A Microwave Nonlinear Network Analyser

THE UNIVERSITY OF CALGARY

A Microwave Nonlinear Network Analyser

by

Robert Walton

A THESIS

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AUGUST, 2000

O Robert Wdton 2000

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Abstract

There has been a dramatic increase in the demand for wireless communication services.

To be successful, a cell phone system must be cost effective and spectrally efficient, and

provide users with long battery life. To meet these demands, the nonlinear behaviour of a

system's microwave components cannot be ignored. This thesis presents the development

and verification of a Nonlinear Network Analyser (NNA) that looks at the amplitude and

phase of the harmonics generated by a nonlinear microwave network up to 18 GHz. There

is no commercial tool that can do this, leaving designers with an incomplete view of how a

network is working. One use for the NNA is to measure the voItage and current waveforms

at a transistor, giving a designer a tool to tune the operation of power amplifiers. The NNA

also provides information useful to the development of more accurate nonlinear models,

which can reduce design time.

Acknowledgments

I would like to acknowledge my supervisors Dr. John McRory and Dr. Ron Johnston

for their help. I am especially grateful to John for the many hours he spent teaching me

about RF when I first started this project Thanks for the time you spent with me talking

over problems, and introducing me to nonlinear RF analysis. And thanks for all your help

with writing and editing this thesis.

Thanks to all the staff and students at TRLabs. I don't think there is a single person who

hasn't helped me in some way or another. Thanks specifically to Rob Randall, Sean Hum

and Carl Conradi for the many fruitful discussions and your help tinkering in the lab.

Thanks to Anthony Lo for all the computer help and to Grant McGibney who explained

everything there is to know about fast Fourier transforms. Thanks to John McRory and

Chris Holdenreid for designing and laying out the test fixture for the MRF284.

From the University of Calgary, thanks to John Shelley and Ed Evanik for milling cir-

cuit boards. Thanks to Frank Hickli and Pat Wals-h for giving me free rein in the machine

shop, and showing me how everything works.

Thanks to George Squires, LeiIa Southwood and T u b s for providing such a great

work atmosphere. Although the work on this thesis is quite specific, 1 feel that the open

atmosphere at TRLabs has let me learn about many aspects of the broad telecomrnunica-

tions field. This thesis would have been impossible to complete without the equipment sup-

plied by TRLabs' sponsors.

Finally, thanks to TRLabs, NSERC and the University of Calgary for the financial sup-

port that made my studies possible.

For

Cindy and for my family.

Thanks for all the support.

Contents

. * . . . . . . . . . . . . . . . . . . . . . . . . . . Approval Page. . . . . . . . .. 11

.-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abstract.. 111

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. iv

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dedication.. v

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents vi

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Tables ix

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Figures. x --. . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols and Abbreviations xlrl

1 Introduction 1

2 Nonlinear Network Measurement 6

2.1 Measurement of Microwave Networks. . . . . . . . . . . . . . . . . . . . . 7

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Nonlinear Effects 1 1

. . . . . . . . . . . . . . . . . . . . . 2.2.1 Microwave Power Amplifiers 12

. . . . . . . . . . . . . . . . . . . . . 2.2.2 Microwave Signal Distortion. 17

. . . . . . . . . . . . . . . . . . . . 2.3 Nonlinear Network Analyser Overview 20

. . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Phase Measurement 2 1

. . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Sampling The Waveforms 22

3 NNA Implementation 24

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 System Overview 24

. . . . . . . . . . . . . . . . . 3.1.1 Hardware Description and Operation 25

3.1 -2 Systematic and Random Errors . . . . . . . . . . . . . . . . . . . . . 27

3 -2 Removing Errors With Calibration . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.1 TheSystemErrorModel . . . . . . . . . . . . . . . . . . . . . . . . 30

3 .2.2 Error Correction Matrix . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2.3 Generating the Error Models . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Linear CaIibration Technique . . . . . . . . . . . . . . . . . . . . . . . . . 36

3 .3.1 SOLT Calibration Mathematics . . . . . . . . . . . . . . . . . . . . 36

3 .3.2 SOLT Calibration Standards ModeUing . . . . . . . . . . . . . . . . 38

3.4 Absolute Calibration Technique . . . . . . . . . . . . . . . . . . . . . . . . 41

. . . . . . . . . . . . . . . . . . . . 3.4. 1 Absolute Amplitude Calibration 41

. . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Absolute Phase Calibration 42

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 De-embedding .. 44

4 NNA Verification 47

4.1 Flat Group Delay Assumption . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2 Timebase Error Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Linear Calibration Verification . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.4 Schottky Diode Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 59

. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Fixture Extraction 60

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 DiodeMeasurements 63

. . . . . . . 4.4.2.1 Comparison of Measured and Modelled Waves 63

4.4.2.2 Voltage and Current Measurement . . . . . . . . . . . . . . 65

. . . . . . . 4.4.2.3 Comparison with Direct VoltageMeasurements 67

vii

5 Power Transistor Measurements 69

5.1 The Fixture Design . . . . . . . . . . . . . . . . . .. . .. . . . . . . . . . 70

5.2 Fixture Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2.1 Fixture Model Extraction . . . . . . . . . . . . . . . . . . . . . . . . 74

5.2.2 Fixture Parameter Verification . . . . . . . . . . . . . . . . . . . . . 77

5.2.3 Calibration and Fixture Deembedding Verification . . . . . . . . . . 80

5.3 Transistor Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.1 Comparison with Model .. . . . . . . . . . . . . . . . . . . . . . . 84

5.3.2 Matching with Tuners or Loadpull System . . . . . . . . . . . . . . 87

5.3.3 Verification of Waveforms with Ohm's Law . . . . . . . . . . . . . 90

5.4 Proposed Amplifier Tuning Technique . . . . . . . . . . . . . . . . . . . . 92

6 Conclusion 96

6.1 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

A NNA LabView Software Guide 102

References 117

viii

List of Tables

Chapter 5

5.1 Scattering parameters of through with amplifier removed . . . . . . . . . . 81

5.2 Scattering parameters of through with amplifier connected . . . . . . . . . . 82

5.3 ExtractedZlOd and measuredZload at different power levels . . . . . . . . . 91

List of Figures

Chapter 2

. . . . . . . . . . . . Voltage and current definitions of a two port network 8

. . . . . . . . . . . . Travelling wave and scattering parameter definitions 9

. . . . . . . . . . . . . . A typical single-stage microwave power amplifier 12

. . . . . . . . . . . . . . . . Typical FET class-A power amplifier load line 13

. . . . . . . Output against input power for linear and nonlinear amplifiers 14

. . . . . . . . . Ideal voltage and current waveforms for a class-B amplifier 15

. . . . . . . Output spectrum of a nonlinear amplifier with a two tone input 17

Intermodulation distortion of a typical digital communication signal . . . . 18

. . . . . . . . . . . . . . . . . . . . . . . . . . . . NNA system schematic 20

Chapter 3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 NNA system 25

3.2 Picture of NNA showing a brass fixture and the oscilloscope inputs . . . . . 27

3.3 Signal flow graph describing one half of the NNA system . . . . . . . . . . 31

. . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Simplified physical model 32

3.5 Greatly simplified error model for one measurement port . . . . . . . . . . 33

3.6 System error model for both measurement ports . . . . . . . . . . . . . . . 33

3.7 Definitions for a standard . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.8 A device in a fixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

. . . . . . . . . . . . . . . . 3.9 Signal flow graph model for fixture extraction 45

Chapter 4

Amplitude and phase deviation of the measured step from being ideal . . . 50

Oscilloscope phase error from Jan Verspecht's dissertation [8] . . . . . . . 52

Repetitive waveform being sampled and then reconstructed . . . . . . . . . 53

Measured timebasedistortion . . . . . . . . . . . . . . . . . . . . . . . . . 54

. . . Spurious tones caused by timebase distortion in a sampled 3 GHz tone 55

Connection of splitter for linear calibration verification . . . . . . . . . . . 56

Measured Sl phasors from 200 MHz to 4 - 4 0 MHz . . . . . . . . . . . . . 58

Measured SZI phasors from 200 MHz to 4400 MHz . . . . . . . . . . . . . 58

Schematic of the diode mounted in the test fixture . . . . . . . . . . . . . . 59

Mode1 for the low reflection diode fixture . . . . . . . . . . . . . . . . . . 60

Measured and simulated waves at the diode . . . . . . . . . . . . . . . . . 63

Voltage across the diode as the input voltage is swept . . . . . . . . . . . . 66

Current through the diode as the input voltage is swept . . . . . . . . . . . 66

Direct voltage measurement and NNA measurements . . . . . . . . . . . . 67

Chapter 5

5.1 An MRF284 mounted in the fixture . . . . . . . . . . . . . . . . . . . . . 71

5.2 NNA system used to measure MRF284 . . . . . . . . . . - . . . . . . . . 73

5.3 Model used to describe the input and output fixtures . . . . . . . . . . . . . 74

5.4 Comparison of S2* amplitude of measured and extracted fixtures . . . . . . 75

5.5 Comparison of SZI phase of measured and extracted fixtures . . . . . . . . 76

xi

5.6 Root choice of A2* parameter . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.7 Extracted real and imaginary output impedance . . . . . . . . . . . . . . . 79

5.8 Extracted real and imaginary input impedance . . . . . . . . . . . . . . . . 79

5.9 Modelled and measured drain waveforms . . . . . . . . . . . . . . . . . . 85

5.10 Modelled and measured gate waveforms . . . . . . . . . . . . . . . . . . . 85

5.1 1 Load line at the package edge . . . . . . . . . . . . . . . . . . . . . . . . 86

5.12 Tuned and un-tuned external Ioad lines . . . . . . . . . . . . . . . . . . . . 88

5.13 Tuned and un-tuned internal load lines . . . . . . . . . . . . . . . . . . . . 88

. . . . . . 5.14 Simplified diagram showing the drain voltage. current. and load 90

5.15 Drain waveforms with two different load impedances . . . . . . . . . . . . 94

5.16 Gate waveforms with two different load impedances . . . . . . . . . . . . 94

Appendix A

. . . . . A 1 NNA interface hierarchy showing panel names and describing inputs 103

xii

List of Symbols and Abbreviations

Chapter 1

CDMA Code Division Multiple Access

LDMOS Laterally Diffused Metal Oxide Semiconductor

NNA Nonlinear Network Analyser

Chapter 2

ai

b i

dB

DC

f 1

f2

FFT

forward travelling voltage wave at port i

reverse travelling voltage wave at poa i

logarithmic ratio of two powers; 1Olog(powerl/power2)

Direct Current

lower frequency for two tone test

upper frequency for two tone test

Fast Fourier Transform

current entering drain

current entering port i

current entering load

thousands of symbols per second

Radio Frequency

scattering parameter; reverse wave at port y over forward wave at port x

drain bias voItage (DC)

voltage from gate to ground

gate bias voltage @C)

voltage across port i

voltage across load

internal voltage generated by source

system reference impedance; normally 50 C2

load impedance offered to amplifier

source output impedance; normally 50 L2

Chapter 3

S

aim measured forward wave at pea i with standard s connected

bL measured reverse wave at port i with standard s connected S

foward wave at port i calibration plane with standard s connected

b f reverse wave at port i calibration plane with standard s connected

forward travelling wave at port i calibration plane

aid forward travelling wave at port i device plane, within fixture

aim measured forward travelling wave at port i

asource forward travelling wave available fiom source

*YX scattering parameter describing port one fixture half

bic reverse travelling wave at port i caIibration plane

bid reverse travelling wave at port i device plane, within fixture

him measured reverse travelling wave at port i

Brx scattering parameter describing port two fixture half

c speed of light in a vacuum

DUT

GPIB

port one error model scattering parameter

one way loss of line in calibration standard, measured in dB at I GHz

dB with respect to 1 mWatt

Device Under Test

port two error model scattering parameter

relative dielectric constant of line in calibration standard

absolute phase calibration parameter

phase from poa one calibration plane to a[ osciLIoscope input

phase from port one calibration plane to bl oscilloscope input

reflection coefficient seen by DUT due to measurement hardware

reflection coefficient of load standard

reflection coefficient of open standard

reflection coefficient of standard number x

reflection coefficient of oscilloscope channel one input

reflection coefficient of oscilloscope channel two input

reflection coefficient of short standard

reflection coefficient of source

General Purpose Interface Bus

giga samples per second

gain of oscilloscope channel one input

gain of oscilloscope channel two input

measurement hardware coupling gains

absolute amplitude calibration parameter

length of line in calibration standard

National Institute of Standards and Technology

incident power measured by power meter in dBm

P~wattsl

R

Rloss

RE

R,,,

SOLT

To ffset

V ~ m

zc 2 .

