diagram of the input impedance match circuit and first highgain stage.
stage in Figure 4.21 for all gain stages, the delay through each gain path was designed
to be approximately the same, and no capacitive compensation was needed. Emitter
degeneration was used in the input emitter coupled pair of each Cherry-Hooper stage
in the lowest gain path to achieve low gain while maintaining high bandwidth. Both
stages in the lowest gain path Gp1 are exactly the same.
Figure 4.22 shows the amplifier that was used in negative feedback around path
Gp4 in order to reduce the DC offsets. In order to achieve a high pass corner frequency
of 500 kHz for the offset cancellation, a 1 nF off-chip capacitor was used.
The four limiting transconductance elements in Figure 4.20 were all integrated
into a single amplifier, shown in Figure 4.23. When an input signal from one of the
gain paths is applied to one of the degenerated emitter coupled pairs, it steers the bias
current of that pair to the side with the highest applied voltage. When the applied
voltage becomes large enough, the amount of current steered limits at IL=6.7 mA,
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 84
550Ω 550Ω
1.9mA
-3.3V
Vfin1
Vfout1 Vfout23.2 pF
6.4 pF
1 nFOff Chip
Vfin2
Figure 4.22: Schematic diagram of the DC offset error reduction circuit.
73Ω
-3.3V
Vin1_L
Vout2
9.0mA6.7mA
73Ω
6.7mA6.7mA
5Ω 5Ω
5Ω5Ω
5Ω
Vout1
Vin2_L
Vin3_L
Vin4_L
Vin1_R
Vin2_R
Vin3_R
Vin4_R
5Ω5Ω
5Ω
Figure 4.23: Schematic diagram of the output summation circuit.
or IL1=9.0 mA for the pair connected to the output of path Gp1. The load resistor
was chosen as 73 Ω so that when it is combined with the parasitic capacitance of
the transistors and the inductance of an output bond wire, the impedance remains
matched to 50 Ω within 10 dB to approximately 8 GHz. A negative power supply
of -3.3 V was used so that the amplifier inputs and outputs may be directly coupled
to a 50 Ω load. Emitter degeneration was used to reduce the gain of the summing
circuit, thereby reducing DC offset errors at the output.
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 85
Figure 4.24 shows the simulated DC transfer characteristic of the logarithmic
amplifier, including the effect of parasitic capacitive and resistive layout parasitics,
for one hundred Monte Carlo iterations. This simulation uses information about
typical process variations in the HP5 manufacturing process, and the variables and
probabilities are set by IBM. Although the logarithmic intercept varies somewhat,
the logarithmic linearity is acceptably reliable for the OSSB application. The fact
that the intercept point varies is attributed to the design of the summation amplifier.
The gain of this amplifier is expected to vary somewhat since Re=5 Ω, which is not
large enough to fix the gain in the presence of process variations. A larger Re was not
used because the amplifier gain would then be quite low, and the voltage headroom
would be reduced. The fact that the logarithmic linearity remains approximately
constant is attributed to the Widlar biasing scheme, described in Appendix E, used
in the CHEF amplifier stages. The stability of the logarithmic response could be
further improved using a more process independent current mirror reference than
the resistor to ground shown in the current mirrors in Figure 4.21.
Figure 4.25 shows the simulated logarithmic response of the amplifier at 4 GHz
for three different temperatures. The observed change in the logarithmic intercept
and slope over the 120 degree Celsius range has no negative impact in the OSSB
application. This is because a small change in intercept may be corrected by changing
the amount of level shifting applied to the input signal, and a change in slope can
be corrected by changing the attenuation of the input signal. The robustness of the
log amplifier signal despite temperature changes is expected from the Widlar biasing
scheme used in the CHEF amplifier stages, described in Appendix E.
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 86
Figure 4.24: Simulated DC transfer characteristic of logarithmic amplifier over onehundred Monte Carlo iterations.
10−3
10−2
10−1
100
0
0.2
0.4
0.6
Input Peak Voltage (V)
Out
put P
eak
Vol
tage
(V
)
−40 degrees Celsius+27 degrees Celsius+80 degrees Celsius
Figure 4.25: Simulated logarithmic response of SiGe logarithmic amplifier at 4 GHzfor three different temperatures.
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 87
DC OffsetFeedback
BranchLow
BranchHigh
Output Buffer
Input Buffer
High1 Low1High2 Low2
1.50 mm
1.33 mm
Figure 4.26: Microphotograph of the SiGe logarithmic amplifier integrated circuit.
4.5.2 Measurements of Implementation 2
A microphotograph of the integrated circuit, fabricated in IBM’s 5HP technology, is
shown in Figure 4.26. The circuit draws 130 mA from the -3.3 V supply. Measure-
ments were performed with the same equipment used to measure the Si logarithmic
amplifier. A connectorized test fixture was designed for the log amplifier, and is
described in Appendix F. The test fixture was used for the OSSB experiments in
Chapter 7. However, for simplicity, wafer probing was used for the measurements
given in this section. The S21 or gain of the amplifier is equal to 39 dB, compared
to a simulated S21 of 40 dB. The measured small signal bandwidth of the amplifier
is 6 GHz, compared to 8 GHz simulated. It is expected that the close proximity
of some circuits created unintentional feedback loops, and this may account for the
lower measured bandwidth. The measured noise figure at 1 GHz is 12.6 dB, which
is the same as the simulated noise figure.
Figure 4.27 shows the measured one-tone response of the amplifier for frequencies
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 88
−60 −50 −40 −30 −20 −10 00
0.1
0.2
0.3
0.4
Input Power (dBm)
Pea
k O
utpu
t Vol
tage
(V
)
100 MHz1 GHz2 GHz3 GHz4 GHz5 GHz6 GHz
Figure 4.27: Measured single ended logarithmic response from 100 MHz to 6 GHz.
up to 6 GHz. The high logarithmic slope of 6.5 mV/dB was achieved by using
relatively large currents in the output summing stage in Figure 4.23. The logarithmic
response error was calculated using the definition given in Section 4.4.2. The log error
at individual frequencies from 100 MHz to 6 GHz was less than 2.5 dB from an input
power level of -52 dBm to -2 dBm. The error for frequencies from 100 MHz to 4 GHz
when fit to a single line was less than 4.5 dB over the same input power range.
Figure 4.28 shows the output waveforms for one of the two log amplifier outputs
for frequencies of 100 MHz and 4 GHz. The rise and fall times of the amplifier are
50 ps. The logarithmic amplitude compression in the waveforms in Figure 4.28 is
evident. The observed noise at lower amplitude levels is partly due to amplifier noise
and partly due to timing noise inherent in the sampling oscilloscope measurement.
Table 4.1 compares the two log amplifier implementations described in this chap-
ter with three other high frequency true logarithmic amplifiers. The second imple-
mentation in this work has the highest bandwidth, and has excellent logarithmic
dynamic range and slope. It is disappointing that the SiGe logarithmic amplifier in
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 89
Input Power
Input Power
− 2.00 dBm− 15.0 dBm
− 40.0 dBm
− 2.00 dBm
− 15.5 dBm
− 42.0 dBm
(a) Logarithmic response at 100 MHz
(a) Logarithmic response at 4 GHz
- 29.0 dBm
- 27.5 dBm
Figure 4.28: Measured real time logarithmic amplifier single ended output wave-forms.
this chapter did not achieve 8 GHz bandwidth as the simulation predicted. The high
gain CHEF amplifiers are what limited the log amplifier bandwidth in simulation.
However, since these amplifiers had a bandwidth of 11.2 GHz when measured sep-
arately on the IC from the last chapter, it is definitely feasible to obtain an 8 GHz
logarithmic amplifier using the same basic design in the same technology used here.
After trying a more compact layout for the second log amplifier, the author suggests
going back to a less crowded layout, as was used in the first log amplifier implemen-
tation.
4.5 Implementation 2: A DC-6 GHz SiGe HBT Logarithmic Amplifier 90
Tab
le4.
1:C
ompar
ison
ofhig
hfr
equen
cytr
ue
log
amplifier
s.C
ircu
itTop
olog
yTec
hnol
ogy
Pow
erG
ain
Ban
d-
Ris
e/D
yna-
Log
Supply
wid
thFal
lm
icSlo
pe
Tim
eR
ange
Acc
iari
Tw
in-G
ain
GaA
sFE
T-
36dB
0.3-
-40
dB
10m
V/d
Betal.[4
5]
Sta
ge-
5G
Hz
Sm
ith
Tw
in-G
ain
GaA
sFE
T-8
V,+
8V70
dB
0.5-
-70
dB
6.3
mV
/dB
[46]
Sta
geH
ybri
d5.
2W
4G
Hz
Cir
cuit
Oki
Tw
in-G
ain
GaA
sH
BT
-8V
48dB
DC
-40
0ps/
40dB
3.3
mV
/dB
etal.[4
0]
Sta
ge1.
06W
3G
Hz
400
ps
Zo
=10
0Ω
Imple
men
t-B
ranch
Silic
on-5
V30
dB
DC
-10
0ps/
40dB
1.2
mV
/dB
atio
n1
Par
alle
lB
ipol
ar0.
75W
4G
Hz
100
ps
Zo
=50
ΩSum
mat
ion
fT
=35
GH
z
Imple
men
t-B
ranch
SiG
e-3
.3V
39dB
DC
-50
ps/
50dB
6.5
mV
/dB
atio
n2
Par
alle
lH
BT
0.43
W6
GH
z50
ps
Sum
mat
ion
fT
=47
GH
z
4.6 Conclusion 91
4.6 Conclusion
In this chapter, two high performance parallel summation logarithmic amplifiers
were presented. It was demonstrated how the branch parallel summation architecture
provides high bandwidth and logarithmic slope while consuming relatively low power.
In the next chapter, the other component required in the COSSB application, a
Hilbert transformer is described. The measured and simulated performance of these
two components is described in later chapters.
Chapter 5
A 10 Gb/s Hilbert Transformer with Q-Enhanced
LC Transmission Lines
5.1 Introduction
The previous chapter described the development of logarithmic amplifiers suitable
for use in the COSSB system. This chapter presents the development of the other
key component for COSSB, a fully integrated 10 Gb/s Hilbert transformer (HT).
The frequency response of an ideal HT is −j · sgn(ω), which indicates an abrupt
transition in the phase response at DC, as shown in Figure 5.1. The impulse response
is given by
h(t) =1
πt. (5.1)
This impulse response exists over an infinite range of t, but for practical purposes
the response is truncated at t =-NΥ to +NΥ, where N is an integer and Υ is a time
step. Since there are negative values of t, this response cannot be implemented using
delays. This can be avoided by shifting h(t) by a time NΥ so that all of h(t) is in
positive time. The time shifted impulse response may then be realized as a direct
form continuous time FIR filter. The tap weights are chosen to be equal to values of
the time shifted impulse response at integer values of Υ, as shown in Figure 5.2.
The structure of the filter is such that it has perfectly linear phase if two or
more taps are used, with the phase response approaching -90 toward DC and the
delay equal to half the length of the delay line. The RMS amplitude ripple decreases
5.1 Introduction 93
ω
ω
ω
ω
ω
ω
ω
+90
−90
|H( )|ω
H( )ω
1
Figure 5.1: Response of filter with an infinite number of taps.
π−1π π π3
......
Summer
Weight Weight Weight Weight
Time Delay Time Delay Time Delay
Σ
1 1
Input
Output
2 2 2Υ Υ Υ
3−1
Figure 5.2: Tapped delay implementation of an HT.Adapted from [47].
with an increasing number of filter taps. This approach of implementing a HT is
uniquely well suited to 10 Gb/s signals because it only requires delay, weighting,
and summation, all of which may be achieved in a broadband fashion. In Sieben’s
experiment on COSSB described in Section 2.4.6, discrete parts were used including
packaged amplifiers, splitters, attenuators, and delay lines to piece together the HT.
Since a four tap HT is not perfect, part of the unwanted sideband or a vestige
remained in the COSSB signal. However, the performance of the COSSB system
in Sieben’s experiment was not limited by this vestige, but by distortion caused by
the Mach-Zehnder modulator. His conclusion, supported by simulations described in
5.1 Introduction 94
the next chapter, is that having more than four taps yields little or no improvement
because the OSSB system performance is limited by the nonlinearity of the Mach-
Zehnder optical intensity modulator [7]. Furthermore, Sieben investigated the effect
of varying the time delay Υ in the filter. The tapped delay HT has a high pass
corner frequency which is ideally at DC, as indicated by the −j · sgn(ω) frequency
response of an ideal HT. This high pass corner frequency may be designed to be
as close to DC as possible by maximizing the delay through the filter, either by
increasing the number of taps at a fixed tap delay, or by increasing the delay Υ
for a fixed number of taps. Minimizing the high pass corner frequency ensures that
cancellation of the unwanted sideband will occur as close to the carrier wavelength
as possible. However, having excessive magnitude ripple in the passband of the HT
is detrimental to the signal. Figure 5.3 shows the magnitude responses of four tap
HTs for different values of the delay Υ. In each case in Figure 5.3, a value of Υ
that is a fraction of the period of a 10 Gb/s signal, or 100 ps, was used. A value of
Υ=55 ps leads to the lowest high pass corner frequency, but places magnitude ripple
in the 1-5 GHz high power region of a 10 Gb/s signal. For this reason, Sieben chose
to use a filter with Υ=37.5 ps instead. Figure 5.4 shows the spectrum of a simulated
10 Gb/s COSSB signal generated without the logarithmic conversion and using a
four tap HT with Υ=37.5 ps as per Sieben’s experiment. As expected, a vestige of
the unwanted sideband is observed. For the present design, the tap delay Υ was
chosen to be 30 ps, slightly less than in Sieben’s experiment. Having Υ=30 ps results
in a total delay of 180 ps in the four tap filter in Figure 5.2, and a 3 dB passband
of 1.7-12.6 GHz. The ideal four tap HT has a nominal group delay that is equal to
half of the total length of the delay line, 90 ps in this case. This is compared to the
theoretical −j · sgn(ω) frequency response, which indicates zero group delay at all
frequencies except DC.
