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A Unified Approach to Design Distributed Amplifiers
Rasit Onur TopalogluPhD. Student
Limitations with Classical Amplifiers
G.BW gm/C •Combining amplifiers in parallel does not help as it also increases the total C
•Gain-bandwidth product is proportional to transconductance over capacitance
•High Gain-bandwidth product is the aim in amplifier design
Tying Amplifier to Device Physics
•These capacitances can be incorporated in or counted as capacitors in a
transmission line
•Input and output have capacitive impedances
Cgs Cds
G
S
D
Basic Transmission Line•A low-pass transmission line can easily be constructed of inductors and capacitors
..
Principle of Distributed Amplification
..
•Couple two transmission lines by amplifiers
..RFin
RFout
Termination of Unwanted Waves
..
..
•There will be forward and backward propagating waves at nodes
RFin
RFout
•Terminate unwanted ones using a load on both lines
Exploitation of Amplifier Capacitances
..
..
•Input and output capacitances of an amplifier can be used to replace capacitors
RFin
RFout
•Even a single transistor amplifier satisfactory
gate line
drain line
Design Considerations for Transmission Lines
•Each lines designed to have a cut-off frequency larger than targeted operation frequency of amplifier by a safe margin
fc=1/( LC)
Zo= L/C
m-derived Sections for a Better Matching
•LC sections (constant-k transmission lines) matched to load using an m-derived section to provide constant Z over a wider range
•m=0.6 is identified as a practical rule of thumb value
m-derived vs. Constant-k Low-pass T-section
•m=1 corresponds to constant-k
m-derived vs. Constant-k Line Z over Frequency
•m=1 corresponds to constant-k
Phase Matching of Lines
•Cgs~4Cds for a transistor
•If L chosen to be constant, C matching required on gate and drain lines for a better amplifier response
•Either add additional C in parallel with drain to increase it=> provides higher BW•Or add additional C in series with gate to reduce it=> provides higher gain
Staggering to Avoid Gain Peak near Cut-off
•Staggering is introducing a deliberate mismatch between gate and drain lines to avoid a peak near line cut-off frequency
•Drain line cut-off chosen as ~0.7 times gate line cut-off
Number of Sections•Increasing number of sections increases gain linearly as opposed to quadratic increase in cascade amplifiers
•Line losses and parasitics prevent an infinite increase
•Optimal number of stages can be explored analytically or by simulation
Ag=1/4 x (Rg2Cin2Zo)
nog=1/2 x Ag
[A monolithic GaAs 1-13GHz traveling wave amplifier, Y. Ayasli, et. al.]
Design Example
[SOI CMOS Traveling Wave Amplifier with NF below 3.8 dB from 0.1-40 GHz, F. Ellinger]
Design Example
Design Example
Design Example
freq (100.0MHz to 100.0GHz)
S(1
,1)
Input Reflection Coefficient
2E10 3E10 4E101E10 5E10
-90
-80
-70
-60
-50
-40
-30
-100
-20
freq, Hz
dB
(S(1
,2))
Reverse Transmission, dB
Design Example
1E9 1E101E8 6E10
-60
-50
-40
-30
-20
-10
0
10
-70
20
freq, Hz
dB
(S(2
,1))
Forward Transmission, dB
freq (100.0MHz to 100.0GHz)
S(2
,2)
Output Reflection Coefficient
SOI CMOS Noise Figure and Gain
20 40 600 70
-60
-40
-20
0
-80
20
freq, GHz
dB(A
C.o
ut)-
dB(A
C.in
)
200 40
0
10
freq, GHz
NFm
in
PHEMT Noise Figure and Gain Technology ComparisonSOI CMOS 90nm, 17mA, 2V
Cgs=0.06pF
Cds=0.015pF
PHEMT
40mA, 2V
Cgs=0.27pF
Cds=0.030pF
Higher capacitance values makes possible to use smaller inductors for same cut-off frequency
Lossy Inductor Model:
Inductor Q assumed 20 @ 1GHz with a parasitic series resistor of 10 and Q being directly proportional to frequency
Design Considerations for PHEMT
•Cds used to decrease the high ratio difference between Cgs and Cds; thereby obtaining a gain with less ripple.
•Compromising high frequency gain, a smoother response is obtained
•Usage of series Cgs would deteriorate low frequency response
•Same inductor value used for both gate and drain lines
PHEMT Gain&Noise Optimization
•Goals are set for gain and noise
•Random optimization used
•Only inductor used for the optimization value; thereby keeping system specific termination and source resistors intact
PHEMT Optimization Results
With some sacrifice in gain ripple, noise figure has been significantly improved and circuit operates up to 47GHz
After optimization
Usage of Transmission Lines
•Using Richard’s transformation, inductors can be replaced by transmission lines.
•Choosing an electrical length of 45 and a reference cut-off frequency equal to the gate line, optimization gave a Zo of 30.6 and an operation range of up to 57 GHz for noise considerations
After optimization
Conclusions
•Distributed amplifiers, an ancient field of study, will continue evolving as a good field to work in
•Broadband techniques will not be able to outdo distributed amplifiers
•60GHz low noise amplifiers for optical circuits are almost here