Chapter 4

incident power measured by power meter in watts

resistance of Ioad standard

effective resistance of the calibration standards' line

row r, column c, of correction matrix

row r. column c, of correction matrix normalised with respect to R33

S hort-Open-Load-Through

one way delay of the calibration standards' line

peak incident voltage wave measured by the power meter

impedance due to fringing capacitance of open standard

impedance due to inductance of short standard

frequency difference between samples

number of frequency samples

estimated input fixture AZ1 scattering parameter

package capacitance between leads of diode package

phase delay of through fixture

frequency of nth sample

gallium arsenide

bondwire inductance of diode package

lead inductance of diode package

%xture group delay of through fixture

fn time delay between trigger and nth sample

o radian frequency

Chapter 5

$1

FET

r'10;ld

rs,,,

I

h

SMA

TRL

2 1

?2

z,,,

reflection coefficient of perfect through terminated with

FieId Effect Transistor

refl ection coefficient offered by NNA at port two calibration plane

reflection coefficient offered by NNA at port one calibration plane

length of quarter wave transformer

wavelena& of signal for quarter wave transformer

Sub Miniature type-A coaxial connector for DC-18 GHz signals

Through-Reflect-Line

impedance offered to quarter wave line

impedance looking into quarter wave line

impedance of quarter wave line

xvii

Chapter 1

Introduction

The last decade showed a dramatic increase in the demand for wireless communication

services. To meet this demand for system capacity, cell phone systems must use the avail-

able spectrum very efficiently. Unfortunately, adjacent channel interference limits how

closely communications signals can be packed together in the frequency domain. If a com-

munication signal on a carrier is amplified by a nonlinear power amplifier it will spread out

in frequency and will potentially interfere with adjacent channeIs. Guard bands, unused

areas of spectrum, separate the bands allocated to different channels, so that signals do not

overlap when they spread out. To reduce the size of this wasted spectrum the nonlinear dis-

tortion from the amplifier which results in adjacent channel interference must be very

small.

Unfortunately, power amplifiers must be operated in nonlinear regions to maximize

their efficiency. Up to two-thirds of the power used by a cell phone in talk mode, is used by

the power amplifier which amplifies the signal before it is sent to the antenna. An attempt

to operate an amplifier in a more linear region unfortunately reduces it's efficiency, result-

Chapter 1 Introduction 2

ing in a shortened battery life. For the power amplifiers used in base stations, inefficiency

results in waste heat. This heat must be removed using large heat sinks and cooling fans, or

it can result in decreased device life. More efficient power amplifiers are cheaper to buiId

and to maintain.

Another issue which makes it very. difficult to amplify modem communication signals

linearly is their digital nature. A Code Division Multiple Access (CDMA) signal is quite

wideband, and can have very high peak to average power ratios. The power in these signals

is very bursty, so, although they may have an average output power of about 25 W, for shoa

periods of time the output power can be 250 W. To manufacture an amplifier that can pro-

duce signals like these without producing nonlinear distortion is very expensive.

The above factors all indicate that nonlinear effects in cell phone systems, particularfy

in power amplifiers, cannot be ignored. A 2 GHz signal amplified by an efficient, nonlinear

power amplifier, can contain harmonics above 10 GHz. Unfortunately, there is no commer-

cial tool which can look directly at the broadband waveforms produced by nonlinear micro-

wave networks. A spectrum analyser can measure, with limited accuracy, the amplitude of

these harmonics in the frequency domain, but cannot measure the phase. A linear network

andyser can measure the amplitude and phase of a single tone entering and leaving a net-

work. However, a linear network anaIyser assumes that the network is linear. It gives no

indication of the actual shape of the waveforms; it assumes they are single sinusoids. This

is, of course, an incredibly useful tool for characterising linear networks such as filters or

for characterising the small signal behaviour of amplifiers. The best way to look at the

shapes of the waveforms in a nonlinear microwave network is actually to use a simulator,

which uses nonlinear models of the network's components to predict the network's voltage

and current waveforms. However, nonlinear models are difficult to generate because it is

not possible to fully measure the output of a nonlinear device. These models are often based


on very large sets of data measured with a linear network anaIyser with different device bias

conditions and input powers. There are many techniques for designing nonlinear circuits

with limited information about how they are operating. However, not having aII the infor-

mation is obviously a big disadvantage and greatly hinders the design process. An instru-

ment that can N l y characterise the microwave signals entering and leaving a device would

increase model accuracy and allow new insight into nonlinear circuit operation.

In this thesis the development and verification of a Nonlinear Network Analyser (NNA)

is presented. This is a system that stimulates a two port microwave network with a signal,

and then looks at the amplitude and phase of the voltage and current waveforms at the net-

work edge. In the time-domain, it gives the actual shape of the waveforms; it does not

assume they are sinusoids as a linear network analyser does. The goal of the research under-

lying this thesis was to build and verify the operation of an NNA capable of measuring har-

monics up to 18 GHz. This tool will Iikely be used b y students for device modelling and

microwave circuit design projects.

NNAs are not comrnercia~ly available, although several prototypes with limited capa-

bilities have been built [I-31. A simple but versatile design, based around a wide bandwidth

sampling oscilloscope, was proposed by Jan Verspecht working for Hewlett-Packard [4].

This thesis presents an implementation of an NNA similar to Jan Verspecht's. A modified

calibration routine is used that assumes the sampling heads of the wide bandwidth oscillo-

scope have flat group delays. This assumption simplifies the calibration routine, and

reduces the cost of the system greatly. The NNA is a rack of mainly commercially available

equipment. A computer controls the equipment and provides a graphical user interface that

automates almost every aspect of the measurement process.

Chapter 2 contains a discussion about microwave network measurement, nonlinear

devices and the theory behind the NNA. This chapter includes an explanation of what the


NNA is designed to do, and why it is useful. The reasons why it is difficult to look at micro-

wave-frequency waveforms are discussed and a technique to determine the voltage and cur-

rent waveforms by measuring travelling waves is presented. The operation of microwave

power amplifiers and the various nonlinear effects discussed in the introduction are

explained. FinaIIy, with the need to measure the nonlinear waveforms generated by net-

works established, the NNA measurement system is introduced-

Chapter 3 focuses on how the NNA works in detail. The NNAs hardware and operation

are presented. Sources of measurement error and some techniques used to reduce them are

examined, The buk of this chapter deals with calibration, the removd of systematic errors

caused by the measurement hardware. The error model used to remove the systematic errors

in a measurement is derived, and a technique for determining these parameters is presented.

Some devices must be put in a fixture before they can be connected to the NNA. De-embed-

ding, the process of removing the effects of a fixture from a measurement, is discussed.

In Chapter 4 results that verify the operation of the NNA are presented. This is difficult,

since there is no similar system that looks at waveforms directly to compare measurements

against. The procedure used was to test any assumptions made, each component part of the

calibration routine, and finally the entire NNA. The flat group delay assumption used to

simplify the caIibration routine is validated- A measurement of the timebase distortion of

the oscilloscope used in the NNA is presented. The effects of this error on a measurement

are shown and a technique for reducing the effects is discussed. Measurements of a spIitter

taken with the NNA are compared with measurements taken using a linear network ana-

lyser, to verify that the bulk of the calibration routine is working. Measurements taken of a

Schottky diode using the NNA are compared with waveforms predicted by a model to dem-

onstrate that the other calibration procedures are working correctly.


Chapter 5 is concerned with the measurement of a MotoroIa MRF284 Laterdly Dif-

fused Metal Oxide Semiconductor (LDMOS) transistor. Charactensing this device's non-

Iinear behaviour is greatly complicated by the low input and output impedances the device

must be offered to operate correctly. The goals of this chapter are to present techniques used

to measure low impedance devices, and to show that the effects of tuners, used to change

the impedances offered to the device, can be removed from measurements. The fixture

which was designed to offer the device low impedances is described, and the extraction

technique used to model the fixture is presented. Measurements taken of the device using

the NNA are compared with predictions from a model. An iterative design technique

method for building an amplifier using the NNA is proposed, and some measurements

which show its validity are presented.

Finally, Chapter 6 gives a brief summary of the work presented. Some possible future

research which could be performed using the NNA is also discussed.

Chapter 2

Nonlinear Network Measurement

In this chapter microwave network measurement, nonlinear devices and the theory behind

the Nonlinear Network Analyser (NNA) are discussed, An NNA measures the voltage and

current waveforms at a calibration plane. The NNA described in this thesis measures the

harmonics in a waveform up to 18 GHz. Although it has already been briefly discussed in

Chapter 1, this chapter contains an explanation of what an NNA is designed to do, and why

it is useful. In Section 2.1 reasons why it is diff~cult to look at waveforms at these rnicro-

wave frequencies are discussed, and a technique to determine the voltage and current wave-

forms by measuring traveliing waves is presented. In Section 2.2 some nonlinear effects

seen in power amplifiers are described. It will be explained why amplifiers cannot always

simply be operated in a linear way- The effects of nonlinear ampIification on digital com-

munication signals are also discussed, In Section 2.3 the NNA measurement system is

introduced, and some fundamental issues related to waveform sampling are presented.

2.1 Measurement of Microwave Networks 7

2.1 Measurement of Microwave Networks

At low frequencies, an oscilloscope probe can be used to look at the voltage and current

waveforms in a circuit directly. At high frequencies it is not that simple because attaching

a probe affects a circuit's operation, and because the voltage and current waveforms in a

network are a function of position. In this section these problems are discussed and a tech-

nique to measure waveforms in microwave networks is explained.

At microwave frequencies it is not possible to probe a circuit without affecting its oper-

ation. Microwave circuits are very sensitive to any change in either the input or the output

impedance they are offered. Even the effects of attaching a probe could greatly affect the

circuit's operation, invalidating any measurements taken.

The distributed nature of microwave circuits means that the voltage and current on a

section of transmission line are a function of distance. Suppose a 1 GHz tone is connected

at one end of a transmission line. The wave travels at, or under, the speed of light depending

on the dielectric constant of the medium. Assuming free space, the voltage 6 inches down

the line was actuaIIy generated by the source 0.5 ns eariier. If the voltage is at the peak of

its positive cycle as the wave enters the line then 6 inches away the voltage will still be at

the peak of its negative cycle. Because the wavelength of the signals used in microwave

circuits is of the same order as the size of the circuits, microwave circuits are referred to as

being distributed. For low frequency circuits, components can be thought of as being

lumped together; only the topology of their connections is important, since the voltage

anywhere along a connecting line is approximately the same. If voltage and current

waveforms are measured in a microwave circuit or system they must be defined at a certain

cross-sectional reference plane.


Both the impedance problem and the measurement reference plane problem can be

addressed if the device or system under test is treated as a two port network. Figure 2.1

shows how reference points are defined at the input and the output planes of a two port net-

work. In the diagram, v represents voItage, i represents current, and the subscripts indicate

port numbers.

Figure 2.1: Voltaze and current definitions of a two port network

One definition of a linear network is simply that it adds no new tones to a signal. If a

sinusoidal voltage is applied to port one, then a sinusoidal current will flow into port one,

and the voltage and current at port two will also be sinusoidal, all at the same frequency as

the applied voltage signal. There are a number of different Linear models that can be used

to describe a two port network in the frequency domain using four phasors at each fre-

quency of interest. These circuit models, which relate voltage and current, are determined

by shorting or leaving open one of the ports. These models can be used to indirectly deter-

mine the current from known voltages. However, this cannot be done at Radio Frequencies

(RF), firstly because it is very difficult to build a short or an open at RF, but also because

many microwave circuits will not work if they are offered a short or an open. In general

linear techniques for determining the current at each port from measured voltages are

invalid when dealing with nonlinear networks.


Instead of measuring the voltage and current waveforms in a microwave network

directly, travelling voltage waves are measured and modelled. These travelling waves are

defined with reference to Figure 2.2 and are represented by complex phasors describing

a1 Two Port Network

61 a2

Figure 2.2: Travelling wave and scattering parameter definitions

their amplitude and phase. The a terms represent forward travelling voltage waves and the

b terms represent reverse travelling voltage waves. The subscripts denote the port number.

The S parameters are scattering parameters that model the ratios of the travelling waves at

a single frequency assuming that the network is Iinear and terminated with a defined refer-

ence impedance. The scattering parameters are defined as

s,, = 51 s,, = 51 a~ at = o a2 a, = o

Travelling waves behave like light waves. If a light ray is incident to a block of glass, some

light will be reflected back, and some will be transmitted through. The phasor a1 describes

the phase and amplitude of a tone incident to a two port network, bl describes the tone that

is reflected, and b2 describes the tone that is transmitted.


To visualise how travelling waves relate to voltage and current, imagine a sinusoidal

voltage source injecting a signal into one end of a transmission line. This voltage results in

a travelling wave moving along the line toward an impedance terminating the other end.