5.2 HT Transfer Function 95
0 2 4 6 8 100
0.2
0.4
0.6
0.8
1
1.2
Frequency (GHz)
Nor
mal
ized
Lin
ear
Mag
nitu
de
Tap Delay=20 psTap Delay=37.5 psTap Delay=55 ps
Figure 5.3: Magnitude responses of four tap HTs for three different values of Υ.
−10 −8 −6 −4 −2 0 2 4 6 8 10−80
−70
−60
−50
−40
−30
−20
−10
0
Normalized Frequency (GHz)
Pow
er (
dB)
Figure 5.4: Spectrum of a COSSB signal generated with a four tap HT.
5.2 HT Transfer Function
Delay lines with gigahertz of bandwidth and 180 ps of delay may be fabricated using
on-chip LC transmission lines. It is useful for design purposes to model the effect
of delay distortion and loss in the LC lines on the transfer function of the HT.
Considering the performance of the filter structure in continuous time, the transfer
5.3 Design of LC Transmission Lines 96
function of the nth delay element is generalized to be
HDn(ω) = |HDn(ω)|e−jω∆HDn(ω). (5.2)
where ideally |HDn(ω)|=1 and ∆HDn(ω)=2Υ. The transfer function of the four tap
HT is then found to be
H(ω) = − 1
3π− 1
π|HD1|e−jω∆HD1
+1
π|HD1||HD2|e−jω(∆HD1+∆HD2) (5.3)
+1
3π|HD1||HD2||HD3|e−jω(∆HD1+∆HD2+∆HD3)
where the (ω) is not shown for HDn(ω) but is understood.
5.3 Design of LC Transmission Lines
One method of fabricating a 180 ps delay line on-chip is to use a metal transmission
line. Simulations performed in Agilent ADS indicate that such a 50 Ω line would
be 31.0 mm long if fabricated using an upper metal layer for the signal and a lower
metal layer 5 µm below as the ground plane, with SiO2 between with a dielectric
constant of 3.9. The length of this line may be reduced dramatically if on-chip LC
transmission lines are used. An LC line with 180 ps of delay may be constructed using
the circuit in Figure 5.5. The characteristic impedance of the line is related to the
inductor and capacitor values according to Zo =√
L/C. Furthermore, the structure
in Figure 5.5 has a cutoff frequency which decreases with increasing L and C. If a
capacitance of 250 fF is chosen, L=625 pH for Zo =50 Ω, and the cutoff frequency
will be greater than 10 GHz. The four tap HT requires three separate delay elements
with a delay of 60 ps each. During preliminary design, each section was designed
5.3 Design of LC Transmission Lines 97
...
VEE VEE VEE VEE
C
L/2
C C C
L L L/2
Figure 5.5: Schematic diagram of the LC transmission line used in the HT.
using the structure in Figure 5.5 with four 625 pH inductors, a 312 pH inductor
on each end, and five 250 fF capacitors. The layout of the inductors only is shown
in Figure 5.6(a). Version 2003A of the Agilent Momentum 2.5D electromagnetic
simulator was used to simulate the inductors. The results of the electromagnetic
simulation were then used to simulate the LC transmission line.
The simulated loss of the 180 ps transmission line was 2.1, 5.8, and 7.6 dB at 2.0,
7.0, and 10.0 GHz respectively, as shown in Figure 5.6(b). The high loss of the passive
line was found to significantly degrade the operation of the HT, and the simulated
performance of the OSSB system in which the HT is used. This loss is due to the
poor quality factor of the on-chip inductors. Fortunately, techniques are available
for canceling the loss of on-chip inductors using negative resistance circuits [48, 49].
In the next section, it is demonstrated how the coupled inductor technique of Q-
enhancement may be used to fabricate reduced loss, on-chip LC transmission lines.
5.3.1 Q-Enhanced LC Transmission Lines
Recently, Georgescu et al. presented a method for Q-enhancement, where a com-
pensating current is applied to a secondary inductor that is coupled to the primary
inductor, i.e. using a transformer, and the loss is canceled by the induced voltage in
the primary [48]. Figure 5.7 shows a realization of the circuit presented in [48]. The
5.3 Design of LC Transmission Lines 98
(a) Layout of passive LC transmission line.
(b) Loss of passive LC line.
Figure 5.6: Layout and loss of passive LC transmission line.
voltage vp across the primary of the transformer is expressed as
vp = iiRp + ipsLp + issM12 (5.4)
where M12 = k√
LpLs, and k is the coupling coefficient of typical value 0.5-0.75. In
order to cancel the inductor loss, ipRp = −issM12 resulting in ip = vp/sLp. The
required secondary current is [48]
is =−ipRp
sM12
=−vpRp
s2M12Lp
. (5.5)
5.3 Design of LC Transmission Lines 99
isL2 Rs
RpL1 sMis
IEE
VEE
VCC
VCC
vp
vpgm
2
ip
Figure 5.7: Transformer based Q-enhanced floating inductor.
Hence, optimum loss compensation occurs when the current through the secondary
is in phase with the voltage across the primary. A differential pair is used to generate
the required current in the circuit in Figure 5.7.
A transmission line with a delay of 180 ps in the 2-7 GHz range was designed
using the Q-enhanced inductors of the form in Figure 5.7, and is shown in Figure 5.8.
A bias current of 1 mA was used for each of the nine Q-enhanced inductors, and the
overall LC line consumes 30 mW. The loss of the transmission line simulated using
ADS Momentum 2003a is 1.9, 3.2, and 3.4 dB at 2.0, 7.0, and 10.0 GHz respectively.
This is approximately half the loss of the passive line at 5 GHz and higher, and the
loss of the Q-enhanced line has significantly reduced frequency dependence in the
4-10 GHz range. It is possible to further decrease the amount of loss using more
bias current in the Q-enhancement circuit, however, it may then be necessary to
stabilize the circuit above 10 GHz using capacitors across the secondaries of the
transformer, as described in [48]. This was not done here since the loss was already
acceptable with a modest amount of Q-enhancement, and the circuit is stable under
these conditions.
5.3 Design of LC Transmission Lines 100
70ps
VCC
V2L V2R
IEF
VCCVCC
50Ω70ps 70ps
Each 70ps Section
VCC
V3R V3L
VCCVCC
V4R
IEF
V4L
VCC
VCC
V1L
IEF
V1R
IEF
VCC
IEF
IEFIEF
IEF
VEE
Vin
VEE
C C C C
L/2 L/2L L L
C=190fFL=470pH
Three
InductorsQ-Enhanced
Figure 5.8: Delay line with emitter follower tap buffers.
After the circuits designed in this chapter were already submitted for fabrication,
the author discovered a relatively simple method of laying out the Q-enhancement
circuit symmetrically [50]. Figure 5.9(a) shows the layout of a symmetrical trans-
former with a center tapped secondary, and Figure 5.9(b) shows the schematic di-
agram of how it is connected. Using this structure doubles the efficiency of the
Q-enhancement by using the fully differential signal current. Furthermore, with the
transformer layed out in this way, all four transformer terminals are close together,
making the metal interconnect to the differential pair short.
Also after the circuits designed in this chapter were already submitted for fab-
rication, the author discovered a much simpler way to modestly Q-enhance an LC
transmission line. Figure 5.10 shows a circuit in which the inductor Q is enhanced
using a simple cross coupled pair, used for example in [49]. The advantage of this
circuit over the transformer based application is that the starting Q of the inductor
is higher than the starting Q of a transformer primary. This circuit is recommended
for use in future implementations of the HT. The transformer based circuit is recom-
5.4 Circuit Implementation 101
PrimaryInputs
SecondaryCenter Tap
SecondaryInputs
(a) Symmetrical transformer with centertapped secondary.
LS1 RS1
RPLP
IEE
VEE
vp
vpgm
2
LS2 RS2
VCC
(b) Schematic diagram.
Figure 5.9: Efficient Q-enhancement circuit using both signal currents.
mended for filters where Q is enhanced into the hundreds, however. Soorapanth and
Wong demonstrated how the use of the circuit in Figure 5.10 in a bandpass filter de-
sign leads to a highly distorted passband [51]. The transformer based Q-enhancement
circuit may be used to fabricate bandpass filters with relatively flat pass-bands, as
research in progress on filters by the author’s colleagues demonstrates.
5.4 Circuit Implementation
As shown in Figure 5.8, signals are taken from the LC delay lines at four locations.
These signals are connected to a summing amplifier through emitter followers, which
provide a DC level shift. The summing amplifier, shown in Figure 5.11, consists
5.4 Circuit Implementation 102
RPLP
IEE
VEE
vp
vpgm
2
Figure 5.10: A floating inductor which is Q-enhanced using a simple cross coupledpair .
of four differential pairs in parallel with their collectors tied together so that their
currents add. Each pair of emitter followers in Figure 5.8 drives one of the differ-
ential pairs in the summing amplifier. The 50 Ω load allows the amplifier output
to be impedance matched and DC coupled to a 50 Ω system. A more complicated
impedance match, such as that used in the logarithmic amplifier, was not used be-
cause the parasitic capacitance at the output node was designed to be smaller by
using smaller currents and HBT devices. Emitter degeneration resistors are used in
each of the four differential pairs in the summing amplifier in order to realize the
tap weights. The two negative tap weights indicated in Figure 5.2 were achieved by
reversing the input connections to the summing amplifiers for these weights. Fur-
thermore, an adjustment was made to the fourth tap weight through simulation to
compensate for the loss in the LC line. Each of the four differential pairs in the
summing amplifier is biased with a current of 5 mA, and so the summing amplifier
consumes 70 mW. This relatively high current is needed to drive the 50 Ω load. The
basic design of the summing amplifier is such that loss is incurred through the HT.
However, a compromise between this loss and the linearity of the HT was chosen to
achieve acceptable performance in the OSSB application. The loss may be reduced
5.4 Circuit Implementation 103
50Ω
Vin1_left
Vout2
2.5mA2.5mA
Vout1
Vin2_left
Vin3_left
Vin4_left
Vin1_right
Vin2_right
Vin3_right
Vin4_right
2.5mA2.5mA
VCC
VCC
VSICS
50Ω
2.5mA2.5mA
2.5mA2.5mA
300Ω
50Ω
50Ω
215Ω
VEE
Figure 5.11: HT summing amplifier.
by 6 dB where possible by using the differential output signal. A microphotograph
of the HT integrated circuit is shown in Figure 5.12. It was fabricated in IBM’s 5AM
technology, which has 47 GHz fT HBTs and 0.5 µm feature sizes. The circuit mea-
sures 1.70 x 1.25 mm and consumes 43 mA from the -3.3 V supply for a total power
consumption of 142 mW. With the Q-enhancement circuits turned off, the circuit
draws 34 mA and consumes 112 mW. The delay line was arranged so that there is
equal length from each tap point to the inputs of the summing amplifier, which is
in the center of the chip. Furthermore, a 50 pF on-chip power supply decoupling
capacitor was chosen so that it would resonate below 500 MHz with the inductance
of the power supply bond wires.
A CMOS supply voltage independent current source (SICS), shown in Figure 5.13,
was used to generate the reference voltages for the Q-enhancement circuits around
5.4 Circuit Implementation 104
VCC
VCC
VCC
VCC
VCC VCC VCC VCC VCC VCC VCC
VCC
EEV
EEV
EEV
EEV
REFR EEV
OUT INROUT L TEST
VEnhance
1.25 mm
1.70 mm
Figure 5.12: Integrated HT microphotograph.
SICSStart−Up Circuit
VEE
VEE
VEE
V = -3.3 VEE
V =0 Vcc
M1 M2
M3 M4
1 mA1 mA
M7
Ibias
255 Ω
VEE V
50 k Ω
40 k Ω
M5 M6
0.4 mA
W=800 m/µL=2 mµ
each
W=60 m/µL=2 mµ
W=180 m/µL=2 mµ
W=200 m/µL=0.5 mµ
W=500 m/µL=0.5 mµ
M8 Mn
...
V
5 pF
5 pF
EEEE
Off Chip
Figure 5.13: Supply independent current source.
5.4 Circuit Implementation 105
the chip [52]. This circuit allows the metal interconnect to the gates of M7 to
Mn to be relatively long without voltage drop. Unfortunately, this circuit would
not start up properly when the chip was returned from the foundry and turned on,
even though the simulation did not indicate any problems. The author had used
fully CMOS implementations of this bias circuit before with complete success in a
previous amplifier design [26]. In order to get the bias circuit to start up without
oscillating, M5 was disconnected using laser cutting from M4, M1 was disconnected
from M2 and M3 using laser cutting, and the 255 Ω resistor to Vee was replaced by
a 47 Ω resistor connected to a voltage a few hundred millivolts below VEE, and this
voltage was tuned to set the HT current to the simulated level. The author is not
certain what caused the start-up problem. It may have to do with the much higher
output resistance of the HBTs compared to the NMOS devices.
Similar to the last chapters, wafer probing of RF signals was used and the VEE,
VCC , Venhance, and RREF connection were wire bonded. An Agilent PSA network
analyzer was used to measure the HT’s small signal parameters.
Figure 5.14 shows S11 and S22 for three measured HT dice. S11 is measured
looking into one end of the LC transmission line with the other end terminated in
50 Ω on-chip, and is lower than -10 dB up to 9 GHz. This indicates that Zo of the
transmission line is close to 50 Ω. S22 is lower than -10 dB up to 8 GHz.
Figures 5.15(a) and 5.15(b) show the simulated S21 and group delay of the
HT including layout resistive and capacitive parasitics for the cases where the Q-
enhancement is turned on and off. When the Q-enhancement is turned off, the gain
above three gigahertz decreases by 1-2 dB. The Q-enhancement has little effect on
the group delay.
Figures 5.16(a) and 5.16(b) show the measured S21 and group delay of the HT
for three different die for the cases where the Q-enhancement is turned on and off.
5.4 Circuit Implementation 106
0 2 4 6 8 10 12 14 16 18 20−30
−25
−20
−15
−10
−5
0
Frequency (GHz)
Mag
nitu
de (
dB)
Chip C S11Chip D S11Chip F S11Chip C S22Chip D S22Chip F S22
Figure 5.14: Measured S11 and S22 of three dice with Q-enhancement on.
Although six die were prepared for test, three die were severely damaged before they
could be measured. The dip in S21 was simulated to be at 5 GHz in Figure 5.15,
and was measured at 7 GHz. This difference is attributed to the failure to simulate
the inductance of on-chip interconnect of the power supply, since no straightforward
means to simulate this inductance was available using the version of the Diva ex-
tractor used. Fortunately, the power supply interconnect was kept short, and the
measured S21 and group delay is relatively close to the simulated response from Fig-
ure 5.15. Figure 5.16(a) shows that the measured gain exhibits amplitude ripple,
similar to the ideal gain, but shows a lower high pass corner frequency. This is
attributed to the fact that although the tap delay of the ideal four tap HT is con-
stant with frequency at T=30 ps, the measured group delay and hence tap delay are
actually frequency dependent. For a better theoretical estimate, the measured gain
could be compared against equation (5.3).
Figure 5.16(b) indicates that the measured average group delay of the HT is
5.4 Circuit Implementation 107
0 2 4 6 8 10 12 14 16 18 20−20
−18
−16
−14
−12
−10
−8
−6
−4
Frequency (GHz)
S21
(dB
)Simulated HT with Parasitics − Q−enhancement onSimulated HT with Parasitics − Q−enhancement off
(a) S21.
1 2 3 4 5 6 7 8 9 1050
100
150
200
250
300
Frequency (GHz)
Gro
up D
elay
(ps
)
Simulated HT with Parasitics − Q−enhancement onSimulated HT with Parasitics − Q−enhancement off
(b) Group delay.
Figure 5.15: Plot of (a) S21 and (b) group delay simulated with resistive and capac-itive layout parasitics.
approximately 120 ps between 2.0 and 7.0 GHz, and the group delay distortion is
±30 ps from 2.0 to 8.0 GHz. Approximately 90 ps of the group delay comes from
the delay line, and 30 ps comes from the summing amplifier. Fig. 5.17 shows the
deembedded measured and theoretical phase response, where ±10 of phase error is
observed from 2.0 to 7.0 GHz.
The simulated and measured noise figure (NF) of HT die C with Q-enhancement
turned on are given in Table 5.1. This table shows that the simulator underestimates
the noise of the HT by 5-7 dB at some frequencies, although the simulation correctly
predicts the noise at 4.0 GHz. The NF was measured using a Rhode and Schwarz
FSEK 30 spectrum analyzer with a NoiseCom NC346C noise source. The measured
NF with the Q-enhancement turned off was the exactly the same as that shown in
Table 5.1, except from 6-8 GHz where it was 2 dB higher with Q-enhancement turned
off because of the increased loss. The noise at the output of the HT consists of noise
from the emitter followers, the summing amplifier, and the ohmic losses in the LC
5.4 Circuit Implementation 108
0 2 4 6 8 10 12 14 16 18 20−20
−18
−16
−14
−12
−10
−8
−6
−4
Frequency (GHz)
S21
(dB
)Chip CChip DChip FIdeal 4 Tap HT
Q−Enhancement Off
Q−Enhancement On
(a) S21.
1 2 3 4 5 6 7 8 9 1080
100
120
140
160
180
200
220
240
Frequency (GHz)
Gro
up D
elay
(ps
)
Chip CChip DChip F
Q−Enhancement On or Off
(b) Group delay.
Figure 5.16: Plot of (a) measured S21 and normalized theoretical S21 and (b) groupdelay for three die with Q-enhancement on and off.
1 2 3 4 5 6 7 8 9−105
−100
−95
−90
−85
−80
−75
Frequency (GHz)
Pha
se (
Deg
rees
)
Chip 1Chip 2Chip 3
Ideal Four TapHT Phase
Figure 5.17: Measured phase of three die with a phase shift corresponding to 120 psof delay subtracted, and theoretical four tap HT phase response with a phase shiftcorresponding to 90 ps of delay subtracted.
line. The base resistance thermal noise from the emitter followers in Figure 5.8 and
of the differential pair transistors in the summing amplifier was kept low in the design
by using larger than minimum length emitters in these HBTs. The noise of the Q-
enhancement circuits constituted less than 5% of the total HT noise in simulation.
Turning the Q-enhancement on or off during the measurement had a negligible effect
5.4 Circuit Implementation 109
Table 5.1: Noise figure of HT die C with Q-enhancement turned on.
Frequency (GHz) Simulated (dB) Measured (dB)
2.0 26.5 30.0
2.5 24.5 29.0
3.0 24.5 27.0
4.0 26.0 26.0
8.0 22.0 28.5
on the output noise power of the HT, which agrees with the simulation.
As a further verification of the HT’s performance, Figure 5.18(a) shows the re-
sponse of the HT to the repeated binary pattern 01001000. The signal was gen-
erated using the Anritsu MP1763B pattern generator and measured using a HP
54750A oscilloscope with a HP 54751A 20 GHz sampling module. For this trace,
the Q-enhancement is turned on. Figure 5.18(b) shows the same trace with the Q-
enhancement turned off. There is little difference in the shape of the signal, and the
noise appears to be less with the Q-enhancement turned off, a surprising result which
appears to contradict the measurements of NF alone. Since the Q-enhancement cir-
cuits are a type of feedback loop, it is possible that some ringing occurs in the
response of these circuits, which would account for the noise at the HT output. The
simulated response of the transmission line in the HT to a sequence of pulses each
with 25 ps rise/fall times and pulse widths of 75 ps is shown in Figure 5.19 for the
cases where Q-enhancement is turned on and off. This simulation indicates that the
Q-enhancement results in some increased ringing. It is important to note that even
if the LC transmission line were designed with ideal inductors and capacitors, it will
still ring in response to a pulse. This is because an LC line with a finite number of
sections is only an approximation to a transmission line. It may be shown that for
an LC transmission line with a fixed delay, the amount of ringing in response to a
5.4 Circuit Implementation 110
pulse decreases as the line is broken into smaller and smaller sections.
The fact that the circuit performs so well even when the Q-enhancement is turned
off is partially attributed to the way in which the fourth tap weight was raised in order
to compensate for loss in the line. Figure 5.18(c) shows the response of an ideal four
tap HT to the same 01001000 pattern. The measured responses are relatively close
to the ideal waveform. The author observed little or no difference in the shape of the
waveform when the Q-enhancement was turned on and off for several other patterns,
and leaving the Q-enhancement turned off made the waveform appear less noisy.
Figures 5.20, 5.21, 5.22 show the measured response of the HT with Q-enhancement
turned off for the binary patterns 10, 1000, and 0111 respectively, along with the
outputs of an ideal four tap HT to these patterns. The response of the HT to these
patterns is similar to the ideal four tap output in each case.
The fact that the HT appears to work without the Q-enhancement is surpris-
ing, but the development of the Q-enhanced transmission line is still useful. The
technology used had a relatively thick top layer of metal for the on-chip spirals. It
is expected that for other technologies where the metal is thinner, Q-enhancement
would be more important. As well, although the weights in the filter may be adjusted
to compensate for loss, this does not compensate for the frequency-dependent loss
of the line. Furthermore, the weights in the summing amplifier can not be adjusted
to account for more than a few decibels of loss without sacrificing bandwidth and
linearity.
The 1 dB compression point of HT die C was obtained by performing power
sweeps using an Agilent 83650L signal generator and Agilent E4417A power meter
with a E9327A power sensor to measure the HT output power. With Q-enhancement
turned off, the measured input referred 1 dB compression point is +5 dBm at 2.0
GHz and +4 dBm at 5.0 GHz. With Q-enhancement turned on, the compression
5.4 Circuit Implementation 111
(a) Upper trace is response of HT IC to re-peated DATA pattern 01001000. Lower traceshows DATA output from the pattern gener-ator. Q-enhancement is turned on.
(b) Same as (a), with Q-enhancement turnedoff.
0 200 400 600 800 1000 1200 1400 1600 1800−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Am
plitu
de (
Line
ar U
nits
)
Time (ps)
(c) Response of ideal four tap HT with Υ =0.30 from Matlab.
Figure 5.18: Responses of four tap HTs to the repeated binary pattern 01001000.
5.5 Conclusion 112
Q−Enhancement Turned Off
Q−Enhancement Turned On
Figure 5.19: Output of transmission line to a sequence of pulses.
point was slightly higher, +7 dBm at 2.0 GHz, and +6.0 dBm at 5.0 GHz. The
measured results for HT die F were very similar. The author is unsure why the
compression point was higher with Q-enhancement turned on. The circuit has the
advantage that only a fraction of the applied voltage to the HT appears across each
inductor. The linearity of the Q-enhancement circuits may be further increased if
needed using the multi-tanh technique [53].
5.5 Conclusion
In this chapter, it was described how the idea of a tapped delay HT, developed by
previous authors, was fabricated as an integrated circuit with enough bandwidth
for 10 Gb/s operation. Methods of Q-enhancing LC transmission lines were also
described. Measurements show that the HT implementation works correctly, and
should be capable of generating single sideband signals. In the next chapter, the
5.5 Conclusion 113
(a) Upper trace is response of HT IC to repeated DATA pat-tern one-zero (10) with Q-enhancement off. Lower trace showsDATA output from the pattern generator.
0 50 100 150 200 250 300 350 400−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Am
plitu
de (
Line
ar U
nits
)
Time (ps)
(b) Response of ideal four tap HT with Υ =0.30 from Matlab.
Figure 5.20: Responses of four tap HTs to the repeated binary pattern 10.
simulated performance of the HT and the log amplifier in the COSSB system are
examined in simulation.
5.5 Conclusion 114
(a) Upper trace is response of HT IC to repeated DATA pat-
tern 1000 with Q-enhancement off. Lower trace shows DATA
output from the pattern generator.
0 100 200 300 400 500 600 700 800 900−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Am
plitu
de (
Line
ar U
nits
)
Time (ps)
(b) Response of ideal four tap HT with Υ =0.30 from Matlab.
Figure 5.21: Responses of four tap HTs to the repeated binary pattern 1000.
5.5 Conclusion 115
(a) Upper trace is response of HT IC to repeated DATA pat-
tern 0111 with Q-enhancement off. Lower trace shows DATA
output from the pattern generator.
0 100 200 300 400 500 600 700 800 900−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Am
plitu
de (
Line
ar U
nits
)
Time (ps)
(b) Response of ideal four tap HT with Υ =0.30 from Matlab.
Figure 5.22: Responses of four tap HTs to the repeated binary pattern 0111.
Chapter 6
Simulations of COSSB System Implementations
6.1 Introduction
In previous chapters, measurements of the logarithmic amplifier and HT were de-
scribed and were shown to agree reasonably well with their simulated performance.
This chapter is devoted to simulation of the COSSB transmitter. Sections 6.2 and 6.3
describe the individual performance of the logarithmic amplifier and the HT in the
COSSB system respectively. Section 6.4 then describes the performance obtainable
using both circuits together. The results indicate what to expect when a COSSB
transmitter is pieced together in the laboratory.
6.2 Performance of the Logarithmic Amplifier
When a digital signal with two perfect signal levels is used, it is not necessary to use a
logarithmic amplifier in the COSSB system. This is because the logarithm of a signal
with two discrete levels will also be a signal with two discrete levels, and so scaling
and level shifting may be used in place of a logarithm. To gage the performance of
the logarithmic amplifier, a better signal would be analog with at least two decades,
or 40 dB of dynamic range. One such signal is a 5 Gb/s 211 − 1 length PRBS signal
filtered with a fifth order Butterworth filter with a cutoff frequency of 2.75 GHz.
To transmit this signal over the COSSB system, the electrical data is first used
to amplitude modulate the optical signal, and then this signal is phase modulated,
as shown in Figure 6.1. In order to design the phase modulation to generate the
6.2 Performance of the Logarithmic Amplifier 117
AmplitudeModulator
PhaseModulator
To Fiber
exp(j t)ω
+Ms(t)
VDC
HilbertTransformer
Laser
LogarithmicAmplifier
Figure 6.1: Minimum phase COSSB transmitter.
optimal COSSB signal, it is necessary to know any imperfections that occurred while
performing the amplitude modulation. For the present simulations, it is assumed
that a Mach-Zehnder amplitude modulator modulates a 1550 nm optical signal at
a modulation depth of 0.25 of the modulator Vπ. That is, the signal applied to
one electrode of the Mach-Zehnder modulator swings above the bias point on that
electrode by 0.25·Vπ, and below the bias point on that electrode by 0.25·Vπ, and the
complementary signal applied to the other electrode swings by the same amount. The
amplitude of the signal on the fiber will have some distortion because of the non-
ideal amplitude modulation characteristic of the Mach-Zehnder modulator, which
was shown in Figure 2.12. This knowledge may be used to ensure that the phase
modulation is optimal as follows. The input signal to the logarithmic amplifier will
be scaled or linearly predistorted by a factor M and have an offset VDC added so that
the log amplifier output looks like the logarithm of the envelope of the amplitude
modulated signal on the fiber.
For the present simulations, the predistorted information signal was saved in
Matlab and loaded into the Cadence Spectre circuit simulator, where it was passed
6.2 Performance of the Logarithmic Amplifier 118
through the SiGe HBT logarithmic amplifier using transient simulation for a dura-
tion of 200 ns, and the effect of parasitic layout capacitances and resistances were
included. Once the logarithmic amplifier output signal was obtained, it was loaded
back into Matlab. Since transient simulation of the logarithmic amplifier does not
include the amplifier noise, a random noise signal with the same bandwidth as the
logarithmic amplifier, 6 GHz, and the same RMS noise amplitude as the amplifier
output noise, 10.6 mV, was added to the output of the logarithmic amplifier. The
Spectre simulator provides the RMS noise voltage at one terminal of the log amplifier
output. If the noise is assumed to have a Gaussian probability density function, the
standard deviation of the noise will be the same as its RMS value. This is useful
when constructing the noise signal in Matlab. Furthermore, it is important to get
the correct RMS noise value for the log amplifier when the appropriate DC level of
the signal is applied. Without the DC offset the gain of the log amplifier is higher
and the output noise is also higher, 16.0 mV RMS.