Coaxial lines are easily built with an impedance of 50 R, so this value is often defined as

the reference impedance. If the impedance at the end of the line is 50 R, the same as the

reference impedance, all the power in the forward wave will be absorbed by the terminating

impedance, since there is no mismatch between the line and load impedances, and there will

be no reflected wave. However, if the load is a perfect short, all the power in the forward

wave is reflected, like light hitting a mirror. When light hits a mirror, the electric fields of

the incident and the reflected waves must add to zero at the mirror's sudace; the incident

and reflected waves must therefore have opposite signs. Similarly, when the forward wave

hits the short, the wave is inverted, or the phase changed by 180°, and it is returned as the

reflected wave. When the two voltage waves add at the short, they add out of phase giving

zero volts. Following the same reasoning, if the forward wave hits an open impedance, the

reflected wave will be reflected with no phase change. When the two travelling waves are

summed, the voltage at the open will actually be twice that of the voltage wave launched

into the line.

The voltage and current at a port can be calculated from the forward and reverse waves

using

where Zo is the reference impedance, and vi and ii are the voltage and current at port i

respectively. It is standard to normalize ai and bi with respect to the reference impedance,

2.2 Nonlinear Effects 11 - -

so that squaring them gives the the power in the forward and reverse waves respectively.

This thesis deals with the indirect measurement of the voltage and current through sampling

the travelling voltage waves. For these purposes it is best to leave the travelling waves un-

normalized. This way they can then be thought of as physical voltages moving down a line,

the sum of which, at any point, results in a real voltage.

The forward and reverse travelling waves are separated using directional couplers. As

will be discussed in Section 2.3, these waves can be sampled a distance from the device

being measured without affecting the impedances offered to the device. Due to the distrib-

uted nature of microwave circuits discussed above, these travelling voltage waves are a

function of where they are measured. A large part of this thesis deals with estimating the

waves at the network edge from the waves sampled a distance from it.

2.2 Nonlinear Effects

Linear microwave circuits can easily be modelled using the scattering parameters described

in Figure 2.2 and in (2-1). At each frequency of interest, four complex scattering parame- '

ters completely model a linear circuit. These scattering parameters can be measured

directly using a linear network analyser. AIthough very expensive, linear networks analys-

ers assume a device is linear; they will not measure the shape of the actual forward and

reverse waves, but assume they are all pure tones. In this section some nonlinear effects

which, it will turn out, can only be fully characterised using an NNA are explained.

Section 2.2.1 focuses on explaining why microwave circuits, specifically power amplifiers,

must sometimes be operated in regions where they behave in a nonlinear way. In

Section 2.2.2 the unwanted signal distortion which results from this nonlinear behaviour is

explained.

2.2 Nonlinear Effects 12

2.2.1 Microwave Power Amplifiers

Microwave signals are amplified by power amplifiers before being sent to antennas where

they are radiated into the air. Most of the signals are carrier tones modulated with informa-

tion which is relatively narrow band when compared with the carrier frequency. It is

assumed in this discussion that these signals can be treated as single tones; a pretty good

approximation to examine some nonlinear effects. Figure 2.3 shows a typical single-tran-

Output Match

Input Match

Figure 2.3: A typical single-stage microwave power amplifier

sistor microwave power amplifier. V', and V&, are the DC bias voltages at the gate and

drain respectiveIy. A voltage v,,,, is generated from a source which has an output irnped-

ance z,,,,. The input match is a circuit which takes the impedance offered by the source,

and changes it to an impedance seen by the gate of the device in order to minimize any mis-

match. The changing gate voltage vW sets up a changing current through the drain of the

device to ground. The drain DC bias inductor has a constant current flowing through it

which the load current iload and the drain current idrain must sum to. When the gate voltage

increases, i ~ , increases resulting in decreasing iIoad and a corresponding decrease in the

load voltage vload across the load impedance Zload-


A load line, shown in Figure 2.4, is used to show how V f i n and idrain are related. The

curved lines are DC bias curves. Each curve represents idfin as a function of v d ~ , , with

vp,, kept at a constant DC value. As vsk is increased, more current flows for a given v ~ , .

The thick line is the load line, which represents how VMn is a linear function of id- The

slope of the load line is determined by yoad. The plotted load line is that of a class-A ampli-

fier. The gate and drain DC bias voltages are chosen so that with no input voltage, the device

operates at the DC bias point indicated on the graph. Now, if a small input tone is applied,

the amplifier state is described by a point moving up and down the load line, only a very

small distance from the DC operating point. However, for the large gate voltage swing indi-

cated on the graph, the load line is compressed at each end. A certain incremental change

in vgate results in different changes in i&,, depending on where on the load line the tran-

sistor is operating. The current is clipped at the bottom as the device enters cutoff and the

current is clipped at the Ieft as the device leaves the saturation region, entering the triode

region.

~riode: Saturation 1 -- id rain

Figure 2.4: Typical FET class-A power amplifier load line

2.2 Nonlinear Effects 14 -- --

When the input to the device is small, the output is not compressed; the behaviour is

predominantly linear. However, when the input voltage increases and the full swing of the

Ioad line is utilized, the device enters what is called compression; the behaviour is now pre-

dominantly nonlinear. Figure 2.5 shows the output power at the fundamental frequency as

a function of the input power. For an ideal linear amplifier, the gain is constant so the power

1 dB Compression , 9' I

Nonlinear

Linear

- input Power (dB)

Figure 25 : Output against input power for linear and nonlinear amplifiers

curve is a straight line. However, the power in the fundamental of the output does not

increase linearly in a real amplifier. A point called the I dB compression point is defined as

the point where the gain has been compressed by 1 dB. If driven much beyond compression,

most devices will suffer junction breakdown or overheat, and can fail if not shut off quickly.

When the device nears compression, any data modulated onto the input tone will become

distorted, as discussed in Section 2.2.2.

So, knowing that this compression occurs, why is the power into an amplifier not simply

backed off so it always behaves linearly? This is done for low output power amplifiers

which are are often used in receivers, or used to drive power amplifiers. Power amplifiers

cannot always be backed off due to issues of efficiency and cost:


Modem digital communication signals have very high peak to average power ratios.

This means that the energy in the signal is not evenly distributed but has large spikes in the

time domain. A signal with a peak to average ratio of 10 dB that has an average power of

25 W, can have peak powers of up to 250 W for short periods of time. To make an amplifier

that could amplify signals like these linearly would be very expensive, since it must be

designed to amplify 250 W signals linearly.

The other issue that forces amplifiers to be operated nonlinearIy is efficiency. The effi-

ciency of an amplifier is a measure of how well it produces output power from the DC

power supplied to it. As discussed in Chapter 1, wasted power reduces battery life in mobile

phones and increases the cost of base station amplifiers.

Looking at Figure 2.4, the actual power delivered to the load is a function of the dis-

tance between the end points of the load line, or the voltage and current swing. There are

numerous classes of amplifier which are more efficient than the class-A amplifier whose

load line is presented- The DC bias point, the input power, and the output impedance at the

fundamentd and harmonic frequencies can be tuned to change the load line. Figure 2.6

shows the drain voltage and current for an ideal class-B amplifier, obtained by adjusting the

Cunent Voltage

Phase (degrees)

Figure 2.6: Ideal voltage and current waveforms for a ctass-B amplifier


gate bias voltage to get a 180° conduction angle of the current. This amplifier is more effi-

cient than a class-A amplifier because when the voltage across the device is high, there is

no current flowing. This reduces the power dissipated in the device and increases the effi-

ciency of the amplifier.

Tuning the waveforms to produce amplifiers with certain characteristics is quite diffi-

cult, primarily because there is no commercial tool which can look at the shape of the Ioad

Iine. A linear network analyser will only look at the linear, or s m d signal, part of the load

line. The current waveform in Figure 2.6 as measured by a commercially available linear

network would be sinusoidal, The best commercial too1 to look at these waveforms is actu-

ally a simdator, which estimates the waveforms using nonlinear models. Unfortunately, the

models are difficult to generate and are often inaccurate, again because there is no tool to

measure nonlinear waveforms directly. These models are normally generated from a very

large number of linear measurements taken at different bias points. The NNA, discussed in

the next section, measures these voltage and current waveforms. It can be used to increase

the accuracy of the device models, and also to actually visualise the waveforms in an arnpli-

fier or other network.

Other methods to estimate how a device is operating are based on evidence that can be

measured using existing tools. For example, when building a class-A amplifier, the DC

drain current gives a good indicator of what is happening. If the input power is increased,

and the DC current suddeniy increases, this is an indicator that the bottom of the current

waveform is clipping more than the top. Another useful tool is the spectrum analyser. This

measures the power of aI1 the harmonics in the output waveform. It won't measure the phase

of the harmonics however, so it cannot actually measure their shape. There are a great


number of ways to get around the probIem of not being able to measure the waveforms

directly. However, all of these techniques are estimates and cannot ever hlly describe how

a device is operating.

2.2.2 Microwave Signal Distortion

As described above, devices must sometimes be used in nonlinear regions of operation.

This can be desirable to tune an amplifier's load line, but it will also distort the shape of the

signal being amplified. Figure 2.7 shows the output spectrum of a fifth order nonlinear

system excited by two tones spaced closely together at frequencies fi and f2. The order of

Frequency

Figure 2.7: Output spectrum of a nonlinear amplifier with a two tone input

a network, in the frequency domain, refers to the maximum number of tones which are

mixed together within the network to generate a new tone. Notice that there are groups of

tones in the output around the first, second, and third harmonic multiples of the input fie-

quency. The groups at the second and third harmonic frequencies are not a big issue,

because, although they may be required for the amplifier to operate correctly, they can be

filtered out before being sent to an antenna. The four unwanted tones around the tones at fi

and f2 cannot be easily removed by filtering because they are so close to the desired tones.

2 2 Nonlinear Effects 18

When a real communication signal is amplified by a nonlinear amplifier, the output

spectrum is spread as shown in Figure 2.8. A 125 kSymbolfs, DQPSK (Differential Quad-

rature Phase Shift Keying) input signal, centred at 1.8 GHz, was amplified by a Mini-Cir-

cuits ZFL-2500, 30 dB gain amplifier, and measured with a spectrum anaIyser. This is a

Frequency (GHz)

Figure 2.8: Intermodulation distortion of a typical digital communication signal

typical signal used in digital communication systems, and can be used to transmit two bits

of information per symbol, without the need to estimate the carrier phase at the receiver.

The input signal was filtered with a 0.35 roll off raised square root cosine filter, to limit the

signal's 3 dB bandwidth to around 125 W. Notice that the output signal is 30 dB larger

than the input signal, but that it has become spread in frequency. The first shoulders, around

2.2 Nonlinear Effects 19 - - - - - . - - - - - -- --

35 dB down from the desired signal, are third order intermodulation distortion products.

The second shoulders, about 6 dB above the noise floor, are 5th order intermodulation dis-

tortion products. This signal spreading is very undesirable, as the unwanted products often

fail within neighbouring frequency bands causing adjacent channel interference. Adjacent

channel interference makes it difficult to receive signals in the neighbouring bands, because

they have an unwanted signal imposed on them.

It is desirable to operate a device in a nonlinear way, to optimize amplifier efficiency

and minimize cost, but this results in intermodulation distortion which cannot be tolerated

if it interferes significantly with neighbouring frequency bands. There are many lineariza-

tion techniques which can reduce the distortion added by a nodinear amplifier. However,

for wideband amplifiers it is difficult to model this intermodulation distortion using existing

techniques. This makes it difficult to investigate new linearization techniques, and to

improve the performance of existing ones. The NNA will give useful information about the

distortion in an amplifier, which can be used to produce models which would help with the

development of linearization techniques. The NNA can also be used to produce improved

models of the devices used in amplifiers. Current models can estimate the drain waveforms

for a single tone, with some degree of accuracy. However, for two tones, or real communi-

cation signals these models are not very accurate. Simulating how a nonlinear device will

operate, and the resulting signal distortion, may make it possible to design amplifiers which

operate nonlinearly, but which produce reduced levels of intermodulation distortion, even

without linearization.

2.3 Nonlinear Network Analyser Overview 20

2.3 Nonlinear Network Analyser Overview

As indicated in Section 2. I, the NNA does not measure the voltage and current at the two

device ports directly. Instead, the forward and reverse voltage travelling waves are sampled

at each port and (2-2) is used to calculate the voltage and current waveforms- Figure 2.9

shows the basic NNA system. The signaI source generates a signal which is connected to

Figure 2.9: NNA system schematic

Signal Source

either port one or port two of the Device Under Test (DUT) using a mechanical switch.

Whichever port is not connected to the source is terminated with a 50 Q load. Directional

couplers on the input and output separate the forward and reverse waves at each port and

tap off about 1% of each wave's power. In the diagram, the a terms represent forward

waves and the b terms represent reverse waves. The subscripts indicate port numbers. The

four travelling waves are then sampled by a very fast oscilloscope which has a 50 GHz front

end bandwidth. The device under test must sometimes be connected within a fixture so it

Wideband Scope --=--7_

:* -<2..s4z -7- .-. q, -7:. - .-:= .... # _

, . - ;,2-:22z-ag-g3 - ;;- .>,;::**- ** .+2X=..?t=.&?.t? ,> , '-'"-I::. ~-~3~L*-43:*~- : : < : - ; - - 2 u ~ . y J . .;-;,i$? .--

- I I

a1 bl b2 a2

- Directional Coupler Directional Coupler

2 3 Nonlinear Network AnaIyser Overview 21

can be probed by the M A . In Chapter 3 the details of the NNA implementation will be

presented. Most importantly calibration, the removal of systematic errors caused by the

directional couplers, cables, and oscilloscope inputs will be discussed, as well de-embed-

ding, the process of determining the waves at the device edge from the waves measured at

the fixture edge.