After the noise was added, the resulting signal was passed through one of four
HTs. The four HTs are an ideal Hilbert transform computed by Matlab, as well as
ideal four, six, and eight tap HTs implemented in Cadence. For the three tapped
delay HTs, various values of the time delay parameter Υ were investigated, and
the values of Υ=0.45, 0.27, and 0.19 were found to give acceptable high pass cor-
ner frequencies and sufficient bandwidth at 5 Gb/s for the four, six, and eight tap
transformers respectively. The value of Υ=0.45 for the 5 Gb/s four tap HT is in
contrast to the value of 0.35 chosen in the previous chapter for the 10 Gb/s case.
The Cadence HTs used ideal delay elements and an ideal adder. The outputs of the
Cadence HTs were streamed out of Cadence, loaded into Matlab, and used to phase
modulate the simulated optical signal. Figure 6.2 shows the spectra of the signals
at the COSSB transmitter output. The spectra have been normalized in frequency
6.2 Performance of the Logarithmic Amplifier 119
to the carrier frequency. As well, the DC content of the signals has the greatest
amplitude and is normalized to 0 dB, and the information is then contained in the
range of approximately -70 dB to -20 dB.
The best suppression of the unwanted sideband is obtained with the ideal Matlab
HT, and the performance improves slightly with an increasing number of taps for
the tapped delay HTs. However, the length of the required delay line within the
HT increases significantly using six or eight taps compared to only four, illustrating
why a four tap HT remains the most appropriate for integration. Figure 6.2(e)
shows the eye diagram for the ideal HT case, and the eye diagrams for the other
configurations are identical, since only the phase of the signal is being used to achieve
single sideband, and the phase is thrown away during direct detection. The inter-
symbol interference (ISI) in Figure 6.2(e) is a result of band-limiting the signal to
2.75 GHz at the start of the simulation in order to obtain an analog signal to test the
logarithmic amplifier. Since the phase of the optical signal is thrown away during
direct detection, the ISI has nothing to do with the phase modulation at zero fiber
length.
Figure 6.2(b) indicates that 15-20 dB of sideband suppression is possible using a
four tap HT. In Sieben’s experiments, he obtained 15-20 dB of measured sideband
cancellation for the case of relatively square, digital pulses [7]. For the simulation to
predict a comparable amount of sideband cancellation for analog signals is encour-
aging for this experiment, which relies on the logarithmic amplifier IC. However, so
far this simulation assumes an ideal four tap HT. The COSSB performance of the
four tap HT IC described in the last chapter will be considered in the next section.
In Section 6.4, the combined COSSB performance of the logarithmic amplifier IC
with the HT IC will be considered.
6.2 Performance of the Logarithmic Amplifier 120
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(a) With ideal Hilbert transform.
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(b) With ideal four tap Hilbert transform.
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(c) With ideal six tap Hilbert transform.
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(d) With ideal eight tap Hilbert trans-form.
(e) Eye diagram with ideal HT after zerofiber length.
Figure 6.2: 5 Gb/s COSSB signals obtained through transient simulation of variousHTs and of the logarithmic amplifier IC.
6.3 Performance of the HT 121
6.3 Performance of the HT
In order to simulate the performance of the HT without the logarithmic amplifier, a
211−1 length 10 Gb/s unfiltered PRBS signal was used. A data rate of 10 Gb/s may
be used, because the HT has more bandwidth than the logarithmic amplifier. Similar
to the last section, a 1550 nm optical signal was amplitude modulated using a Mach-
Zehnder in simulation, this time at a modulation depth of 0.20. The COSSB signal
is generated as in Figure 6.1, however, the logarithmic amplifier was not used and
it was replaced by a short circuit. The scaling and offset applied to the information
were optimized so that the input to the HT looked as similar as possible to the
logarithm of the signal envelope on the fiber, as required by COSSB theory. Since
the 10 Gb/s data was not filtered and consists of relatively square bits, scaling and
level shifting will generate a signal that looks relatively close to the logarithm of the
signal envelope on the fiber.
Using the scaled and level shifted data signal as an input, transient simulation
of the HT over a 200 ns duration was performed in Cadence including the effect of
layout capacitances and resistances. Once the output of the HT was obtained and
loaded into Matlab, a noise signal with approximately the same noise bandwidth,
10 GHz, and RMS value, 590 µv, as the noise of the HT was added to the HT
output. The resulting electrical signal was filtered at 13 GHz before it was used to
phase modulate the optical signal at the transmitter. Filtering the HT output helped
remove unwanted energy and was found to improve the transmission characteristics.
Figure 6.3(a) shows the spectrum of the transmitted COSSB signal and Fig-
ure 6.3(b) shows the corresponding eye diagram. Figure 6.3(a) indicates that be-
tween 15 and 20 dB of sideband cancellation is possible. This is approximately the
same as what Sieben observed for a 10 Gb/s signal, except in this experiment the
6.3 Performance of the HT 122
−20 −15 −10 −5 0 5 10 15 20−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
Normalized Frequency (GHz)
Mag
nitu
de (
dB)
(a) Spectrum. (b) Eye diagram.
Figure 6.3: Transmitted 10 Gb/s COSSB spectrum and eye diagram with transientsimulation of HT IC without logarithmic amplifier.
HT has been successfully integrated.
The signal in Figure 6.3(a) requires only the HT IC, an amplitude modulator,
and a phase modulator. Since these parts are all available, this signal should be
obtainable experimentally. It is instructive to consider the transmission properties
of this signal over long lengths of fiber. Figure 6.4 shows the eye diagrams of the
detected signal from Figure 6.3(a) after transmission over various distances for the
case where only self-homodyning post detection equalization is used. Recall from
Section 2.3.2 that this type of equalization is typically performed by passing the
detected signal through a microstrip line, the delay of which increases with increasing
frequency. To simulate dispersion, the fiber transfer function from equation (2.30)
was used with a dispersion parameter of D = 18 ps/(nm · km). Figure 6.4 indicates
that the eye stays open after 200 km, even though no optical dispersion compensation
is being used. Figure 6.5 shows similar eye diagrams for the case where the minimum
phase dispersion compensation technique from Section 2.4.5 is used. For this case,
6.3 Performance of the HT 123
(a) After 100 km. (b) After 200 km.
(c) After 300 km. (d) After 500 km.
Figure 6.4: Eye diagrams of COSSB system using only the HT and using onlyself-homodyning post detection equalization.
the eye remains open after transmission over 700 km of dispersive fiber without
optical dispersion compensation. This indicates that construction of the minimum
phase dispersion equalizer from Figure 2.10, while beyond the scope of this thesis,
would be very useful. The logarithmic amplifier and HT developed in this thesis is
a necessary component of that equalizer.
Granted, the above simulations are not totally realistic because some important
6.3 Performance of the HT 124
(a) After 100 km. (b) After 200 km.
(c) After 300 km. (d) After 500 km.
(e) After 700 km. (f) After 900 km.
Figure 6.5: Eye diagrams of COSSB system using only the HT and using onlyminimum phase post detection equalization.
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 125
effects have been ignored. If a signal were transmitted over hundreds of kilometers of
fiber, some optical amplifiers would be required. These would contribute noise and
distortion. If these effects were taken into account, the transmission distance ob-
tained while maintaining comparable eye diagrams would decrease somewhat. Still,
the eye diagrams in Figure 6.9 give an idea of the performance degradation versus
distance due only to dispersion.
Furthermore, the above simulations indicate the transmission distances that are
possible when only post detection equalization is used. However, in this author’s
opinion, a more intriguing possibility is when the dispersion is partially compensated
using optical dispersion compensation and OSSB. As an example, consider the case
where, based on a rough estimate of the amount of dispersion in a fiber-optic link,
the system engineer inserted optical dispersion compensation to cancel out half of the
estimated dispersion. Normally, such imprecise compensation would give inadequate
performance. However, if this technique were used with OSSB and microstrip self-
homodyning post detection compensation, the system eye diagrams would be exactly
the same as those shown in Figure 6.4, however all of the distances will have doubled
since the optical dispersion has been halved. This approach combines the benefits
of both dispersion management techniques.
6.4 Combined Performance of Logarithmic Amplifier and
HT Circuits
6.4.1 Performance at a Mach-Zehnder Modulation Depth of 0.25
In this section, the performance of the logarithmic amplifier IC and the HT IC to-
gether in the COSSB system will be evaluated. To start with, a 1550 nm optical
signal was again amplitude modulated using a Mach-Zehnder modulator at a mod-
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 126
ulation depth of 0.25. The electrical data consists of a 211 − 1 PRBS signal filtered
at 2.75 GHz. This signal is simply an example, and it will serve to illustrate the
usefulness of the log amplifier. Signals for which the logarithmic amplifier are im-
portant include predistorted or QAM signals for broadband radio-on-fiber systems,
and multilevel baseband signals. Furthermore, the logarithmic amplifier is especially
important for binary signals that are band-limited or when they are transmitted at
modulation depths of 0.25 or higher, as will be shown.
Figure 6.6(a) shows the normalized envelope of the amplitude modulated optical
signal. The relatively high modulation depth of 0.25 results in the signal having high
extinction, meaning that the amplitude approaches zero. Figure 6.6(b) shows the
logarithm of this signal, which is the ideal output of the logarithmic amplifier. Since
the signal in Figure 6.6(a) contains information over the 40 dB of dynamic range
between 0.01 and 1.0, the logarithm of this envelope looks much different than the
envelope itself, and the use of the logarithmic amplifier is important in achieving
effective single sideband transmission.
The output of the logarithmic amplifier is exactly the same as that used in Sec-
tion 6.2, where an ideal HT was assumed. However, this time the output of the
logarithmic amplifier with the log amplifier noise added was then scaled and input
to the HT IC in simulation. The output of the HT IC then had the HT IC noise
added to it. For all 5 Gb/s simulations in this chapter, the signal at the output of
the HT IC was filtered at 6 GHz. This helped remove unwanted energy from the
phase modulation signal and was found to improve the transmission characteristics
of the signal. The resulting signal was used to phase modulate the optical signal.
For comparison purposes, a COSSB signal was also generated using only the HT IC,
and not the log amplifier IC. Figure 6.7 shows the spectra and eye diagram at the
COSSB transmitter output for the two cases. It is observed that the inclusion of the
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 127
30 31 32 33 34 35 36 37 38 39 400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (ps)
Line
ar A
mpl
itude
(a) Optical signal envelope.
30 31 32 33 34 35 36 37 38 39 40−6
−5
−4
−3
−2
−1
0
Time (ps)
Line
ar A
mpl
itude
(b) Logarithm of optical signal envelope.
Figure 6.6: Scaled optical signal envelope and its logarithm for a modulation depthof 0.25.
logarithmic amplifier improves the sideband cancellation by approximately 5 dB.
Using the dispersive fiber transfer function from equation (2.30) with a dispersion
parameter of D = 18 ps/(nm · km), the effect of dispersion on various signals was
examined. Figure 6.8 shows the eye diagram of the comparable DSB signal after
propagation over 400 km of uncompensated dispersive fiber. This signal is badly
distorted because the dispersion-induced phase distortion of the signal results in
frequency selective power fading during detection. Figure 6.9 shows the eye diagram
after 400 km for the case where the only the HT IC was used, and the log amplifier IC
was not included. For this simulation, self-homodyning post detection equalization
was simulated for the received optical signal. A distance of 400 km was chosen,
because this is the approximate distance that a 5 Gb/s signal must propagate for
dispersion to be significant. A 10 Gb/s signal only has to travel one quarter of this
distance, or 100 km, for dispersion to be significant. The four-to-one relationship
arises from the fact that frequency is squared in the dispersive fiber transfer function
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 128
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(a) With HT IC and without logarithmic am-plifier.
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(b) With HT and logarithmic amplifier ICs.
−200 −150 −100 −50 0 50 100 150 200−0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time (ps)
Am
plitu
de
(c) With HT and logarithmic amplifier ICs.
Figure 6.7: Spectra and eye diagram of 5 Gb/s COSSB signals filtered at 2.75 GHzfor a modulation depth of 0.25.
from equation (2.30). The signal in Figure 6.9 is badly distorted, and so using the HT
IC alone for such a signal gives poor performance. Minimum phase post-detection
compensation was also tried for this signal, however the eye diagram was still closed.
Figure 6.10 shows the eye diagram of the COSSB signal generated using both
the log amplifier and HT ICs and using self-homodyning post detection equalization.
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 129
Figure 6.8: Eye diagram of 5 Gb/s signal recovered from a DSB system after 400 kmof uncompensated dispersive fiber for a modulation depth of 0.25.
Figure 6.9: Eye diagram of 5 Gb/s signal recovered from COSSB system with HTIC, without logarithmic amplifier, and using only self-homodyning post detectionequalization after 400 km. The modulation depth is 0.25
In this case, the shape of the eye is improved, and there actually is an eye opening
up to 600 km. However, the signal is somewhat noisy and distorted. Some of this
distortion relates to the fact that the 5 Gb/s signal was band-limited to 2.75 GHz at
the transmitter in order to obtain an analog signal in order to test the logarithmic
amplifier. The band-limited signal had some ISI at the transmitter, and the imperfect
sideband cancellation allows for some dispersion induced degradation of the signal.
Still, the received signal at 400 km is unusable without the log amplifier, and adding
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 130
(a) 400 km. (b) 600 km.
(c) 800 km.
Figure 6.10: Eye diagrams of 5 Gb/s signals recovered from COSSB system with HTIC and with logarithmic amplifier and using only self-homodyning post detectionequalization. The modulation depth is 0.25.
the log amplifier opens the data eye.
Next, consider the eye diagrams for the case where the log amplifier IC is included
and where minimum phase post detection equalization is used at the receiver, shown
in Figure 6.11. In this case, the noise and distortion remain significant, and the
benefits of minimum phase compensation are less evident.