In this section some issues which are fundamental to the operation of the NNA are pre-

sented. In Section 2.3.1 it is explained how the NNA compares rotating phases between dif-

ferent frequency tones and in Section 2.3.2 the sampling technique used to measure the

signals is explained.

23.1 Phase Measurement

Although the oscilloscope takes measurements in the time domain, the NNA calibration,

and most network rnodelIing, is done in the frequency domain. A linear network analyser

need only measure the phase between a single incident tone and the fundamental of the

waveform that is either transmitted or reflected. A NNA must also measure the phase

between tones at different frequencies; for example, a single incident tone and the third har-

monic in the output waveform. It is quite difficult to see how we can measure the phase

between signals at different frequencies, since the phases between tones at different fre-

quencies rotate with time.

In order for a phase measurement to be useful, the position, or time on the waveform at

which it is taken must be defined. A wave that is increasing through zero volts at the refer-

ence time is defined as having zero phase. The choice of reference time is not as arbitrary

as it seems! Changing the reference time is equivalent to adding or removing group delay

to all four measurements. In the time domain, this is equivalent to simply moving the wave-

2 3 Nonlinear Network Analyser Overview

form to the left or the right; the shape is unchanged. This reference time is defined at the

start of the time window sampled by the oscilloscope, which is determined by the oscillo-

scope trigger input.

2.3.2 Sampling The Waveforms

Every time the NNA acquires waveform data and takes a phase measurement the measure-

ment must be the identical. To achieve this, a stable trigger point on the repetitive wave-

form is required. The trigger frequency must be a common denominator of all the tones

present in the waveform being acquired. With this requirement met, an integer number of

cycles for any tone will pass before the next trigger. At the trigger point, each tone will

always be at the same angle in its cycle, resulting in a repeatable measurement. For most

measurements, the 10 MHz reference signal from the back panel of the signal source is used

as a trigger.

The time window over which the oscilloscope collects data must contain an integer

number of cycles of each tone present in a wave. The Fast Fourier Transform used to

extract frequency spectra from the sampled waves assumes the data is cyclic. The FFT

effectively repeats the data in the time window out to infinite time, and takes a Fourier

series. A discontinuity between the last sample and the first sample will act like a step when

the data is repeated, causing frequency spreading in the extracted spectra. Since every tone

present must be a multiple of the trigger frequency, the time window length must be a mul-

tiple of the trigger period to prevent discontinuities. Wlndowing is the process of multiply-

ing the time domain data by some function, so that there are no discontinuities when the

FFT effectively lays the sampled windows end to end. These windowing functions tend to

remove data at the start and the end of a time sequence, and can affect the shape of the

2.3 Nonlinear Network Analyser Overview 23

extracted frequency spectrum. For this application, the data does not need to be windowed

because the waveforms in the NNA are cyclic, and the oscilloscope is set up so there is no

discontinuity between the end of one window of data and the start of the next.

Chapter 3

NNA Implementation

The previous chapters introduced the NNA, describing why it is useful and what it does.

The goal of this chapter is to describe how the NNA works. In Section 3.1 an overview of

the system is given and sources of error and the techniques used to reduce them are dis-

cussed. In Section 3.2 an error model used to remove the systematic errors from measure-

ments is developed. In Section 3.3 the linear part of the calibration routine which is very

similar to that performed by a commercial linear network analyser is discussed. In

Section 3.4 the absolute calibration, which can be thought of as correcting the shape of the

measured waves is described. Section 3.5 focuses on de-embedding, the process of rernov-

ing the effects of a fixture from a measurement.

3.1 System Overview

In this section an overview of the NNA is given and some errors inherent to the system and

the techniques used to reduce them are described. The NNA is built using mainly off the

shelf measurement equipment. There are a number of components linked together over a

3.1 System Overview 25

bus to a Macintosh computer. The Macintosh controls the system using an application writ-

ten with the National Instruments LabView development package. The appIication has a

graphical user interface, which controls every aspect of the measurement process. This

LabView application is described in Appendix A, In Section 3.1.1 the operation of the

NNA is presented and in Section 3.1.2 some errors present in the NNA measurements are

discussed.

3.1.1 Hardware Description and Operation

The NNA samples the forward and reverse travelling waves at the input and output ports

of a two-port Device Under Test (DUT). Figure 3.1 shows a diagram of the basic measure-

ment system. An HP-83650A signal sweeper generates a tone that can be connected to

Figure 3.1: NNA system

- , . HP-83650A . . L:-:.-&,2., G--?-:??- l ..r. > , *. *:.=-.,.. ;-.. .,_.:5O;'GH2Sweeper:$:> ; , . : . , - ~ ? . ; ~ ; & & d ~ 7 -.&sp.:-*>. ;+;; s .. ,I

.. , . . 4-z~-+:;.yyry;:<.??+ Lt -..;< j R ~~~~-..~--+.:~~~*:;~:=~~~j; ,;::- -:b.f-:q~z.>.:2. r... - --,

-;-,3.22k&2<>-&- -

--- HP-54750A

-! > - : . : T L ~ ~ , ? $ T L ~ ~ ~ T J Z ~ - - ~ - - - d '.b F -..m-r::.zh'* &j-gg,e$g!!lg!?o~y$

. ~ ~ , ~ < - & ~ ~ ~ ~ - : ~ : . d . a T n g -.."p.r321qq~:3g&-452:*J.: + =..I..: "*-.)7-*:q<p*=, . -r- Fi'r- F . . * . -. - . . .

-

h Narda 4226-20 Narda 4226-20 Directional Couplers Directional Couplers


either port of the DUT using an HP-8762C mechanicaI switch. The switch is controIIed by

an HP-11713A switch controlIer, not shown on the diagram- Two Narda 4226-20, 0.5 to

18 GHz bandwidth directional coupIers on each measurement port separate the forward and

reverse travelling waves. The four resulting signals are sampled by an HP-54750A, 50 GHz

sampling oscilloscope. The equipment is connected via a GPIB bus (General Purpose Inter-

face Bus) to a computer running software developed with LabView. The sampled wave-

forms are transferred to the computer, and an FFI' is performed to extract the amplitude and

phase of all the harmonics. The waves at the device edge are then inferred from the meas-

ured waves by removing the systematic errors caused by the test system.

Figure 3.1 shows a single tone sweeper as the signal source. To fully characterise some

nonlinear systems, multi-tone or broadband probing signals are required. Two tone signds

are generated by combining the output of two single tone sources. Arbitrary wideband sig-

nals can be generated using an HP-8780A vector modulator controlled by in phase and

quadrature signals from a Tektronix AWG-520 1 GS/s arbitrary waveform generator.

If triggered by the 10 MHz reference signal from the source, the oscilloscope will be

able to sample any waveforms whose component tones are muItipies of 10 MHz, This

10 MHz clock can be divided an integer number of times to sample signals that are not a

multiple of 10 MHz. For example, to test a device with two tones spaced 1 MHz apart, the

trigger signal must be reduced in frequency by a factor of 10. For a single tone measurement

the oscilIoscope couId be triggered directly with a portion of the probing signal. However,

the oscilloscope can only be triggered at a maximum rate 2.5 GHz, which often makes this

impossible. As described in Section 3.2, a calibration is performed by sampling a tone at

each frequency of interest. Most measurements will require calibration at frequencies

above 2.5 GHz, preventing the probing signal from being used to trigger the osciIloscope

directly.

3.1 System Overview -- - ----

3.1.2 Systematic and Random Errors

A measurement taken with the NNA includes many systematic and random errors inherent

in the measurement hardware. The effects of systematic errors can be removed, but the

effects of random errors can only be minimized. This section discusses these errors and

some techniques to reduce or remove them.

The measured waves are linearlyJiltered by the NNA. Figure 3.2 shows part of the NNA

system. The waves which have been separated by the directional couplers are measured by

the oscilloscope a distance from the actual device . Each component tone in the waveforms

Signal Source

Switch

Directional Couplers

Device

Oscilloscope Inputs

Directional Couplers

. Fixture

Figure 3.2: Picture of NNA showing a brass fixture and the oscilloscope inputs


is attenuated and phase shifted by the measurement system, resulting in a systematic meas-

urement distortion. The calibration routine, described in Section 3.2 removes the effect of

these errors.

The signals scunpled by the oscilloscope are noisy. Some of this noise is thermal and

some is due to the quantizing of the signal by the 12 bit analogue to digital convertors in

the oscilloscope. This noise is random and essentially uncorrelated with the signal so it can

be removed by averaging. Around 64 waveforms are collected and averaged in the oscillo-

scope, resulting in a waveform with reduced noise. The full 4096 sample points in the oscil-

loscope are used, meaning that many cycles of each tone are stored- The FFT, used to

extract a waveform's frequency spectrum, inherently takes the average phase and amplitude

of each of the cycles present in the sampled time window. These two sources of averaging

can reduce the noise floor of the final measurements to as much as 60 or 70 dB below the

maximum signal present.

There is a random error in the timing of the oscilloscope samples. This jitter is inherent

in the oscilloscope, and is also caused by noise on the trigger signal. It resuIts in a horizontal

smearing of the measured waveforms. The effects of jitter are largely removed by the aver-

aging performed to remove noise. However, averaging a signal with jitter is equivalent to

low pass filtering it. The attenuation caused by this effect is systematic and is removed by

the calibration described later. An amplitude calibration is therefore only valid if the jitter

present during a measurement is similar to the jitter present during the calibration. This is

true if the same source is used for both the measurement and the calibration. When a dif-

ferent source must be used for the measurement, the jitter from each source should be sim-

ilar. The oscilloscope can be used to statistically compare the jitter of the two sources. Jitter


is added by attenuating the trigger signal and reduced by increasing its amplitude. There are

also analytic techniques for characterising and removing the amplitude distortion caused by

jitter [5,6],

Temperature drifr limits the repeatability of measurements. The amplitude and phase

responses of the oscilloscope are a function of temperature. This effect is small, but over a

number of days the effect can result in inaccurate measurements. These errors are mini-

mised by calibrating the NNA shortly before it is used, and recalibrating if the temperature

changes. Linear network analysers suffer from the same problem-

Short term drifting effects also affect the system. If the phase of the probing signal

changes during the measurement time the results will be inaccurate. This has not been

obsenred to be a significant problem, but it may become so when using less accurate

sources or when taking averages over a long time period to reduce measured noise on small

signals. This problem can be minimized by averaging the frequency spectra from many

short measurements instead of averaging many samples taken over a long period together.

The many amplitude measurements of each tone are averaged together, as are the many

phase measurements. This removes the problem of averaging in the time domain where the

many different measurements with different phases can add up destructively to filter the

signaI.

There is a systematic error in the timing of the oscilloscope sampling. The oscilloscope

has a very high input bandwidth, but it can only take one sample for each trigger it receives.

After each successive trigger, it waits a longer amount of time before sampling. The wave-

form is constructed by combining these samples together. The clock used to time the sam-

pling has a systematic error which advances or retards the sampling times with respect to

3.2 Removing Errors With Calibration 30 - --

their ideal positions. This error is small and can be ignored for single tone, or narrow band

measurements. Section 4.2 in the verification chapter presents a method to measure and

reduce this distortion, and shows its effects on measurements.

3.2 Removing Errors With Calibration

A calibration is used to calculate the waves at a calibration plane from the measured

waves which has been distorted by the measurement system. The calibration generates a

model of the test system between a calibration plane and the oscilloscope's samplers for

each frequency of interest, This is done by measuring waveforms while standards having

accurately known characteristics are connected to the NNA. The modelled waves at the cal-

ibration plane are then compared with the measurements to produce an error model at each

frequency of interest. These models are used to remove the systematic errors. The calibra-

tion pIane is always defined at a connector. This allows simple calibration standards to be

used, and simplifies the absolute calibration routine described below. The model used to

characterise the errors in a measurement is derived in Section 3.2.1. In Section 3.2.2 a

matrix representation of the error model is presented and in Section 3.2.3 the calibration

routines used to determine the parameters in this matrix at each frequency of interest are

introduced.

3.2.1 The System Error Model

The goal of this section is to develop a simple error model whose parameters can be easily

determined. Figure 3.3 shows a model describing one half of the NNA system, assuming

there is no cross talk between the two NNA ports. Each black arrow represents a phasor

valid at one frequency. To characterise the test system a separate model must be generated

at every frequency of interest. This model is not compact; many of the phasors can be com-

3.2 Removing Errors With Calibration 31

Figure 3-3: Signal flow graph describing one half of the NNA system

bined together to simplify it. The inner box is a four port network describing the directional

couplers, the switch and the cables. The parameter a,,,,, is the travelling wave available

from the source and rso,, is the source's reflection coefficient. A reflection coefficient is

defined as the ratio of the reflected wave phasor to the incident wave phasor of a linear net-

work probed with a single tone. The parameters rscopel and rsCoF2 are the reflection coef-

ficients of the two oscilloscope inputs used to measure the incident and reflected waves.

GscoPel and Gscope2 represent the gain of each of the oscilloscope inputs. The a1 parameters

represent forward waves at port one, and the bl parameters represent reverse waves at port

one. The m subscripts denote measured waves, while the c subscripts denote waves at the

caIibration plane.

3.2 Removing Errors With Calibration - - - -

The model is greatly simplified by looking only at the outer dotted box indicated in

Figure 3.3. The system can now be described as having simply the source, the measured

waves and the device waves as inputs and outputs as indicated by the grey arrows in

Figure 3.4. The T,,,,, and TcOup parameters model the reflection coefficients seen by the

DUT. The G parameters indicate the coupling gains between the two waves at the calibra-

tion plane and each of the two measured waves. If the directional couplers had perfect direc-

tivity then the G12 and GZ1 terms would be zero.

bc

Figure 3.4: Simplified physical model

To further simplify the model, the a,, input can be written as a linear function of a,

and b,, and treated as internal to the network. The new model now has am and b, as inputs

and b, and a, as outputs. Figure 3.5 shows the new two-port model, and relates the new C

parameters to the G parameters in Figure 3.4.

Figure 3.6 is a signal flow graph showing an error model for both ports of the NNA-The

subscript numbers represent the port number. The eight parameters are phasors which must

be determined at each frequency of interest. This model is very similar to the model used

in a linear network analyser which assumes that the two measurement ports are isolated [7].


G2 I C,, = - Gll 1

C,, = - Gl 1

Figure 3.5: Greatly simpIified error model for one measurement port

Port 1 Error Box DUT Port 2 Error Box

- - a1c ~ - ~ - 3 9 c

a1 rn C21 - 8 8 - 021 62m

Figure 3.6: System error model for both measurement ports

The difference is the CZ1 term. In a linear calibration, where only relative measurements are

required, this term is set to one. Only the ratio of the transmitted and reflected tones to the

incident tone is important in a linear measurement, so there is no need know the absolute

size of the incident wave. However, in order to measure a waveform's shape, the NNA must

measure the absolute magnitude and phase of each tone present.

The four C terms describing the port one error model represent physical properties of

the couplers and lines. The CZL term is inversely proportional to the gain of the measured

incident wave with respect to the wave incident to the calibration plane. The C12 term rep-


resents the gain of the measured reflected wave with respect to the reflected wave at the cal-

ibration plane. The Cll and C22 terms are leakage terms. The CI1 term models the

component of the forward wave that is measured at the reverse port. The CZ2 term models

the component of the reverse wave that is measured at the forward port. The calibration will

remove the effect of dl these errors.

Unfortunately, as shown in Figure 3.3, the C22 term also contains the two reflection

coefficient terms. In a linear network andyser these terms will correct for any mismatch

from the 50 l2 reference impedance in a measurement In the NNA however, these terms

should not be included. The calibration routine attempts to extract what the measurement

would be without the mismatch. Unfortunately, this linear correction is not strictly valid

when measuring nonlinear networks. In practice this error can be ignored as long as the

mismatch from 50 R of the measurement system is not great. For weakly nonlinear circuits,

the error introduced is insignificant if the return losses looking into the measurement ports

are more than 20 dB.

3.2.2 Error Correction Matrix

The linear error model in Figure 3.6 can be represented with the following matrix equation:

The R parameters are determined using a relative calibration similar to that performed in a

linear network analyser. The K and parameters are absolute calibration parameters 141.

Once the R parameters and the absolute calibration parameters have been found at each fre-

3.2 Removiug Errors With Calibration 35

quency of interest, (3-1) can be used to determine the waves at the calibration plane from

the measured waves.

3.23 Generating the Error Models

To determine the parameters in (3-1) a calibration must be performed at each frequency of

interest- This calibration is divided into a relative calibration and an absolute calibration-

Although the absolute calibration is performed after the relative calibration, it is easier to

understand the process the other way around.

The goal of the absolute calibration can be viewed as correcting the shape of one wave.

Suppose a single tone is input to an ideal opamp configured to produce a square wave. Due

to systematic errors in the test system, each harmonic will be attenuated and phase shifted

by a different amount when measured. As a result, the measured transmitted waveform is

no longer a square wave even though the actual wave leaving the device is. The absolute

calibration makes sure that the amplitude of each harmonic in the alc waveform, and the

the phase of each harmonic in the blc are measured correctly. Although the phase of one

waveform and amplitude of a different waveform are corrected, with the goal of determin-

ing the error model, this is equivaIent to correcting the amplitude and phase of a single

waveform. In the time domain, the tones will combine together correctly resulting in a

waveform with the correct shape and amplitude.

For the sake of understanding the calibration routine, the absolute calibration can be

thought of as correcting the shape of a single waveform at the port one calibration plane.

The god of the linear, or relative, calibration is to correct the shape of the other three cali-

bration plane waveforms with respect to this known waveform. For exampie, suppose that

the port two calibration plane is connected directly to the port one calibration plane using

3.3 Linear Calibration Technique 36

a zero length through. In this case, the bZc waveform leaving the through must be the same

as the al, wave entering it. Or if a short is connected to the pon one measurement plane,

the reflected wave blc must be an inverted version of the incident wave al, The linear cal-

ibration also corrects for the finite directivity of directional couplers.

3.3 Linear Calibration Technique

The linear calibration determines the R parameters in (3-1). A set of standards with pre-

cisely known characteristics is measured on the NNA. By comparing the measured waves

and the waves predicted by the standards' models, the error parameters can be found. For

calibrating to a connectorised reference plane the Short-Open-Load-Through (SOLT)

method is well established. The SOLT calibration routine used to determine the R parame-

ters is described in Section 3.3.1 and the models which characterise the standards are

described in Section 3.3.2.

3.3.1 SOLT Calibration Mathematics

The R12, and Ru terms are f i s t determined by making measurements of the wave-

forms at port one with a short, an open and a load connected [S]. This must be done at each

frequency of interest. The three standards have known reflection coefficients TI, r2, and

r3 respectively. The modelled forward and reverse waves for each of the three measure-

ments are related by


where the superscripts indicate the measurement number. Substituting parts of (3-1) into

(3-2) gives

which can be written in matrix form and solved for the unknown R parameters, yielding

Measurements of the same standards are then taken at port two. Using a similar devel-

opment, the following matrix equation is written to determine three more R parameters

from these fourth, fifth, and sixth measurements:

where R x y = R,,,,R,, . The RXy parameters are normalized at this point because they

cannot be fully determined until R33 is known. A measurement of a through with power

incident to port one is used to determine R33. For this seventh measurement, the incident

wave at port one is equal to the reverse wave at port two, or

3 3 Linear Calibration Technique 38

Substituting parts of (3-1) and (3-5) into (3-6) gives

which can be solved for yielding

To sum up, the R parameters from (3-1) can be compIetely determined at each fre-

quency by taking seven measurements: a measurement of a short, an open, and a load on

port one and port two, followed by the measurement of a zero length through with power

incident to port one.

3.3.2 SOLT Calibration Standards Modelling

The short, open, and Ioad standards are very accurately machined. They are described by

models whose parameters are traceable to the National Institute of Standards and Technol-

ogy (NIST). The model parameters are supplied by the manufacturer of the standards, who

has measured them on a machine calibrated with standards verified to be accurate in a MST

lab. This section describes the models for the HewIett-Packard standards used to calibrate

the NNA [9].

Figure 3.7 shows a diagram of the standards. The standards have a delay line before

being either shorted, left open or connected to a broadband load. An offset is a length of

line connecting either the short, the open or the load to the standard's connector. The con-


Calibration / connector plane

I L

1- 1

,---------A 1 Toffset

Figure 3.7: Definitions for a standard

nector plane is defined for male and female connectors so that when they are connected

together, the connector's reference pla~es lie on top of each other. The offset delay is the

one way delay from the connector reference plane to the internal standard. It is given by

where I is the length of the offset, c is the speed of light, and E, is the relative dielectric con-

stant of the line. For accurate standards the dielectric is normally air.

The resistance R1,, models the skin effect in the line, and is calculated using

where dBIo,, is the one way loss in dB along the line at 1 GHz. The factor of a half is equiv-

alent to taking the square root of the power lost, and the frequencyfiGHzl, given in GHz

accounts for the frequency dependence of skin loss.

3.3 Linear Calibration Technique 40 -- - -

The open standard is modelled as a lossy delay line left open at the end with a capacitive

impedance Zc to account for fringing. The open standard's reflection coefficient is given by

where RIoss and TOE,, are given above, and Zc is modelled as a third order polynomial func-

tion of frequency given by

2, = C,+C,f +c , f2+c3f3 . (3-12)

The short standard is modelled as a lossy delay line shorted to ground at the end with

an inductive impedance ZL. The short standard's reflection coefficient is given by

where RIos, and ToRse, are given above, and ZL is modelled as a third order polynomial func-

tion of frequency given by

The load standard is the simplest to model. The broadband load used in the standard is

assumed to be ided. Therefore the load's reflection coefficient is simply given by

3.4 Absolute Calibration Technique 41

Absolute Calibration Technique

The absolute calibration parameters in (3-I), K and 0, have yet to be determined. The K

term relates the amplitude of the measured waves to the amplitude of the waves at the cal-

ibration plane at a given frequency. The angle 4, corrects for any frequency dependent

phase shift, or deviation from a flat group delay, present in the system. In Section 3.4-1 it

is explained how the K term is found and in Section 3.4.2 how Qi, is found.

3.4.1 Absolute Amplitude Calibration

K isdetermined by simply connecting a power meter to the port one calibration plane. A

tone is applied to port one at each frequency of interest. Measurements are taken using the

NNA and the power meter. K is chosen such that the extracted incident power at port 1 is

equal to the value from the power meter-

The FFT used by the NNA returns the peak voltage of each tone in a waveform. Since

the travelling waves are not normalized to 50 Q they are essentially voltage waves. The

power meter, which is calibrated to account for its return loss, measures the power that is

incident, or available, to it. Therefore the forward voltage wave at the caIibration plane

should equate to the peak voltage measured by the power meter. The measured power in

watts is a function of the peak voltage wave incident to the power meter Vp,


Converting P into dBm, since this is what the power meter normally measures, gives

which is solved for Vp, which is the same as lalcl

To calculate K, (3-18) is equated to the relevant part of (3-1) giving

Vpm = ~layrn + ~lzbfrnl

which is then solved for K yielding

TI

3.4.2 AbsoIute Phase Calibration

Theoretically, the phase calibration can be performed by connecting a wideband source

with a known signal shape to the port one calibration plane. The angle @ would then be

chosen at each frequency so that the calibrated measured phase agrees with the known

phase of that harmonic. A "golden diode" with a model assumed to be perfect can be used

as a phase standard [2]. A more traceable solution is to use a wide bandwidth sampling

oscilloscope [4]. A wideband oscilloscope is calibrated using a "nose to nose" method that


estimates the impulse response of the sampling heads. The output from a wideband source

is measured using this calibrated oscilloscope, and used as a standard to calibrate the NNA.

The "nose to nose" calibration method requires two or three wideband scopes which

would greatly increase the cost of the system. Instead, the oscilloscope inputs used in the

NNA are assumed to have flat group delays. A typical oscilloscope response has only a

a.75O deviation from this assumption up to 18 GHz [8]. Using this assumption a simple

phase calibration routine is possible. This assumption will be discussed in Section 4.1

where the phase response of the oscilloscope is estimated and compared with published

results obtained using the "nose to nose" method. By assuming the oscilloscope inputs have

flat group delays, the phase calibration problem is reduced to finding the phase response

between the calibration plane and the oscilIoscope inputs using a linear network analyser.

The relative calibration will account for any difference in the length of the oscilloscope

group delays.

One lead of a linear network analyser is connected to the port one calibration plane. The

other lead is connected to the lines that enter the a1 and bl osciIloscope channels sequen-

tially. The resulting S2* phase measurements, (I, and Qb, are identical to those that would

have been obtained by the NNA with an ideal impulse generator connected to the port one

calibration pIane. To develop the equation for cP, the values measured with the linear net-

9 work analyser are treated as if they actually were measured by the NNA as a,, and b:, .