It was hypothesized that since the eye diagram was poor after 400 km for the
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 131
(a) 400 km. (b) 600 km.
(c) 800 km.
Figure 6.11: Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and with logarithmic amplifier and using only minimum phase post detectionequalization. The modulation depth is 0.25.
system without the logarithmic amplifier, that the recovered OSSB spectrum for
this system would have large power fades in it. However, the simulation indicated
that this was not the case. Figure 6.12 shows spectra recovered from OSSB systems
with the system containing the log amplifier plotted in black in the background,
and the spectra from the system with no log amplifier in yellow in the foreground,
which will show up as a light gray when viewed in black and white. There are
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 132
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
System without logarithmic amplifier.
System with logarithmic amplifier.
Figure 6.12: Spectra recovered from OSSB systems after 400 km with and withoutlogarithmic amplifier.
subtle differences between the two recovered spectra, however it is not obvious from
this plot that the system without the logarithmic amplifier yields a much worse eye
diagram when recovered. Filtering the recovered spectra at 4 GHz before plotting the
recovered signal eye diagrams was tried, however this had a negligible effect on the
eye diagrams, indicating that the problem with the spectrum for the system with no
log amplifier lies at frequencies below 4 GHz. Davies suggested that the distortion
in the signal from the system without the log amplifier may be contained in the
phase of the recovered signal [54]. This indicates that although the types of post
detection compensation discussed in this thesis fail to recover the signal, another
method which compensates for the particular distortion of this signal may succeed.
This possibility is beyond the scope of this thesis, and was not investigated further.
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 133
30 31 32 33 34 35 36 37 38 39 400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (ps)
Line
ar A
mpl
itude
(a) Optical signal envelope.
30 31 32 33 34 35 36 37 38 39 40−2
−1.8
−1.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
Time (ps)
Line
ar A
mpl
itude
(b) Logarithm of optical signal envelope.
Figure 6.13: Scaled optical signal envelope and its logarithm for a modulation depthof 0.20.
6.4.2 Performance at a Mach-Zehnder Modulation Depth of 0.20
In this section, we consider the obtainable performance when the system simulations
are identical to those in Section 6.4.1, but a Mach-Zehnder modulation depth of
0.20 is used instead of 0.25. As a result, it will be shown that the log amplifier is
unnecessary at this lower modulation depth.
Figure 6.13(a) shows the envelope of the amplitude modulated optical signal. The
modulation depth of 0.20 results in the amplitude reaching approximately 0.18 on
the lower end, instead of about 0.01 as in the last section. As a result, the logarithm
of this envelope, shown in Figure 6.13(b), looks more like a scaled version of the
envelope itself, and the logarithmic amplifier becomes less important.
Figure 6.14 shows the spectra and eye diagrams of the signals at the output of
the transmitter for the cases where the HT IC is used and the log amplifier is or is
not used. The improvement in sideband cancellation obtained with the log amplifier
is not as significant as in the last section, as expected.
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 134
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(a) With HT IC and without logarithmic am-plifier.
−10 −8 −6 −4 −2 0 2 4 6 8 10−70
−65
−60
−55
−50
−45
−40
−35
−30
−25
−20
Frequency (GHz)
Mag
nitu
de (
dB)
(b) With HT IC and with logarithmic ampli-fier.
(c) With HT and logarithmic amplifier ICs.
Figure 6.14: Spectra and eye diagram of 5 Gb/s COSSB signals filtered at 2.75 GHzfor a modulation depth of 0.20.
Figure 6.15 shows the eye diagram of a DSB signal created with a modulation
depth of 0.20 after 400 km of uncompensated fiber. The signal is badly distorted,
again showing the motivation for performing single sideband modulation.
Figure 6.16 shows the eye diagrams at incremental distances for the COSSB
system where only the HT IC is used and self-homodyning post detection equalization
6.4 Combined Performance of Logarithmic Amplifier and HT Circuits 135
Figure 6.15: Eye diagram of 5 Gb/s signal recovered from a DSB system after 400 kmof uncompensated dispersive fiber for a modulation depth of 0.20.
is used. The eye remains open for longer distances than in the last section even
though the log amplifier is not being used, showing that the log amplifier is not
required here. As well, the lower modulation depth reduces nonlinear distortion
from the Mach-Zehnder and improves transmission distance. The price is reduced
signal-to-noise ratio in an optical system. Figure 6.17 shows the eye diagrams for the
case where minimum phase post detection equalization is used. These eye diagrams
are improved over the self-homodyning equalization case.
Figure 6.18 shows the eye diagrams when self-homodyning detection is used and
both the log amplifier and HT ICs are used. Comparing this to Figure 6.16, it is ob-
served that there is little improvement in the eye diagram, as expected. Figure 6.19
shows the eye diagrams for the case where the log amplifier is included and mini-
mum phase dispersion compensation is used. The minimum phase eye diagrams are
improved compared to the self-homodyning case, but are not substantially different
than for the case where the log amplifier was not used. In short, if a modulation
depth of 0.20 or lower is used, the HT alone should be sufficient to achieve good
COSSB transmission.
6.5 Conclusion 136
(a) 400 km. (b) 1000 km.
(c) 2000 km.
Figure 6.16: Eye diagrams of 5 Gb/s signals recovered from COSSB system with HTIC and without logarithmic amplifier and using only self-homodyning post detectionequalization. The modulation depth is 0.20.
6.5 Conclusion
In this chapter, simulations showed that the HT IC allowed for COSSB transmis-
sion at bit rates of 5 and 10 Gb/s over uncompensated dispersive fiber lengths of
600 and 200 km respectively using only post detection equalization. Furthermore,
the logarithmic amplifier was shown to improve performance for the case of a band-
6.5 Conclusion 137
(a) 400 km. (b) 1000 km.
(c) 2000 km. (d) 3000 km.
Figure 6.17: Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and without the logarithmic amplifier and using only minimum phase postdetection equalization. The modulation depth is 0.20.
limited 5 Gb/s signal at a modulation depth of 0.25. The next chapter contains actual
measurements of the SSB spectra generated at the output of a COSSB transmitter.
6.5 Conclusion 138
(a) 400 km. (b) 1000 km.
(c) 2000 km.
Figure 6.18: Eye diagrams of 5 Gb/s signals recovered from COSSB system with HTIC and with logarithmic amplifier and using only self-homodyning post detectionequalization. The modulation depth is 0.20.
6.5 Conclusion 139
(a) 400 km. (b) 1000 km.
(c) 2000 km. (d) 3000 km.
Figure 6.19: Eye diagrams of 5 Gb/s signals recovered from COSSB system withHT IC and with logarithmic amplifier and using only minimum phase post detectionequalization. The modulation depth is 0.20.
Chapter 7
Measurements of COSSB Transmitters
7.1 10 Gb/s COSSB Experiment Using the HT
Figure 7.1 shows a block diagram of the COSSB digital signal measurement system.
More details of the equipment are given in Appendix G. The key components are
the UTP phase modulator, which is driven by the amplified HT output, and the
Sumitomo intensity modulator, which is driven by the amplified digital input data.
A JCA amplifier drives the intensity modulator, and this amplifier is a digital limiting
amplifier, meaning that the output is a 7 Vpp square wave regardless of the input
amplitude. If the input signal is below approximately 100 mV, the output signal
simply switches between 0 and 7 Vpp at approximately 1 MHz. Since this digital
limiting amplifier was chosen, it was decided to put the phase modulator before the
intensity modulator and to delay the input signal to the intensity modulator. This
arrangement of optical modulators is contrary to all of the minimum phase COSSB
modulators shown so far in this thesis. The intensity modulator has two meters of
fiber between the body of the modulator and the input or output connector, and the
phase modulator has eighty centimeters of fiber between the body of the modulator
and the input or output connector. The length of the fiber leads on the modulators
should not be shortened, or inter-modal optical distortion may result. Hence, there
are 2.8 m of fiber between the optical modulators, and approximately the same length
of SMA cable is needed to delay the signal going to the second optical modulator,
as described in Appendix G. When the 10 Gb/s signal propagates through such a
long length of cable, there will be a low pass filter effect. However, if this signal goes
7.1 10 Gb/s COSSB Experiment Using the HT 141
to the JCA amplifier, it will be restored to a square wave. The only disadvantage
of doing this is that the optical intensity modulator is polarization sensitive, and a
polarization adjuster can not be placed before it as that would create a much longer
length of fiber between the modulators. Although having the phase modulator first
gave the best results, it made it difficult to reliably set the polarization during
the experiments. The polarization would change over periods of a few seconds.
Changes in polarization showed up when they caused a sub-spike in power beside
the carrier and clock spikes in the optical spectrum due to interactions with the
optical filter used. For this reason, some experiments in later sections in this chapter
were performed with the intensity modulator first and the input signal to the HT
was delayed by the required amount. These problems could be overcome by using
a cascaded amplitude and phase modulator on a single substrate, a device which
already exists but was not readily available at the bandwidth required. Furthermore,
it should be noted that the DATA signal served as the basis for one modulator
signal, and the DATA signal was the basis for the other modulator signal. It may
be argued that slight differences in the two signals will degrade the best obtainable
performance, and that one of the signals should be passed through a splitter and
used for both modulators. This was tried, and the results were no better because
the JCA limiting amplifier restores one signal to a square wave but the other signal
experiences the loss of the splitter. Sieben had to put up with similar imperfections
in his experiments [7].
A Micron Optics tunable Fiber Fabry-Perot (FFP) bandpass filter with 400 MHz
bandwidth was used to measure the the optical spectra. To view the optical spectra
in real time, a 1 Hz triangle wave was used to sweep the filter, and the analog output
of the optical power meter was connected to an oscilloscope. To record the optical
spectra, the FFP was swept at 1 mHz while a computer downloaded readings from
7.1 10 Gb/s COSSB Experiment Using the HT 142
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CO
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7.1 10 Gb/s COSSB Experiment Using the HT 143
the optical power meter. The fact that the FFP has only 400 MHz bandwidth is
amazing, since the center wavelength of 1550 nm corresponds to a center frequency
of approximately 200 THz. The filter is somewhat non-linear, so that the wavelength
does not increase linearly with increasing applied voltage, although it is fairly close.
Furthermore, it exhibits some hysteresis, so that the center frequency of the filter
does not alway correspond to a given voltage. It was necessary to use a modest
exponential distortion of the frequency before the data was plotted so that the clock
spikes on either side of the optical carrier were equidistant from the carrier. However,
the magnitude response of the filter was assumed perfectly flat, and no changes were
made to the spectral power levels prior to plotting.
Figure 7.2 shows the measured frequency spectrum and eye diagram for an optical
signal modulated with a 10 Gb/s signal using COSSB modulation at 16 dBm of
optical intensity power, and with 130 mVpp input to the HT and 40 dB of gain after
the HT. A 231 − 1 length PRBS data signal was used for all broadband experiments
in this chapter. The lower sideband has a measured average spectral power density
which is 7.5 dB higher than the upper sideband, compared to 11.6 dB simulated.
All measurements in this chapter were made with the Q-enhancement of the HT
turned off, and when it was turned on it had no noticeable impact. The input to the
phase modulator for this measurement was approximately 4.5 Vpp, and the power
of this signal measured on a power meter was 14.5 dBm. Figure 7.2(a) also shows
the laser spectrum, and it is observed that the upper sideband has been canceled
down to the laser power across the band within the accuracy of the measurement. No
changes have been made to the optical power, these spectra are at the absolute optical
power recorded. The intensity modulation power of 16 dBm corresponds to a 1.4 V
signal, and since the Vπ of the modulator is approximately 6 V, this modulation
power is 0.23·Vπ. This is approximately the same as the 0.20 modulation depth
7.1 10 Gb/s COSSB Experiment Using the HT 144
−10 −5 0 5 10−60
−55
−50
−45
−40
−35
−30
−25
−20
−15
Normalized Frequency (GHz)
Opt
ical
Pow
er (
dBm
)COSSB SignalLaser Only
(a) COSSB Spectrum.
7 mV/div25 ps/div
(b) Eye diagram.
Figure 7.2: Spectrum and eye diagram of 10 Gb/s COSSB signal for 16 dBm ofintensity modulation power.
used in the simulations in the last chapter. Data was also recorded for intensity
modulation powers which are 5 dB lower and 4 dB higher than this. When the
intensity modulation is lower than 16 dBm, there is less than 10 dB of signal power
above the laser spectral floor and there is less signal to noise ratio in the eye diagram.
Figure 7.3 shows the optical spectrum and eye diagram for an intensity modulation
power of 20 dBm or 0.375 ·Vπ. Here, the lower sideband has an average spectral
power density which is 6.8 dB higher than the upper sideband. This is comparable
to the performance at 16 dBm, except now the signal has a better SNR. However, at
this higher intensity modulation power some distortion in the optical signal envelope
is expected from the Mach-Zehnder which is not accounted for by the HT.
The fact that approximately 7 dB of average spectral suppression was obtained
instead of the 11.6 dB simulated suppression is partially attributed to the failure of
the simulation of the HT to account for substrate coupling on the IC. Although the
time domain measurements shown in Chapter 5 did not indicate a serious problem,
7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 145
−10 −5 0 5 10−60
−55
−50
−45
−40
−35
−30
−25
−20
−15
Normalized Frequency (GHz)
Opt
ical
Pow
er (
dBm
)COSSB SignalLaser Only
(a) COSSB Spectrum.
7 mV/div25 ps/div
(b) Eye diagram.
Figure 7.3: Spectrum and eye diagram of 10 Gb/s COSSB signal for 20 dBm ofintensity modulation power.
substrate coupling could be a problem with certain data patterns. Other factors
such as mismatches in the phase and intensity modulation signals, distortion in the
modulator driver amplifiers, frequency dependent loss in the modulators, and any
extra group delay distortion in the measurement setup contribute to the discrepancy.