Parts of (3-1) are used to relate these "measured" waves to the reverse wave at the calibra-

9 9 tion plane b The parameter b , , is defined to have zero phase at all frequencies to prop-

erly calibrate the NNA, giving

This can be solved for @, yielding

The calibration method discussed above only removes errors up to a connectorised calibra-

tion plane. This is sufficient to measure connectorised devices, but not for a device mounted

in a test fixture or other circuit. For example, many transistors must be mounted in a test

fixture that provides transmission lines for the input and output connections. Chapter 5 dis-

cusses measurements of a device that requires a fixture that not only physically connects

the device but also includes impedance transforming networks. One use for the NNA is to

help build and tune amplifiers. In this case, the device is embedded within the amplifier

matching networks, bias tees and other components. De-embedding is the process of cal-

culating the waves inside the fixture from the waves measured at the calibration plane.

Figure 3.8 shows the various measurements planes.

Port 1 Fixture Port 2 Fixture - * Test Lead

I I I I I I Co~nector

/ Port I Cal Plane

I \ Port 2 Cal Plane

Port 1 Device Plane Port 2 Device Plane

Figure 3.8: A device in a fixture

De-embedding effectively moves the calibration plane from the connectors to the

device edge. This is done using the model in Figure 3.9. The c subscripts indicate waves at

the calibration plane and the d subscripts indicate waves at the device plane. Notice that the

port two fixture is defined with its port one to the right instead of at the left as is standard,

This is done so the two fixtures both have port two at the device plane and port one at the

calibration plane. This symmetry allows the same equations to be used for removing the

effects of both the fixtures from the measurements.

Port 1 Fixture Port 2 Fixture

Figure 3.9: Signal flow graph model for fixture extraction

In parts of Chapter 4 and Chapter 5 methods for extracting the fixture models will be

discussed. The models are simply a set of scattering parameters at each frequency of inter-

est. The signal flow graph in Figure 3.9 is solved to determine the de-embedded waves from

the waves at the calibration planes yielding

3.5 De-embedding 46

Solving (3-24) for bid gives

Substituting (3-25) into (3-23) gives

Due to the symmetry added by reversing the port two fixture model, the equations at port

two are the same, but with the A parameters exchanged for B parameters

For measurements where tuners or other components are inserted as well as a fixture,

the scattering parameters of the components can be chained together to produce a single

combined fixture model at each port.

Chapter 4

NNA Verification

In this chapter experiments that verify the operation of the NNA are discussed. This is dif-

ficult, since there is no similar system that looks at waveforms directly to compare meas-

urements against. The procedure used was to test any assumptions made, each component

part of the calibration routine, and finally the entire NNA. In Section 4.1 the flat group

delay assumption used to simplify the calibration routine is discussed. Measurements taken

of a 15 ps rise time step are presented, as well as a measurement of an oscilloscope impulse

response taken by Hewlett-Packard. The timebase error in the oscilloscope is plotted in

Section 4.2. The effects of this error on a measurement are shown and a technique for

reducing the effects is discussed. In Section 4.3 experiments used to verify the linear cali-

bration routine are discussed. The linear part of the calibration determines seven-eighths of

the emor model, so this verification is very important Results in Section 4.4 show that the

absoIute calibration is working correctly. Measurements taken of a Schottky diode using

the NNA are compared with waveforms predicted by a model. Because the diode circuit

4.1 FIat Group Delay Assumption 48

tested was very simple, the voltage across the diode could be measured directly with the

oscilloscope. The absolute calibration routine was tested by comparing a voltage measured

with the NNA with this direct voltage measurement.

4.1 Flat Group Delay Assumption

As described in Section 3.4.2, the absolute phase calibration was greatly simplified by

assuming that the oscilloscope inputs have flat group delays. This means that the signal

sampled by the oscilloscope is simply a delayed version of the signal connected to the input

on the front of the osciUoscope. Obviously, for this to be completely true, the inputs must

have infinite bandwidth. Real circuits cannot be built with infinite bandwidth. This section

examines the flat group delay assumption. Measurements are presented which give an idea

of the error introduced by assuming a flat group delay, and give a maximum frequency at

which this assumption is valid.

The HP-54750A wide bandwidth oscilIoscope used in the NNA has two 20 GHz inputs,

used to measure the waves at port one, and two 50 GHz inputs used to measure the waves

at port two. The specified bandwidth is the frequency at which the input signal is attenuated

by 3 dB before being sampled. The amplitude response is not an issue for the NNA because

the absolute amplitude calibration will correct for any errors it introduces in a measureme-

nent. However, the phase responses of the oscilloscope inputs are not corrected by the cal-

ibration, because they are assumed to act as a simple group delay. The phase response of

the osci1ioscope is not specified by Hewlett-Packard, but it cannot be too bad or the oscil-

Ioscope would be useless. The osciloscope was designed primarily to look at time domain

pulses, where small deviations in the phase response would go largely un-noticed. How-

ever, the NNA makes frequency domain measurements of multi-tone signals, where errors

at certain frequencies may cause more drastic problems.

4.1 Flat Group Delay Assumption 49

To get an initial estimate of the oscilloscope inputs' phase responses, a very high speed

step was measured. Any deviation from a perfect step response could be attributed to either

an imperfection in the pulse, or the phase response of the oscilloscope. An HP-8 130 pulse

generator was used to trigger a TD-1108A tunnel diode supplied by Picosecond Pulse Labs.

A tunnel diode behaves like any other diode. If the voltage across it is slowly increased, at

some point it will turn on and start conducting current. However, when a tunnel diode first

turns on, it produces a very fast step, even if the voltage that turned it on changed only

slightly. The TD-1108A was biased until it almost fired and was then triggered with the

pulse generator, producing 15 ps rise time voltage steps. A perfect step is described by the

Fourier transform pair

where t is time, o is radian frequency, u(t) is the step function, and 6 ( 0 ) is an impulse

function. The impulse part of the frequency representation is at DC and represents the aver-

age voltage of the step. The l/jo part indicates that the phase of every frequency component

is at -90" but that the power falls off asymptotically with frequency. Note that the frequency

domain representation indicates that at DC there is an infinite imaginary component. How-

ever a phasor at DC does not rotate with time, so the imaginary component can be ignored

or set to zero.

Figure 4.1 shows the amplitude and phase response of the measured pulse. The plots

where normalized so that they indicate the deviation of the pulse from being ideal. This was

obtained in the frequency domain by dividing the measured frequency data by simulated

data from the right side of (41). It could have also been obtained by correlating the meas-

ured time domain response with the step from the left side of (4-1)- The first thing to note


4 5 6 Frequency (GHz)

0 1 2 3 4 5 6 7 8 9 10 Frequency (GHz)

Figure 4.1: Amplitude and phase deviation of the measured step from being ideal

is that the amplitude response was attenuated by 7 dB at 10 GHz. This indicates that the

step was not ideal, since the osciUoscope input used was specified to have a 3 dB bandwidth

of 50 GHz. The finite rise time of the pulse, the impulse response of the diode, and timing

jitter all cause errors in the pulse shape. The phase plot shows a d .5" deviation up to

8.5 GHz. It is possible that this error is due to the oscilloscope impuIse response, but it is

more likely due to the impulse response of the diode. At 8.5 GHz the measured signal

power was -80 dB smaller than at DC. The response up to about 8 GHz was almost identical

for a large number of measurements. Above this frequency, different measurements gave

different responses indicating that the power was too small at these frequencies to obtain an

accurate measurement. Measurements taken using all four oscilloscope input were almost

identical. If this phase error were caused predominantly by the oscilloscope inputs, it would


likely differ between the 20 GHz and the 50 GHz inputs. From these measurements, the

only conclusion that can be made is that the oscilloscope likely has less than +2S0 of phase

error up to 8.5 GHz. The very bad amplitude response of the measurement, which is defi-

nitely not due to the oscilloscope, suggests that the oscilloscope response is actually a lot

better than this worst case limit of &.So u p to 8.5 GHz.

Jan Verspecht, working with the Hewlett-Packard Network Measurement and Descrip-

tion Group in Brussels, has taken more accurate phase response measurements. With the

goal of actually developing a traceable phase standard they came up with the "nose to nose"

calibration technique [lo]. The input of one oscilloscope is connected to the input of

another. The first osciIloscope is set to sample continuously. With each sample, due to the

way sampling circuitry works, a small impulse is created which is then measured by the

second oscilloscope. This impulse is distorted by the impulse response of the first oscillo-

scope and then by that of the second- By connecting the three possible combinations of

three oscilIoscopes two at a time, the impulse response of each can be determined.

Figure 4.2 shows the phase error for the HP-54 120, an earlier, 20 GHz version, of the

oscilloscope used in the NNA [8]. There is only a M.75' error in the phase up to 18 GHz.

Notice that the phase error starts rapidly increasing beyond the 20 GHz specified bandwidth

for the oscilloscope. This result is a lot more conclusive than the one obtained by measuring

the step response of the diode. It indicates that the flat group delay assumption is valid up

to about 18 GHz for the 20 GHz inputs used to measure the port one waves. Most likely,

the assumption is valid up to an even higher frequency for the 50 GHz inputs used to meas-

ure the waves at port two.

4.2 Timebase Error Measurement

Figure 4.2: OsciIIoscope phase error from Jan Verspecht's dissertation [a]

4.2 Timebase Error Measurement

There is a systematic error in the timing of the oscilloscope sampling. The clock used to

time the sampling has a repeatable error which advances or the retards the sampling point

with respect to its ideal position. In this section an estimation of this error is presented, and

its effects on a typical NNA measurement are shown. A technique to reduce this error is

also discussed.

The oscilloscope has a very high input bandwidth, but it can only take one sample for

each trigger it receives. After each successive trigger, it waits a longer amount of time

before sampling, as shown in Figure 4.3. In the diagram, the vertical dashed lines are trig-

gers which occur, in this case, once for each repetition of the signal to be sampled. The

4.2 Tiebase Error Measurement 53

Trigger Trigger 41 . Trigger Trigger

I I I I

I I I I

1 I I I

Time + L

Time +

Figure 4.3: Repetitive waveform being sampled and then reconstructed

times t l to tq indicate the increasing offset between the trigger and each successive sample

time. The waveform on the right shows how the sampled signal is reconstructed by com-

bining these samples together with the correct timing. For legibility the diagram shows one

trigger for each cycle of the waveform, When measuring real signals there are normally

many cycles for each trigger.

Figure 4.4 shows this error as a function of the time delay between the trigger edge and

a sample being taken. This plot was obtained by sampIing a single 10 GKz tone. The time-

base error in the oscilloscope acts to modulate this tone. Down converting the measured

signal in software and low pass filtering it resulted in a complex signal describing the error.

Integrating the phase of this error signal to a given time, gave the timing error for that sarn-

pling delay.

The error is cyclic with a period of 4 ns. This is due to the internal timing mechanism

of the oscilloscope. After receiving a trigger edge a 250 MHz oscillator is started [ll].

Then, after an integer number of cycles, a ramp generator is started. When the ramp reaches

a specified value the sample is taken. The clock results in a coarse timing offset with mul-

4.2 Timebase Error Measurement 54

Time Delay (ns)

Figure 4.4: Measured timebase distortion

tiples of 4 ns, and the ramp produces the remaining portion of the desired delay. The main

error is due to an error in the slope of the ramp, resulting in the observed 4 ns cyclic error

as the ramp is used to provide between 0 and 4 ns of delay.

The effect of this timebase distortion in the frequency domain is to add spurious tones

spaced at 250 MHz multiples from a tone being sampled. For a single tone or narrow band

measurements, the effects of this timebase distortion on the real tones are removed by the

calibration routine. For measured waveforms with more than 250 MHz bandwidth around

any harmonic, this distortion may cause errors and can be reduced if required [12,13]. The

4.2 Timebase Error Measurement 55

frequency domain data is extractec from the time domain data, taking into account the

known sample times. A standard FFT assumes the samples are evenly spaced, which is

what causes the spurious tones.

Figure 4.5 shows the frequency domain representation of a 3 GHz tone sampled with

the oscilloscope. The circles were obtained by taking a standard FFT- The crosses were

obtained using the technique which takes into account the actual time the samples were

taken. The corrected transform has reduced all the spurious tones down into the noise at

around -65 dBm, a reduction of up to 25 dB or by a factor of over 300 times.

0 Uncorrected

.................................. o x :

: x x , i x O -6 - - - . - - ! - - - - - - - I - - - * . - - I - - - - - . A -

. X - c3

-90 I I I I I I I I I I 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

Frequency (GHz)

Figure 4.5: Spurious tones caused by timebase distortion in a sampled 3 GHz tone

4 3 Linear Calibration Verification 56

Linear Calibration Verification

The linear calibration accounts for seveneighths of the error parameters that must be deter-

mined by the calibration routine. This section, which verifies that the linear calibration is

working correctIy, goes a long way toward indicating that the NNA takes valid measure-

ments.

The linear calibration was tested by comparing measurements taken of a Mini-Circuits

ZFRSC-42 splitter using the NNA with measurements taken using a linear network ana-

lyser. The splitter was chosen because it had a simple response and because it was lying

around on a bench and no one else wanted it. It was designed to take a signal from DC to

4200 MHz at port three and split it evenly between ports one and two. For the purpose of

the verification, the splitter was connected in the NNA as shown in Figure 4.6- Between

I I

I I I *

Calibration plane I Calibration plane 2

Figure 4.6: Connection of splitter for linear calibration verification

port one and two of the splitter there is a specified 7 dB isolation if port three is terminated

in 50 R. To make the response a little more interesting, port three of the splitter was left

open.