7.2 COSSB Experiments Using the HT and the Logarithmic
Amplifier
7.2.1 Experiment Using a 1.9 GHz Sinusoid
In order to quantify the performance of the COSSB system when the logarithmic
amplifier is added, a sinusoid was first used as the data signal. Sinusoids at 1.9 GHz
were generated by two different signal sources, and were filtered at the output of
the sources using Lorch 8BP8-1800/300-S bandpass filters to remove any harmonics
at the input of the system. The rest of the test system was similar to that shown
7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 146
in Figure 7.1, except that the JCA amplifier was not used since it is nonlinear. An
intensity modulation power of 23 dBm was used. The resulting COSSB spectra were
then measured for the case where the logarithmic amplifier is or is not used. Fig-
ure 7.4 shows the spectra for the two cases. There are harmonics present because
of the nonlinearity of the Mach-Zehnder amplitude modulator, and the best an ex-
perimenter can hope to do is to cancel all of the tones in the unwanted sideband,
and leave the desired sideband unchanged. In either case in Figure 7.4, better than
20 dB suppression of the fundamental tone in the lower sideband was obtained. The
fact that this signal is upper sideband is simply because the signal polarization was
such that the phase and intensity modulation inputs were 180 out of phase. The
next highest power tone is the second harmonic. Note that the optical envelope
contains even harmonics, but the detected optical signal does not. Essentially no
suppression of the second harmonic was obtained using only the HT, as expected.
However including the logarithmic amplifier yielded 10 dB of second harmonic sup-
pression, which is a strong indication of the value of the logarithmic amplifier. The
third and higher harmonics are very low power. The third harmonic in the HT only
signal for the upper sideband is located just below 6 GHz, and is barely noticeable,
and is smaller than the third harmonic in the lower sideband. Simulations of a
sinusoidal signal in a COSSB system without a logarithmic amplifier confirm that
the harmonics in the desired sideband are sometimes suppressed. In the spectrum
of the signal with the logarithmic amplifier, the third and fourth harmonics in the
lower sideband are suppressed by approximately 4 dB each. The frequencies of the
second and higher harmonics for the two signals don’t line up perfectly because not
all of the nonlinear frequency response of the filter could be equalized. However, the
power levels are unaltered and directly from the optical power meter. The intensity
modulator had to be placed first for this experiment for precise optical polarization
7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 147
−10 −8 −6 −4 −2 0 2 4 6 8 10−55
−50
−45
−40
−35
−30
−25
−20
−15
−10
Normalized Frequency (GHz)
Opt
ical
Pow
er (
dBm
)
With HT OnlyWith HT and Logarithmic Amplifier
Figure 7.4: Spectrum of 1.9 GHz COSSB signal for 23 dBm of intensity modulationpower.
control.
It is also observed that the third harmonic of the upper sideband is suppressed
in the spectrum for only the HT in Figure 7.4. In fact, Davies showed that the odd
harmonics are suppressed in alternating sidebands, as shown in Figure 4.13 of his
Ph.D. dissertation [6].
7.2.2 Experiment Using Filtered 5 Gb/s Data
Figure 7.5 shows the measurement system used to quantify the performance of the
logarithmic amplifier for the case of a 5 Gb/s signal filtered at 2.9 GHz. This
setup is similar to the simulations in the last chapter. The filter cutoff of 2.9 GHz is
somewhat higher than the 2.75 GHz simulated cutoff frequency. However, the change
in performance that this causes should not invalidate the experiment. A data rate
7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 148
1550
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7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 149
of 5.5 Gb/s was also tried, and no difference in the results was observed.
It is somewhat difficult to determine the DC offset that should be added to the
log amplifier input so that the output signal appears like the logarithm of the optical
signal envelope. Figure 7.6 shows the measured input and out waveforms for the
logarithmic amplifier for the repeated DATA sequence 01001111. It is necessary
that the bits of data applied to the intensity modulator that cause the optical signal
to extinguish are stretched out by the logarithmic amplifier. In the example shown,
the signal in Figure 7.6(b) has been inverted and then logged compared to the signal
in Figure 7.6(a). Nonetheless, this example shows the type of distortion that is per-
formed by the logarithmic amplifier. Due to the particular arrangement of inverting
modulator driving amplifiers, the inversion of the DATA signal which drives the log-
arithmic amplifier compared to the DATA signal for the intensity modulator, and
even the use of inverting modulation points on the Mach-Zehnder modulator, the
optical signal can be lower or upper sideband. Whether the signal was upper or lower
sideband was always carefully predicted before each experiment. It is also critical
to predict if the signal is upper or lower sideband in order to get the delay between
the modulator input signals correct, as described in Appendix G. Once the COSSB
signal optical spectrum was displayed on the oscilloscope, the logarithmic amplifier
offset and the delay could be optimized in real time. The intensity modulator could
even be switched from a non-inverting bias point to an inverting bias point in or-
der to view the degradation in sideband cancellation when the logarithmic amplifier
performs the logarithm with the wrong polarity due to an incorrect DC offset.
Figure 7.7 shows the measured optical spectrum for the 5 Gb/s COSSB signal for
systems with and without the logarithmic amplifier. These measurements were ac-
tually taken with the intensity modulator placed first in the OSSB system, followed
by the phase modulator. This data was used because the sideband cancellation from
7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 150
(a) Input waveform. (b) Output waveform.
Figure 7.6: Logarithmic amplifier waveforms.
the system with the phase modulator placed first was actually 2-3 dB worse for this
power level. This could have been caused by sub-optimal optical polarization for the
intensity modulator for this configuration, a problem which was already discussed in
Section 7.1. The spectra for the COSSB system without the logarithmic amplifier
has 6.4 dB contrast in average spectral density from 0-2.9 GHz, whereas the spec-
trum for the system with the logarithmic amplifier has 6.1 dB contrast in spectral
sideband suppression from 0-2.9 GHz, slightly worse but approximately equal within
the accuracy and repeatability of the measurements. Furthermore, the maximum
sideband cancellation at any one frequency is approximately 10 dB for these signals.
Based on the simulations in Section 6.4, the sideband cancellation at 2 GHz is ex-
pected to go from approximately 10 dB to 15 dB when the logarithmic amplifier is
added. However, simulation from Section 6.2 earlier in that chapter also predicted
15-20 dB maximum sideband cancellation for the 10 Gb/s digital signal, and only
about 12 dB was actually achieved. For this reason, better than 12 dB maximum
sideband cancellation should not be expected for the experiment in this section, due
to limitations in the HT and in the optical components. So, it is not surprising that
7.2 COSSB Experiments Using the HT and the Logarithmic Amplifier 151
−6 −4 −2 0 2 4 6−60
−55
−50
−45
−40
−35
−30
−25
−20
−15
−10
−5
Normalized Frequency (GHz)
Opt
ical
Pow
er (
dBm
)
With HT OnlyWith HT and Logarithmic AmplifierLaser Power Only
Figure 7.7: Spectrum of 5 Gb/s COSSB signal for 17 dBm of intensity modulationpower.
no significant improvement is obtained by adding the logarithmic amplifier for the
5 Gb/s signal. The addition of the logarithmic amplifier for the 1.9 GHz sinusoid in
Section 7.2.1 suppressed the second harmonic, but this harmonic was approximately
17 dB below the fundamental, well below the noise and distortion floor of the broad-
band spectra observed so far. In short, the addition of the logarithmic amplifier for
the 5 Gb/s, 17 dBm intensity modulation power signal does not improve the side-
band cancellation, but this appears to be only partially due to imperfections in the
logarithmic amplifier.
Figure 7.8 shows the COSSB spectra for systems with and without the logarithmic
amplifier and eye diagrams for the COSSB and DSB signals for a 20 dBm intensity
modulation signal for the 5 Gb/s signal filtered at 2.9 GHz. The DSB eye diagram
7.3 Conclusion 152
is shown just to prove that it is basically the same as the COSSB eye diagram,
demonstrating that the phase modulation does not degrade the eye diagram at the
output of the transmitter. The spectra for this power level are based on data taken
with the phase modulator placed first in the COSSB system followed by the intensity
modulator, since the data from this case was the best for this intensity modulation
level. Here, the contrast in the average spectral density between the sidebands
between DC and 2.9 GHz is approximately 5.7 dB without the logarithmic amplifier
and is 6.7 dB with the logarithmic amplifier. This shows a small improvement
when the logarithmic amplifier is added, but it is hardly worth the increased system
complexity in this case. The spectrum for the system with the logarithmic amplifier
is also observed to increase in power by a few decibels beyond approximately 2.7 GHz.
These frequencies lie near the cutoff of the 2.9 GHz low pass filter, and so the input
signal to the logarithmic amplifier may be somewhat distorted by the low pass filter.
The phase shift of the logarithmic amplifier may combine with this distortion to
impede the sideband cancellation at these frequencies.
7.3 Conclusion
In this chapter, measurements of a 10 Gb/s optical single sideband system indicate
that 7 dB of broadband sideband suppression is obtainable using the HT IC for the
case of a digital signal. Measurements of a COSSB system using a 5 Gb/s signal
filtered at 2.9 GHz show that approximately 7 dB of sideband suppression is also
available whether or not the logarithmic amplifier is used. However, measurements
of a COSSB system using a 1.9 GHz sinusoid clearly show improved suppression
of all harmonics when the logarithmic amplifier is added. The logarithmic amplifier
seems best suited for narrow-band COSSB applications, and the HT was proved very
7.3 Conclusion 153
−10 −8 −6 −4 −2 0 2 4 6 8 10−60
−55
−50
−45
−40
−35
−30
−25
−20
−15
−10
−5
Normalized Frequency (GHz)
Opt
ical
Pow
er (
dBm
)With HT OnlyWith HT and Logarithmic AmplifierLaser Power Only
(a) COSSB Spectrum.
7 mV/div50 ps/div
(b) COSSB eye diagram.
7 mV/div50 ps/div
(c) DSB eye diagram.
Figure 7.8: Spectrum of 5 Gb/s COSSB signal and eye diagrams of 5 Gb/s COSSBand DSB signals for 20 dBm of intensity modulation power.
7.3 Conclusion 154
successful in broadband applications.
Chapter 8
Conclusions
In this thesis a logarithmic amplifier and HT were developed for the COSSB appli-
cation. While developing the logarithmic amplifier, a mathematical characterization
and design procedure for CHEF amplifiers was developed. This characterization dif-
fers from the one presented by Ohhata et al. because it is developed for HBTs for
which the base resistance is less than approximately 100 Ω, which is more appro-
priate for modern HBT technologies [24, 30]. The equations by Ohhata et al. are
not valid for this case. Furthermore, the mathematics presented here is different in
that resistor R2 is included. In addition, the equations necessary to design for the
important condition Q ∼= 1/√
3 are described. Furthermore, the work here is novel
in that equations for the DC transfer characteristic and output noise of the CHEF
amplifier are developed and are used to form a comprehensive design procedure.
This procedure is useful because it gives the design engineer an understanding of the
effect of the numerous component values in the CHEF amplifier. This work has been
published in the IEEE Journal of Solid State Circuits [25].
While designing a logarithmic amplifier for the COSSB application, the exist-
ing series linear-limit and parallel amplification, parallel summation architectures
were evaluated. The series linear-limit amplifier was found to have insufficient band-
width, and the parallel amplification, parallel summation architecture was found to
have insufficient logarithmic dynamic range. Using existing descriptions of each ar-
chitecture [38, 41], a novel generalized mathematical analysis of parallel summation
logarithmic amplifiers was developed. This analysis was the first, to the author’s
knowledge, which described the exact path gains and limiting currents required to
156
obtain a logarithmic response and then proved the ensuing logarithmic relationship
between the amplifier output current and input voltage. Furthermore, the analysis
made it clear that the logarithmic slope is proportional to the limiting currents in
the summing amplifier. As well, this analysis was used to choose the gains and lim-
iting current in a hybrid parallel summation architecture, which was implemented
in two different technologies, the second of which achieved the highest bandwidth to
date for a true logarithmic amplifier, DC-6 GHz. This amplifier is novel in that it
used branching amplification paths in order to achieve 39 dB of gain, 6 GHz band-
width, and matched group delay among the gain paths in a 1.33 mm by 1.50 mm
integrated circuit, fabricated in a 47 GHz fT technology. Furthermore, a novel and
efficient design for implementing the progressive compression logarithmic amplifier
with matched group delay among the paths was suggested. Previously published pro-
gressive compression logarithmic amplifiers did not have matched group delay paths,
or they required more amplifiers to implement [55]. Finally, circuits for reducing DC
offset errors in DC coupled logarithmic amplifiers were described and implemented
successfully.
The logarithmic amplifier implementations presented in this thesis were specifi-
cally designed for the OSSB application and have a power consumption that is likely
too high for hand-held radios. This is unfortunate, because many radios use demod-
ulating logarithmic amplifiers as receive strength signal indicators (RSSI). However,
the mathematical description and procedure for choosing the amplifier gains and
limiting currents that was developed here is useful for engineers designing logarith-
mic amplifiers in any application. In many cases, the only difference between the
logarithmic amplifiers presented here and those used in RSSI applications is a re-
laxed bandwidth constraint for RSSI and the addition of envelope detectors on the
output of each path. When one considers that RSSI circuits are used extensively in
157
military radio transceivers, and that circuits in these applications must have excel-
lent logarithmic linearity, then it is critical to choose the logarithmic amplifier path
gains and limiting currents correctly. The mathematical description of logarithmic
amplifiers in this thesis shows how to achieve that goal. The work on logarithmic
amplifiers has also been published in the IEEE Journal of Solid State Circuits and
has been patented [36, 56].
The HT in this work is the first published fully integrated 10 Gb/s HT to the
author’s knowledge, which is a significant engineering achievement. This circuit
was used to generate a 10 Gb/s OSSB signal in the laboratory, only the second
such experiment in which a 10 Gb/s OSSB signal was created with an HT, to the
author’s knowledge [7]. The implementation of the HT described in this thesis serves
as a useful example for engineers working on tapped delay filters for equalization or
predistortion in fiber optic networks, and for engineers designing tapped delay filters
for ultra wideband radios, which have similar broadband requirements to circuits for
fiber optics. A letter on the HT is scheduled to appear in the May issue of IEEE
Microwave and Wireless Component Letters.