The scattering parameters of the splitter were measured on an HP-85 10 linear network

analyser, between 200 MHz and 4400 MHz in 200 MHz steps. The same measurement was

4.3 Linear Calibration Verification 57

then taken using the calibrated NNA. Figure 4.7 and Figure 4.8 show the resulting S1 I and

measurements respectively. Note that as the frequency increases the points move anti-

clockwise. The NNA and HP-85 10 measurements agree quite accurately. As the frequency

increases, the magnitude of S1 increases, indicating less power is entering port one. Cor-

respondingly, SZL decreases as the frequency goes up indicating that less power is leaving

port two*

Small deviations between the measurements are due to the way the NNA calculates the

scattering parameters compared with the way the linear network analyser calculates them.

The NNA calculates the waves at one port and completely ignores any mismatch at the

other port. It then calculates S1 from these waves. The linear network analyser calculates

Sl I from the waves at port one, removing the effect of any mismatch at port two. This is not

done by the NNA, because it is designed to measure what the actual waves are, not what

they would be if the other port were terminated with exactly 50 a. These results are very encouraging and indicate that the linear part of the calibration is

working correctly.

4.3 Linear Calibration Verification 58

270

Figure 4.7: Measured SI phasors from 200 MHz to 4400 MHz

270

Figure 4.8: Measured Szl phasors from 200 MHz to 4400 MHz

4.4 Schottky Diode Measurement 59

4.4 Schottkg Diode Measurement

In order to verify that the entire NNA was working correctly, measured waveforms were

compared with waveforms predicted using a model. The HSMS-8 10 1, a high frequency,

gallium arsenide (GaAs) diode, was chosen as a test device because it has an accurate

model [14]. A test fixture was built with a connector on both ends of a 50 !2 transmission

line. The diode was soldered in the middle of this line, shunting it to ground, as shown in

Figure 4.9. The device model included a PSpice chip model and the lead inductance Lr, the

Measurement plane

Connector Connector

-". /

50 ohm line

@I . - - - - - - - - - - - ' MHSMS-8101 GaAs Diode

- Figure 4.9: Schematic of the diode mounted in the test fixture

bondwire inductance LB, and the package capacitance between the two leads Cp. For this

diode LL=l nH, LB= 1 n H and Cp=80fE The diode model was simulated using the

HP-EEsof harmonic balance microwave simulator software. The NNA was connected to

this fixture, and a 1 GHz tone applied to port one. The diode clipped the bottom of this

waveform, producing harmonics which could be seen with the NNA. In Section 4.4.1 the

extraction technique used to model the fixture is described. Finally, in Section 4.4.2 results

of a number of experiments performed with the diode are presented.


4.4.1 Fixture Extraction

The NNA calibration routine removed errors up to calibration planes which were defined

at the fixture connectors. The effects of the fixture on the measurements were removed as

described in Section 3.5 on de-embedding. In this section the technique used to model the

fixture halves is presented.

Four scattering parameters are required to thoroughly describe a fixture half. However,

for low reflection, symmetrical fixtures, this model can be simplified. A fixture mode1

resulting from assuming that there is little reflection is shown in Figure 4.10. This is a sim-


F

Port 2 Cat Plane \ Port 2 Cal Plane

Device Plane

Figure 4.10: Model for the low reflection diode fixture

plified version of the model which was first presented in Figure 3.6. TheA parameters refer

to the port one fixture and the B parameters refer to the port two fixture. The a terms repre-

sent forward waves while the b terms represent reverse waves. The subscript numbers rep-

resent the port number, a subscript c denotes waves at the calibration plane, while a d


subscript denotes waves at the device, or measurement, plane. Note, that in keeping with

the de-embedding equations developed in Section 3.5, the port two fixture file is flipped left

to right from the way scattering parameters are normally defined.

To extract the fixture model parameters, the fixture was measured without the diode on

a linear network analyser. This gave a set of four scattering parameters at each frequency

of interest: SI l, S12, SZI and S22, where port one is on the left and port two on the right. The

following equations are used to determine the A and B parameters from the measured S

parameters:

A l l = S11

The parameters AZ2 and &2 are not shown in Figure 4.10, because they are assumed to be

zero as indicated in (4-2). Equation (4-2) involves taking the square root of the forward and

reverse fixture scattering parameters. This leaves a single sign common to AZ1, A12, B21,

and B I Z unknown. The sign is determined by assuming the entire fixture can be approxi-

mated by a simple delay. This delay is used to estimate AZ1 and the sign is chosen so that

the error between this estimated value and the extracted value is minimized.

Assuming that the whole fixture can be modelled as a simple delay, the phase of the

measurement $ is a function of the radian frequency o and the fixture delay ~fi,,,,:


Unfortunately, Tfixture cannot be determined simply by dividing both sides by o because @

wraps around every 2n radians. Instead, both sides are differentiated, giving

which can be rearranged to obtain the fixture's group delay

The linear network analyser takes samples every A f Hz. If Af is smaII, so that does not

wrap around between frequency samples, this differentiation can be treated discretely using

- O(fn) -@(fn- 1) 'fixture - 2nA f

where f, is a frequency between the second and the last frequency measured. In practice, to

minimize the effect of measurement error, Zfixmre is calculated between the first and the Iast

frequency samples, using

where N is the number of frequency points sampled. AZIest is then estimated using

where the factor of a half is required since A2* describes only half the fixture. The sign of

the square roots in (4-2) is chosen to minimize the error E, where

E = IIAzl- A21 eztll


4.4.2 Diode Measurements

The diode was soldered into the test fixture which was connected to the NNA. A 1 G I 3

tone was applied to port one of the fixture. The calibration removed errors up to the edge

of the test fixture, and the effect of the fixture on the measurements was removed to give

the waves at the diode package. In this section three experiments performed with the diode

in order to verify the operation of the NNA are discussed.

4.4.2.1 Comparison of Measured and Modelled Waves

Figure 4.1 I shows a comparison between the measured and the modelled waves with a

1.8 V peak incident tone. When the input voltage goes negative, the diode starts to conduct,

shorting the incident wave to ground. The reverse wave b1 is small when the diode is off,

Time (ns)

Figure 4.11: Measured and simulated waves at the diode


and large when the diode turns on. The positive part of the transmitted b2 wave is not

greatly affected by the diode when it is off, but is clipped when the diode turns on.

These waveforms agree well with those predicted by a model. There are small differ-

ences which cart be attributed to errors in the model, and are unlikely to be caused by inac-

curacies in the NNA. Two differences, and their possible causes are described below:

First, the ringing in the measured bl waveform is at a lower frequency than the model

predicts. This could only be attributed to massive errors in the NNA measurement which

would greatly change the shape of the overall measurement. Since the general trends of the

measurement are correct, it is more likely that this is a small error in the model.

Second, the measured transmitted waveform has a greater peak-to-peak value than

modelled, but the reflected waveform is smaller than modelled. This was verified not to be

an error in the calibration routine by applying power to port two of the fixture. The reflected

and transmitted waves were identically shaped to those in the first measurement, despite the

ports being switched. The reflected b1 wave from the first measurement was now seen at

bl, and the transmitted b2 wave was now seen at b l . This experiment ruled out the discrep-

ancy between the measured and modelled waves being caused by a systematic error in the

NNA. In the first measurement the bl reflected wave was too small but in the second meas-

urement the b1 transmitted wave was too big. The difference in the wave shapes is likely

due to an error in the model.

A small resistance or inductance between the diode and ground not accounted for in the

model could cause both the errors. A series resistance in the fixture would increase the cir-

cuit's time constant, decreasing the ringing frequency as observed. A series resistance or

inductance would prevent the diode from shorting the incident wave as well as the model

predicted. The reverse wave would then be smaller and the fonvard wave not as well clipped


as the model predicted. The model does not take into account the width of the transmission

line, or the vias to ground in the circuit; both of which could be the source of the error.

4.4.2.2 Voltage and Current Measurement

The voltage across and the current entering the diode are calculated using

where vi and 4 are the voltage and current at port i, Zo is the reference impedance, and ai

and bi are the forward and reverse waves at port i. Recall that the a and b waves are not

normalized as is often done, so are defined as voltage waves, not power waves.

The input voltage was swept from 0.25 to 2.5 V peak. Figure 4.12 shows the voltage

across the diode and Figure 4.13 shows the current through the diode. The current is actu-

alIy the sum of the currents entering port one and port two. For small input voltages, the

diode hardly turns on; the voltage is-sinusoidal and there is little current flowing, As the

input voltage increases, the diode conducts more during the negative part of the input tone;

more current flows and the voltage across the diode is clipped. These measurements are,

again, consistent with the operation of a diode.

To further confirm the correct operation of the NNA, the voItage measured at port one

of the device pIane is identical to the voltage measured at port two. This is to be expected,

since the port one and port two device measurement planes are both where the diode con-

nects to the transmission line.


0.5 1 1.5

Time (ns)

Figure 4.12: Voltage across the diode as the input voltage is swept

-20 f I I J

0 0.5 I 1.5 2

Time (ns)

Figure 4.13: Current through the diode as the input voltage is swept


4.4.2.3 Comparison with Direct Voltage Measurements

When power is incident to port one of the test fixture the a2 wave has a very low amplitude.

This is because most of the b2 wave leaving the test fixture is absorbed by the load at port

two of the NNA and not reflected back. Because a2 is approximately zero, the voltage

across the diode, calculated using (4-101, can be assumed to equal the b2 wave. This pro-

vides an opportunity to fuaher verify the operation of the NNA.

Port two of the fixture is connected directly to an input of the wideband oscilloscope.

Figure 4.14 compares this oscilloscope measurement with measurements taken using the

calibrated NNA. A measurement taken with the NNA but without the systematic errors

removed is also shown. This un-calibrated measurement was scaled in amplitude to make

1 1.2 1.4 1.6 1.8 2 Time (ns)

Figure 4.14: Direct voltage measurement and NNA measurements


a fair comparison since it is attenuated 20 dB by the directionaI couplers. The calibrated

NNA measurement agrees almost precisely with the voltage measurement taken directly

with the osciI2oscope. Assuming that the oscilloscope has a flat group delay, this is another

indicator the caIibration technique is working correctly. This was very good evidence that

the absolute phase and the absolute amplitude calibrations were working correctly.

The un-calibrated b2 wave deviates only slightly from the calibrated wave. Even if this

deviation were acceptable, the linear calibration is required to correct the other waveforms

with respect to b2. For a device with a greater mismatch from 50 R, a2 would be of similar

size to b2, and the waves would add incorrectly to give the voltage at port two. So, although

it may appear that the calibration only has a small effect, for other measurements its effect

can be significant. This will be seen in Chapter 5, where a device with a three ohm output

impedance in measured.

Chapter 5

Power Transistor Measurements

In this chapter the measurement of a Motorola MRF284 Laterally Diffused Metal Oxide

Semiconductor (LDMOS) transistor is described. This is a 30 W device designed for base

station applications at frequencies from 1000 to 2600 MHz. LDMOS transistors, like Field

Effect Transistors (FETs), have a gate next to a channel which is sandwiched between the

drain and source regions. In a regular FET, where the drain and source are both on top of

the substrate, a bondwire connects the source to the package ground. An LDMOS device

has the source on the bottom of the substrate and the drain on the top of the substrate. This

makes it possible to directly connect the source to the package ground. Removing the

source bonding wires greatly reduces source parasitics minimizing loss and feedback in the

device,

AIthough the MRF284 is a high power device, signals in modem systems will still drive

it into nonlinear modes of operation. Characterising this nonlinear behaviour is greatIy

complicated by the Iow input and output impedances that the device must be offered to

operate correctly. The goals of this chapter are to develop techniques to measure the wave-

5.1 The Fixture Design 70

forms of low impedance devices, and to show that the effects of tuners, used to change the

impedances offered to the device, can be removed from measurements. The waveforms at

the edge of the -84 were measured with a single 1.97 GHz tone incident to the gate.

The fixture which was designed to offer the device low impedances is described in

Section 5.1. In Section 5.2 the extraction technique used to model the fixture is developed.

In Section 5.3 measurements taken of the device using the NNA, are compared with pre-

dictions from a model. Finally, a method for building an amplifier using the NNA instead

of nonlinear models is proposed in Section 5.4.

5.1 The Fixture Design

The fixture holds the MRm84 so it can be connected to the NNA. It is basically a simple

amplifier circuit, providing electrical connections, DC bias, and impedance matching at the

gate and drain. Tuners on each measurement port change the impedance offered to the

MRF284 to affect its operation. Mechanical tuners have loss so they cannot offer low

impedances directly to the MRF284. Instead, the fixture has impedance translating trans-

formers to map impedances from the centre of the smith chart, which can be offered with

tuners, to low impedances.