The logarithmic amplifier and HT were successfully tested in the COSSB system.
The tests with a 1.9 GHz sinusoid verified the complete COSSB theory, including the
requirement for a logarithm. All tests performed with the HT verified the operation
of and provided rare measurement data for the COSSB system.
8.0.1 Future Work
It should now be possible to integrate an entire COSSB transmitter. It would consist
of an optical phase modulator cascaded with an intensity modulator, and an HT and
a driver amplifier to drive the phase modulator. A logarithmic amplifier could also be
used in the case of narrow-band signals, such as optical subcarrier signals. If the two
158
optical modulators are physically very close together, it may be necessary to delay
the electrical signal used for intensity modulation until the electrical signal used
for phase modulation has passed through the logarithmic amplifier and HT. Such
a 10 Gb/s COSSB transmitter would be an effective way to deal with dispersion,
and could be used on its own or alongside existing optical dispersion compensation
methods.
Some further suggestions for future work include:
• The OSSB system simulations could be compared with the performance of
duobinary transmission to evaluate the comparative advantages and disadvan-
tages of each technique.
• The HT could be implemented in CMOS technology, to allow it to be integrated
with any other signal processing technology in optical transceivers.
• The HT could be implemented at 40 Gb/s. This would be interesting to try
because the delays required for the on chip transmission line will be one quarter
of that given in this thesis. A 40 Gb/s HT would be even more useful than
the 10 Gb/s one, because of the severe dispersion at 40 Gb/s. However, the
requirements on group delay flatness would also be more severe for a 40 Gb/s
HT.
• If inductors are used for the on chip transmission line in the HT instead of
transformers, then the higher Q of the inductors compared to a transformer
primary will reduce the loss of the line. Furthermore, if the problem of exces-
sive transient ringing could be overcome, the line could be Q-enhanced using
the simple cross coupled pair in Figure 5.10. These ideas could be implemented
with the aim of improving the HT performance and improving the average side-
159
band cancellation. If the transient ringing of the Q-enhanced transmission line
could be reduced, then the resulting Q-enhanced LC line would have applica-
tion in all tapped delay filters for equalization or predistortion in fiber optic
networks, and for tapped delay filters for ultra wideband radio.
• The design procedure for logarithmic amplifiers could be modified for envelope
detecting logarithmic amplifiers.
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Appendix A
Amplifier DC Transfer Characteristic
The notation labeled in Figure 3.1 is used throughout this appendix. The parasitic
emitter resistances of the HBTs will be ignored for simplicity. Using IC2 − IC1∼=
IC2 − (IEE1 − IC2) ∼= 2IC2 − IEE1 and IC4 − IC3∼= 2IC4 − IEE2,
V1 − V2∼= R1(2IC4 − IEE2) + VBE6 − VBE5
+ Rf (2IC2 − IEE1). (A.1)
Next, it is noted that for transistor k
VBEk∼= VT · ln
(
ICk
IES
)
(A.2)
where IES is the scaling current proportional to the base-emitter junction area for a
given transistor. Using this equation for Q1 and Q2 and solving for IC1 and IC2 and
comparing gives
IC2∼= IC1 · e−
VinVT ∼= IEE1
1 + eVinVT
(A.3)
IC4∼= IEE2
1 + e(V1−V2)
VT
. (A.4)
For purposes of simplification, it is noted that IC5∼= IC1 + IC3/βDC and IC6
∼=
IC2 + IC4/βDC . Equation (3.1) is derived using equations (A.1)-(A.4) and using the
tanh function expressed in exponential form.
Next, it is recognized that
Appendix A 168
Vo1 − Vo2∼= (IC4 − IC3)(R1 +R2)
∼= (2IC4 − IEE2)(R1 +R2). (A.5)
Equation (3.2) is derived by substituting equation (A.4) into (A.5) and again using
tanh expressed in exponential form. Equation (3.2) overestimates the slope of the
transfer characteristic somewhat for small applied voltages because the parasitic HBT
emitter resistances have been ignored here for simplicity. When these parasitics are
included, one of IC1 or IC2 and one of IC3 or IC4 must be found iteratively.
Appendix B
Analysis of the Emitter Follower Load
The CHEF amplifier is usually followed by an emitter follower output buffer. The
amplifier will be loaded by the input impedance of the emitter follower, ZinEF , which
in turn depends on the input impedance of the stage connected to the output of the
emitter follower. Figure B.1(a) shows one example, where the output of the emitter
follower is connected to a differential pair. The differential pair could represent the
input to another CHEF amplifier stage, or a buffer to the output of the integrated
circuit. Figure B.1(b) shows the high frequency small signal circuit of one emitter
follower and a differential mode half circuit of the differential pair input. Using this
circuit, ZinEF is given by
ZinEF∼= Z1
sCµEFZ1 + 1+ rbEF (B.1)
where
Z1∼=
[
s2(R3 + reDP )
+s
(
R3 + reDP + rdEF
rdEFCπEF+reDP/2 + rdDP
rdDPCπDP
)
+
(
reDP/2 + rdDP
rdEFrdDPCπEFCπDP
)]
/
s2 (B.2)
and where R3 = reEF +rbDP . The magnitude of ZinEF decreases with frequency, and
so it may be modeled by a capacitor to first order. However, at high frequencies, the
impedance predicted by (B.1) includes a frequency dependent negative resistance. A
more detailed prediction of the CHEF amplifier frequency response may be obtained
by using (B.1) in (3.10) to obtain ZL, and then using this ZL in (C.2) to obtain
Appendix B 170
CπEF
rbEF
reEF
vbe1vbeEF
rdEF
icEF =
vo2
QEF2
reDP
Q8
QEF1
Q7
Rc Rcvo1 QDP1 QDP2
CµEF
vbeDP
2rdDP
icDP =vbeDPCπDP
rbDP
IDPVBIAS
VEEVEE
vo1
ZinEF
(a)
(b)
Rc
Figure B.1: Schematic diagram of (a) emitter follower output buffers and differentialpair load and (b) high frequency small signal circuit of one emitter follower and adifferential mode half circuit of the differential pair.
the frequency response. When this was done, it was found that there are still two
complex poles which largely determine the amplifier frequency response and whose
pole quality factor behaves in roughly the same way as shown in Figure 3.6. The net
effect is to only modify the response in a modest way.
Appendix C
Derivation of Equation (3.11)
Using nodal analysis, vo1/vbe1 was found for the circuit in Figure 3.3(a) and is given
by equation (C.2). The zero in (C.2) is given by
z1 ∼=(R1 +R2)(R
′
f + rd5)
rd5Cπ5(R′
f + rb5)(R1 +R2) − R1r′d3 +R1R2. (C.1)
R2 is of the order of r′d3 and R′
f >> rd5, so that the zero will be at a relatively high
frequency. Furthermore, in Figure 3.3(a), Q5 forms an emitter follower feedback
circuit. As Ohhata et al. describe in [24], the bandwidth of this emitter follower
is much greater than that of the common emitter amplifier formed by Q3, R1, and
R2. As a result, the pole due to Cπ5 will be at a much higher frequency than the
amplifier bandwidth and may be neglected for simplicity. With Cπ5 set to zero, and
assuming r′d3 >> R′
f/β, equation (C.2) reduces to equation (3.11).
vo1
vbe1=
N(s)
D(s)∼= 1
rd1
[
srd5Cπ5(R′
f + rb5)(R1 +R2) − R1r′
d3 +R1R2 + (R1 +R2)(rd5 +R′
f )]
/
[
s2Cπ5C1rd5r′
d3(R1 + rb5 +R′
f ) + sCπ5rd5(r′
d3 +R1) + C1r′
d3(rd5 +R′
f )
+R1 + r′d3 +1
ZL
s2Cπ5C1r′
d3rd5
(R1 +R2)(rb5 +R′
f ) +R1R2
(C.2)
+sr′d3
Cπ5rd5(R1 +R2) + C1(R1 +R2)(rd5 +R′
f)
+ (r′d3 +R′
f/β)(R2 +R1)
]
Appendix D
Example Calculation of an Amplifier Noise
Contribution
Figure D.1 shows half of the small signal circuit of the amplifier including the dom-
inant noise sources. For example, consider the case where only i2c1 is calculated and
all of the thermal noise voltage sources are short-circuited and the remaining shot
noise current sources are open-circuited. Assuming β >> 1, the output PSDs at
nodes vo1 and vo2 due to i2c1 are given by
|v2o1(t)|∆f
=|v2
o2(t)|∆f
∼=i2c1r
2d1(R1 +R2)
2(R′
f + rd5)2
∆f4r′d12(R1 + r′d3)
2. (D.1)
The mean square differential noise voltage between terminals vo1 and vo2 due to a
given noise source is found for low frequencies to be
v2o = |vo1(t) − vo1(t)|2
= v2o1(t) + v2
o2(t) − 2vo1(t)vo2(t)
= v2o1(t) + v2
o2(t) − 2C12
∣
∣
∣v2
o1(t) · v2o2(t)
∣
∣
∣
1/2
(D.2)
where v2o1(t) and v2
o2(t) are the mean square noise voltages at nodes vo1 and vo2
respectively, and C12 is a measure of the correlation between vo1(t) and vo2(t) and
always lies in the range −1 ≤ C12 ≤ 1. Substituting equation (D.1) into (D.2)
with C = −1, since the noise voltages are anti-phase and fully correlated, results in
v2o(t) = 4v2
o1(t). The noise current source i2c2 contributes an equal amount of noise.
The contributions of the remaining noise sources may be found in the same way.
Appendix D 173
R1
rd5
vo1
β
rd3β
rb5
vbe5
rd3
vbe3
rd5
vbe5
R2Rf
eR2
re1
er2
ic12
er
rb1
2b1
e1
f
re3
rd1βvbe1rd1
vbe1vbe3
+−
+−
+−’
’
Figure D.1: Half of the amplifier small signal circuit including dominant noisesources.
Appendix E
Widlar Biasing
In Figure E.1, degeneration resistor Re is shown. For this amplifier, the gain is equal
to
vout
vin
∼= − Rc
Re + rd1(E.1)
where vin = vin1 − vin2 and vout = vout1 − vout2. It is assumed that the circuit is
symmetrical, so that the small signal parameters of Q1 and Q2, for example, are
equal. It is also assumed that if Re >> rd1, then vout/vin∼= −Rc/Re and the gain
is only dependent on the ratio Rc/Re. In this situation, the gain may be precisely
controlled using resistive matching layout techniques. However, using resistor Re is
undesirable for two main reasons. In a high gain amplifier where a large value of
Rc/Re is required, then Rc must be large compared to the case where Re is zero.
Larger resistances increase the time constants within the amplifier, and lower the
bandwidth. As well, Re generates substantial thermal noise. For these reasons, it is
desirable if Re is zero.
Figure E.2 shows the differential pair without Re and with a Widlar-type current
source for I2 with a β-helper transistor [57]. It is assumed that the base currents of
Q3 and Q4, supplied by Q5, are large enough to set the operating point of Q5 so that
it has β >50. If this is not true, then a resistor should be added from the emitter of
Q5 to VEE so that the emitter current of Q5 is sufficiently large to give it β >50.
The benefit of the Widlar bias configuration will now be explained. The following
relationships are observed for the circuit in Figure E.2:
Appendix E 175
ReRe
Rc Rc
Vout1,vout1 Vout2,vout2
Vin1,vin1 Vin2,vin2
VEE
IEE
Q1 Q2
VCC
Figure E.1: Differential pair.
I1 ∼= IES3eVBE3/VT (E.2)
I2 ∼= IES4eVBE4/VT (E.3)
VT ln
(
I1IES3
)
∼= VT ln
(
I2IES4
)
+Rm2I2 (E.4)
This equation may be rearranged to give
I2 ∼=VT
Rm2ln
(
I2IES4
I1IES3
)
(E.5)
This shows that I2 is proportional to absolute temperature (PTAT) to first order,
because it is dependent on VT (= kT/q). However, it should be noted that IES is
itself strongly temperature dependent. Specifically,
IES =AEqDnn
2i
NAW(E.6)
n2i = BT 3e−EG/kT (E.7)
Appendix E 176
Rc Rc
vout2
vin1 vin2Q1 Q2
VCC
vout1
VCC
VEE
Q4Q3
Q5
Rm1
Rm2
I1I2
Figure E.2: Differential pair with Widlar current biasing.
where AE is the cross sectional area of the base-emitter junction, Dn is the concen-
tration of ‘donor’ or phosphorous atoms, ni is the concentration of holes or electrons
in silicon at a given temperature, NA is the concentration of ‘acceptor’ or boron
atoms, W is the effective width of the base, B is a material parameter =5.4 ×1031
for silicon, and EG is the bandgap energy =1.12 electron volts for silicon [58]. How-
ever, the temperature dependence of IES is mainly due to n2i , and this term should
cancel in the ratio IES4/IES3.
The larger the ratio IES4/IES3 in equation (E.5) and hence the ratio of emitter
lengths of Q4 to Q3, the larger the current I2 is and the more steeply it increases
with increasing temperature. Half of I2 is the quiescent bias current of Q1 or Q2.
Hence the transconductance of Q1 or Q2 becomes
Appendix E 177
gm1,2 =IC1,2
2VT
∼= 1
2Rm2ln
(
I2IES4
I1IES3
)
. (E.8)
Using this, the differential gain in equation (E.1) with Re=0 becomes
vout
vin
∼= − Rc
2Rm2ln
(
I2IES4
I1IES3
)
. (E.9)
The significance of this equation is twofold. It is evident that the gain is no longer
directly proportional to temperature, since the PTAT current source counteracts the
inverse dependence of gm1 and gm2 on temperature. Furthermore, the gain is depen-
dent on the ratio Rc/Rm2, which may be accurately set despite variations in process
using resistive matching layout techniques. In this thesis, some emitter-coupled pairs
are biased using this scheme. This improves both the frequency response and the
noise performance of the amplifiers compared to the case where the amplifiers are
degenerated with Re, all while maintaining gain that is independent of temperature
and process to first order. This is all assuming that I1 is fixed in Figure E.2, which
it isn’t if it is set using Rm1 to VCC as shown. For a commercial product, it would
be desirable to fix I1 using a proper current reference, such as the supply voltage
independent current source used in Chapter 5 and described in [52].
Appendix F
Design of the Logarithmic Amplifier Test Fixture
Figures F.1(a) and F.1(b) show the circuit boards used to test the logarithmic am-
plifier. They were fabricated with Rogers Corporation 4003 circuit board material.
The main circuit board in has a 0.016 inch thick substrate and contains four 50 Ω
coplanar waveguide lines for connecting the two signal inputs and outputs. It also
contains traces for connecting VCC , VEE, the power connection for the DC offset error
reduction circuit, and one connection for each terminal of the off-chip 1 nF capacitor
for the offset reduction circuit. The power supply of the DC offset reduction circuit
is separate so that it may be turned on (VCC) for narrowband AC applications, and
may be turned off (VEE) for the OSSB application. The IC sits on a pad which is
connected to VEE (=-3.3 V). If the chip is epoxied onto the main circuit board and
the two AC inputs and two AC outputs are wire bonded to the circuit board, the
bond wires must traverse the 1 mm height of the IC, leading to at least 1 nH of bond
wire inductance. This amount of inductance makes the circuit difficult to impedance
match up to 10 GHz. For this reason, two of the small circuit board shown in F.1(b)
may be epoxied to the main circuit board, one for the AC input signals and one for
the AC output signals. These small circuit boards are made from a 0.008 inch thick
substrate, which yields a 0.012 inch thick board when the half ounce copper and
gold plating are added on each side of the substrate. This is approximately the same
height as the IC. These small circuit boards have two 50 Ω coplanar waveguide lines
each. This leads to shorter bond wires for the AC signals, and reduced inductance.
Since the logarithmic amplifier is a high gain amplifier, it should be placed in an
enclosed box to prevent high levels of radio signals in the 50 MHz to 5.1 GHz range
Appendix F 179
Front Side
Back Side
(a) The two sides of the main circuit board.
Front Side
Back Side
(b) Top-mount circuit board.
Figure F.1: Logarithmic amplifier circuit boards.
Appendix F 180
Figure F.2: Logarithmic amplifier test fixture.
from reaching the IC through the air and appearing at the logarithmic amplifier
output. Figure F.2 shows a picture of the enclosed test fixture used to test the
logarithmic amplifier. It uses 50 Ω SMA connectors whose dielectric extends through
the wall of the test fixture, and a Tusonix feed-through filter for VEE. The inside of
the lid of the test fixture was lined with material designed to absorb radio signals,
so that the no signals would resonate inside the box.
A through measurement of one input and one output of the test fixture was
taken using a circuit board with a 50 Ω transmission line connecting the input to
the output. The loss of the test fixture was 3 dB at 5 GHz, which is unexpectedly
high. It is unknown if this problem relates to the coplanar waveguide lines on the
circuit boards, or to the connectors used. Nevertheless, the approximate 5 GHz of
Appendix F 181
bandwidth of the test fixture was adequate for the 5 Gb/s tests in Chapter 7.
When wire bonding the logarithmic amplifier, there are several pitfalls which
can prevent the amplifier from having its approximate 39 dB gain up to the 4-5 GHz
bandwidth of the test fixture. In addition to keeping the AC bond wires short, which
was already discussed, the following points should be understood:
• The AC bond wires must not touch the edge of the IC. They should touch the
bond pads, and arc clear of the edge of the chip. If the bond wires touch the
edge of the chip, the amplifier gain will decrease by 10 dB.
• It was found that in some cases where both inputs are wire bonded, the two
inputs can couple together, causing an approximate 10 dB loss in gain. It is
has not been established if the fields of the wire bonds couple in the air, or if
the tails of the bond wires, caused by wedge bonding, couple through the ring
surrounding the chip. The simplest solution to this problem is to leave one of
the inputs unbonded. Since the input circuits are emitter followers, the circuit
will still work properly when one input is unconnected. This is what was done
for the amplifier used in the experiments in Chapter 7. When this is done,
if the full amplifier gain is desired, then the DC offset error reduction circuit
should be turned on, and AC coupling should be used when connecting to the
one input.
• VEE must be decoupled on the top layer of the board within a few millimeters
of the chip. When this is not done, the gain of the amplifier decreases by
several decibels above 500 MHz. An 0402 package style 1 nF capacitor was
used to decouple VEE for the amplifiers tested in this thesis.
Appendix G
Description of Equipment Used for COSSB
Experiments
Table G.1 lists the major equipment used in the COSSB experiment. It does not
include several DC power supplies that were needed to power all of the parts. It also
does not include several attenuators that were used to provide the right signal levels
to the modulators, the HT IC, and the logarithmic amplifier IC. Figures G.1- G.3
show pictures of the 10 Gb/s optical experiment setup.
It was necessary to align the delays of the signal going to the phase modulator
and through the fiber to the intensity modulator, and of the signal being applied to
the intensity modulator. The output of the phase modulator had eighty centimeters
of fiber, and the input to the intensity modulator had two meters of fiber. The
JCA amplifier had 400 ps of delay. As a first attempt at matching the delay of the
intensity and phase modulation paths, cables were chosen connecting to the input
of the JCA amplifier whose total length were equal to the length of the fiber whose
delay was attempting to be matched, 2.8 m. It was observed that when the delay
through the intensity modulation path was approximately 1 ns or larger either too
big or too small, the resulting modulated optical power spectrum had nulls in it at
several frequencies where the excess phase difference caused components of the two
sidebands to interfere destructively. Line stretchers were used to tune the delay in
600 ps ranges. As the delay of the two paths began to align, the nulls became fewer
and fewer, until single sideband modulation was achieved. The delay of the cables
connecting the pattern generator to the JCA amplifier were measured to be 15.34 ns.
Appendix G 183
Tab
leG
.1:
List
ofm
ajo
req
uip
men
tuse
din
CO
SSB
exper
imen
ts.
Nam
eM
anufa
cture
rPar
tSer
ial
TR
Lab
sA
sset
Num
ber
Num
ber
Tag
Num
ber
Optica
lP
has
eM
odula
tor1
Unip
has
eTel
ecom
munic
atio
ns
AP
EP
M-1
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3747
0320
7P
roduct
s
Tw
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nnec
tor
adap
ters
2U
nknow
nN
one
Non
eN
one
for
phas
em
odula
tor
10G
b/s
Chir
p-F
ree
LN
Sum
itom
oO
saka
T.M
XH
1.5-
1014
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16-0
083
Non
eIn
tensi
tyM
odula
tor
Cem
ent
Co.
,Ltd
.(0
2-04
6-85
10)
Tw
oop
tica
lpol
ariz
atio
n3
TR
Lab
sdes
ign
Non
eN
one
Non
ead
just
ers
1550
nm
Nar
row
Lin
ewid
th4
TR
Lab
sD
esig
nN
one
Non
eN
one
Las
er
Lig
htw
ave
Multim
eter
and
Hew
lett
Pac
kard
8153
Aan
d29
46G
1020
240
086
Pow
erSen
sor
Module
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Appendix G 184
List
ofM
ajo
rE
quip
men
tU
sed
inC
OSSB
Exper
imen
ts(c
ontinued
).N
ame
Man
ufa
cture
rPar
tSer
ial
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Lab
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sset
Num
ber
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ber
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ber
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eA
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one
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etec
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icon
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orD
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e
Appendix G 185
List
ofM
ajo
rE
quip
men
tU
sed
inC
OSSB
Exper
imen
ts(c
ontinued
).
1.E
stim
ated
ratings
bas
edon
curr
ent
JD
SU
nip
has
eA
PE
phas
em
odula
tors
:20
0m
Wm
axim
um
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lin
put
pow
er,27
dB
mm
axim
um
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pow
er,V
πat
DC
=6
V,V
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=11
V.N
odat
ash
eet
isav
aila
ble
for
this
phas
em
odula
tor.
2.T
he
phas
em
odula
tor
optica
lco
nnec
tors
are
larg
erth
anst
andar
dP
C/F
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nnec
tors
,an
dan
adap
ter
must
be
use
d.
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ach
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ariz
atio
nad
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nta
ins
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AP
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unja
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edfive
met
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per
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tnum
ber
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lase
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idth
isap
pro
xim
atel
y6.
5M
Hz.
Appendix G 186
Polarization Adjuster forIntensity Modulator
Cable to IntensityModulator
APC/FC to PC/FC Patch Cable
1/64 Clock Output forTriggering HP Oscilloscope
Micropositioner HT in TestFixture
GSGSG WaferProbe
CapacitorsBlocking
Line Stretchersfor HT Input
PatternGenerator
Laser Microscope
Attenuator
Figure G.1: 10 Gb/s optical experiment setup using only HT, Part 1 of 3.
PSPL 5828Amplifier
PSPL 5865Amplifier
BlockingCapacitor Modulator
APE PhaseAttenuator
Figure G.2: 10 Gb/s optical experiment setup using only HT, Part 2 of 3.
Appendix G 187
FFP TunableFilter
Optical Power MeterWith Analog Output
Polarization Adjuster forFFP Tunable Filter
Variable OpticalAttenuator
IntensityModulator
APC/FC to PC/FC Patch Cable
OpticalIsolator
LeCroy Oscilloscope(Not Shown)
Analog Output to
BiasTee
JCA Amplifier
Attenuator
Figure G.3: 10 Gb/s optical experiment setup using only HT, Part 3 of 3.
Circuit Board for Setting Log AmplifierDC Offset
LogarithmicAmplifier
Mini−CircuitsFilter
Figure G.4: 5 Gb/s optical experiment setup using HT and logarithmic amplifier,Part 1 of 1.
Appendix G 188
Other delay figures include 400 ps from the PSPL 5865-107, 240 ps from a PSPL
5828, 200 ps from the probe tips on the input and output of the HT, and 200 ps
from the HT itself. Based on the above information, the delay through the 2.8 m of
fiber was approximately 14 ns, corresponding to a propagation velocity in the fiber
of 2 × 108 m/s.
In the above discussion, it was described how the phase of the intensity modu-
lation signal was adjusted until single sideband is achieved. It is critical to know
whether to expect an upper sideband and lower sideband signal. If the HT signal
is 180 degrees out of phase at mid-band, the resulting optical signal will have good
cancellation of the unwanted sideband at mid-band frequencies, but mediocre can-
cellation at frequencies above and below this. This will still look like pretty good
single sideband, and the only way to know that it is off by 180 degrees is if one
knows which sideband they are expecting to be suppressed. As mentioned in Sec-
tion 2.4.1, the signal will be lower sideband if the HT signal is in phase with the
intensity modulation signal, and will be upper sideband if it is 180 degrees out of
phase either due to excess phase shift or due to the use of inverting amplifiers. As
well, an upper sideband signal in the wavelength domain is a lower sideband signal
in the frequency domain. In fact, there are several things that can cause a signal to
change from lower to upper sideband, including:
• If one signal from the pattern generator is used to drive the intensity modulator,
and the logical complement from the pattern generator is connected to the HT.
• If any inverting amplifiers are used, such as the PSPL 5828.
• If the intensity modulator is biased for inverting modulation, such that when
the electrical signal swings high, it extinguishes the optical intensity.
Appendix G 189
• If any inverting combination of HT and logarithmic amplifier inputs and out-
puts are used.
• If the down slope of a triangle wave is used to sweep the FFP optical filter
instead of the up slope.
During the COSSB experiments in this thesis, the signal was always predicted to
be either lower or upper sideband before trying to equalize the delay of the phase
modulation signal, but either type of signal was generated depending on how many
PSPL 5828 inverting amplifiers were used. It is noted that optical USB, which
is LSB in the frequency domain, must be transmitted if microstrip post detection
equalization is to be used. This ensures that the microstrip will equalize the phase
distortion caused by fiber dispersion [7]. If optical LSB is transmitted and microstrip
equalization is attempted, the phase distortion due to fiber dispersion will be made
worse, and the equalization will fail.
In addition to having correct phasing, the question of how much voltage should
be used to drive the phase modulator arises. In general, as the voltage applied to
the phase modulator is increased from a low level to the optimal level, the signal
will go from DSB to SSB. If the voltage applied to the phase modulator is increased
even further, the desired sideband will appear distorted, and both sidebands will rise
in power with increasing applied voltage to the phase modulator. The optimal level
appeared to be in the 4-6 Vpp range for most tests. Since this signal is the amplified
HT output, however, the RMS voltage of the signal applied to the phase modulator
will only be approximately one volt or less. Ideally, it would be known how much
voltage is needed to achieve one radian of phase shift, but this was not known for
the modulator used.
Table G.2 shows the measured power readings versus applied voltage for the
Appendix G 190
Table G.2: Power characteristic of the Sumitomo intensity modulator.
Applied Voltage (V) Optical Output Power (dBm)
0.0 -27.6
1.0 -29.0
2.0 -31.4
3.0 -36.3
4.0 -45.8
4.3 -47.7
5.0 -39.6
6.0 -33.3
7.0 -30.0
8.0 -28.2
9.0 -27.2
10.0 -27.0
Sumitomo intensity modulator. This test was performed several times during the
OSSB experiment in order to check for the most linear bias points of the modulator.
For example, this table shows that approximately 1 V is a linear inverting bias point,
and 7.0 V is a linear non-inverting bias points. The choice of bias point was always
confirmed experimentally by measuring the detected eye diagram. The absolute
power readings in the table are the power of the laser after it passes through the
Sumitomo modulator, several connectors, and a 25 dB attenuator.
DC blocking capacitors were placed on the outputs of the pattern generator in
order to reduce the possibility of damaging it. A DC offset had to be added to
the logarithmic amplifier input through a bias tee so that the logarithmic amplifier
output waveform was similar to the logarithm of the optical signal envelope. A
schematic of the breadboard tuning circuit used to tune the DC offset is shown in
Figure G.5.
Appendix G 191
VEE
150Ω
5 kΩ
100Ω
5 kΩ
Vout
Figure G.5: Logarithmic amplifier DC offset tuning circuit.