Figure 5.1 is a picture showing the device mounted in the fixture. The thick lines con-

nected to the gate and drain leads are quarter wave impedance transformers. The optimum

impedances that should be offered to the device, provided by MotoroIa, are l+j 1.4 i2 at the

input and 2.5-j0.9 R at the output. The fixture was not designed to optimally load the gate

and drain, but to map the impedances which can be offered by a tuner or load pull system

into low impedances. The quarter wave transformer was designed to perform this imped-

ance translation at 1.97 GHz and at odd harmonics multiples. With no tuners, it was

designed to offer around 3 i2 to the transistor at the odd harmonics, and around SO Q at the

5.1 The F i e Design 71

Gate Bias Vgate

DC Bias Network

h/ 4 Transformer.

Gate

- Drain Bias Vdrain

50 R line

SMA Connector

Drain

Source

Figure 5.1: An MRF284 mounted in the fixture

even harmonics. The following equation was used to calculate ZG,, the impedance of the

quarter wave lines:

where ZI and are the desired impedances at each end of the line and I = h/4 indicates

that the length of the line is one quarter of the wavelength. For this design, ZI was 50 i2 and

must be translated to Z2 which was 3 Q. This gave a line impedance of 12.25 Q.

The short traces connecting the transformers to the coaxial SMA connectors are simply

50 R lines. The networks running from the device edge to the big wires are for DC bias.

They supply the gate bias V&,, and the drain bias V , - J ~ , . The bias networks were designed

5.2 Fixture Extraction 72 - --

to offer an open to the device at every harmonic multiple of 1.97 GHz. Note that the series

capacitors required to block DC from leaving the amplifier are not in the fixture; they are

external to the fixture and are not shown in Figure 5.1.

The circuit board contained many plated-through vias connecting the ground plane on

top of the board to the bottom of the board. The bottom of the circuit board was soldered to

a brass plate by using a hotplate and solder paste- The brass plate was then screwed to a

Iarge heatsink cooled with a fan. The flange of the MRF284 was bolted directly to a miI1ed

groove in the brass plate to supply a source ground connection, and also to provide a good

path for heat to leave the device. *

Figure 5.2 shows a schematic of the entire measurement system used to measure the

waveforms at the edge of the MRF284. It is similar to the low power NNA measurement

system described earlier. The four 20 dB attenuators reduce the sampled waves so the oscil-

loscope can measure them safely. The 10 dB attenuator is rated for 100 W and prevents the

directional coupler on port two from being over driven. The 6 dB attenuator is the smallest

that can be used to limit the power entering the switch to the specified 1 W. The capacitors

are part of the bias network, external to the fixture. The tuners are not always present, but

can be used to offer the device different impedances. The 40 dB amplifier boosts the tone

from the sweeper so that the device can be driven into compression. If the device input is

matched, about 4 W is needed to reach compression.

5.2 Fixture Extraction

As shown in Figure 5.2, the device is separated from the calibration planes by a fixture half,

a capacitor and possibly a tuner. It is important that the calibration planes offer close to

50 Q. A deviation from 50 R can cause a small error in the calibration, as discussed in

Section 3.2.1. If no tuners are used, the capacitors can be included in the calibration if they

5.2 Fixture Extraction 73

50 GHz Sweeper

Wide Bandwidth Oscilloscope

Ch.1 Ch2 Ch.3 Ch.4

r - - - - - - - - - - - - - I ~ ~ r e f

Calibration Plane Calibration Plane

Figure 5.2: NNA system used to measure MRF284

are not too reflective. Due to the reflective nature of the tuners it is important that they are

not included in the calibration.

The deembedding process will remove the effects of the fixture and possibly the capac-

itor and tuners from the measurements. When de-embedding, the fixture parameters are

chained together with the scattering parameters of the tuners and capacitors if required.

This technique is good when using tuners, since they can be adjusted, quickly measured on

a linear network analyser, and then replaced in the system. The NNA does not need to be

completely re-calibrated just because the tuners have been adjusted.


The technique used to extract the fixture parameters is described in Section 5.2.1, and

in Section 5.2.2 and Section 5.2.3 some measurements that verify the extracted fixture

models are presented.

5.2.1 Fixture Model Extraction

In this section a technique to determine the scattering parameters describing the fixture

is developed. Scattering parameters at each frequency of interest model the input and output

fixture halves. The frequencies of interest are 1.970, 3.950, 5.91C2, 7.880, 9.850, and

11.820 GH.; multiples of the fundamental up to the sixth harmonic.

The MT956 fixture characterisation and measurement software package from Maury

Microwave was used to extract the fixture models [15]. Figure 5.3 shows the fixture model

which was first presented in Section 3.2.1. For this highly reflective fixture, a Through-


btd a2d

Figure 5.3: Model used to describe the input and output fixtures

Reflect-Line (TRL) caIibration routine was used to determine theA and B scattering param-

eters [ld]. Three similar fixtures were built with different standards between the fixture

halves [17]. The through standard was made by butting both fixture halves together. The

line standard was built be connecting the two halves by a short piece of 12.25 i2 transmis-


sion line. The reflect standard, needs only to be modelled to within 180° to help with a

square root sign choice, so the fixture without the device soldered in was used as an open.

It was decided that three separate fixtures be built, each with a different calibration

standard, instead of building just one fixture and connecting different standards. The advan-

tage is that the standards don't have to be connected and disconnected to the fixture. The

disadvantage is that the fixtures must all be built identicdly. The brass was machined to

within less than a thousandth of an inch, and the fixtures were built as carefully as possible

so that standards were identical except for the way the two halves were joined. The software

generated a model of the input and output fixture from measurements of these standards

made using a linear network analyser.

To verify the fixture extraction was working correctly, the extracted input and output

fixture models were chained together. Figure 5.4 compares the amplitude of this extracted

Figure 5.4: Comparison of SZ1 amplitude of measured and extracted fixtures


model's SZL and the amplitude obtained by measuring the through fixture directly with a

linear network analyser. Note that only every tenth point on the lines is marked.The two

measurements lined up exactly. This should be expected since one part of the TRL algo-

rithm used to extract models of the fixture halves took a measurement of the through. This

test, however, helped indicate that the extraction was working correctly.

The fixture extraction includes taking a square root which leaves the sign of the Azl and

A12 pair, and the BZI and B12 pair unknown. Figure 5.5 compares the SZ1 phase of the meas-

ured and the extracted fixture models, arbitrarily choosing both signs to be positive. The

bottom graph shows the error between the two signals. There is no error at most frequen-

cies. However, there are some large errors, all multiples of 90". These errors are caused by

choosing the wrong signs for the square roots. Actually, the problem is worse than indi-

Frequency (GHz)

Figure 5.5: Comparison of SzI phase of measured and extracted fixtures

h

V) 200 Q)

2 ES)

0 . Y

L

2 & -200

-400

x : - - - . - - - * - - . - - --- .=.=.-: - . - . - - . . . . : -.....=----' - . - - . . . - - - : -... - i c - - - - i . : = - - - : - -

X . . = I t . =

X - x . %

I - -=- .x- - - ..-. * . - . . . . . , - .X . - - - -, . . - . . * - - - .-. - . -=. . - - - - - X - - . . - - - 5 - . F - - - - - - X

I I I I I I

0 2 4 6 8 10 12 14 Frequency (GHz)

5.2 Fixture Extraction 77 . .

cated: if both fixture halves have the wrong sign, when they are combined together the

resulting model will actually have the correct sign. Statistically, half of the frequency points

have the wrong sign chosen. The visible errors were at frequencies where only one of the

signs was incorrect.

These signs cannot be determined by assuming the fixture has a simple group delay, as

was done in Section 4.4.1 ; over the 1.97 to 1 1.82 GHz frequency range of interest, the fix-

ture has many resonance points. Instead, the fixture parameters from 50 MHz to 1 1.82 GHz

were extracted taking the positive roots. At the low frequencies, where the fixture is short

compared to the wavelength, the phase delay must be less than 180° so the signs must be

positive. The sign at each successive frequency point was chosen to prevent any Large dis-

continuities fiom appearing in the extracted Azl or BZL parameters. Figure 5.6 shows the

phase of AZ1. The phases resulting fiom positive and negative root choice are shown in grey.

For simple fixtures, choosing the phase to minimize large discontinuities is easily auto-

mated. For this fixture, with its many resonance points, this was done by hand. The resulting

phase is shown with the thick black line. Although there are frequencies where the signs

could not be chosen with absolute certainty, these points are not at frequencies of interest.

The god of the extraction was onIy to model the fixture halves at 1.97 Gflj and harmonic

multiples. At these frequencies the phase is well determined.

5.2.2 Fixture Parameter Verification

To verify the extraction technique, the impedances looking into the fixture halves were cal-

culated from the extracted models. Figure 5.7 and Figure 5.8 show the impedance offered

to the device output and input respectively. The output fixture offered a real impedance at

each frequency of interest, indicating that the quarter wave transformer was working cor-


-300 I I I I I I I 0 2 4 6 8 10 12 . 14

Frequency (GHz) Figure 5.6: Root choice of A21 parameter

rectly. The real impedance offered was around 3 SZ at the odd harmonics and 50 12 at the

even harmonics. This agreed with the simulation used to first design the fixture. The input

fixture behaves as expected but with a fundamental frequency of 2.2 GHz instead of the

desired 1.97 GHz. Unfortunately, the input quarter wave transformer was built slightly

shorter than designed. This error will change the input match slightly, but, since the fixture

was not designed to offer an optimum input match, this is not too important. For measure-

ments with the device driven into compression, an input tuner is required anyway.

5.2 Fixture Extraction

-4% 1 I I I I I

2 4 6 8 10 12 14 Frequency (GHz)

Figure 5.7: Extracted real and imaginary output impedance

Frequency (GHz)

Figure 5.8: Extracted real and imaginary input impedance


5.2.3 Calibration and Fixture De-embedding Verification

To verify that the calibration and de-embedding routines were working correctly, a meas-

urement was taken of the through fixture standard using the NNA. The through fixture has

the input and output fixture halves butted directly together. An input tone was swept from

1.97 GHz to 11.82 GHz and applied to port one. The errors up to the fixture edge where

removed using a calibration. The effects of the fixture and the external blocking capacitors

on the measurements were then de-embedded, to give the forward and reverse travelling

waves at the device plane where the two fixture halves were butted together.

The calibration must be performed with the 40 dB arnpIifier shown in Figure 5.2

removed from the NNA. The amplifier was tuned to operate at 1.97 GHz and was quite

narrow band. The calibration could not be performed with the amplifier present because it

blocks the signals used to calibrate at the higher harmonic frequencies. This will not affect

the measurement of signals at poa two at all. However, the calibration at port one is only

valid at 1.97 GHz. At other frequencies, the return loss looking into the amplifier output is

only one or two dB. This large reflection coefficient may invalidate the calibration at these

frequencies.

Table 5.1 shows the scattering parameters where the fixtures bun together with the

amplifier not connected. The impedance offered by the fixture at port one T,,,,, and the

impedance offered at port two rlOad are also shown. The S21 and S12 parameters are approx-

imately one, as would be expected. The S1 I and Sn parameters would normally be zero for

a good through. However, scattering parameters are defined with both ports terminated in

a reference impedance. In this case, port one of the through is terminated with T,,,,,, the

reflection coefficient looking into port two of the input fixture half, and port two is termi-


Table 5.1: Scattering parameters of through with amplifier removed

nated with rload, the reflection coefficient looking into port two of the output fixture haIf. t

The equation for S1 , the reflection coefficient that should be measured at port one is

s;, = S , , + s 2 1 1 2rl,ad

- '2zr10ad

where the S parameters describe the ideal through. Since SI1 = S21 = 1 . and Sl = SZ2 = 0 , 8

then SIl = rload. A similar argument shows that the reflection coefficient that should be

measured at port two is r,.,,,. The results are excellent for the first four harmonics, but

show small errors at the higher frequencies. This is most likely due to the fact that the NNA

calibration plane does not offer exactly 50 C2 to the fixture. This results in a slight error for

the I? estimations. Also, as discussed in Section 3.2.1, the error model is only strictly valid

assuming that the NNA ports offer 50 Q. The caIibration will try to correct the waves to

remove the effect of any mismatch from 50 S Z . The calibrated waves are estimates of what

the actual waves would be if there where no mismatch. Other possible sources of error are

physical differences between the fixture part of the standards, and of course repeatability

5.2 F i e Extraction 82

errors. A final possible source of error is a frequency offset between sources in the NNA

and in the linear network andyser used to model the fixture. The linear network analyser's

clock may be slow or fast with respect to the NNA source's clock. The fixture extraction

may have actually been performed at slightly different frequencies than the measurements.

The errors observed are only up to 3 O in phase and about 5% in amplitude. To put the angle

error in perspective, light travels 0.25 mm in the time it takes a 10 GHz waveform to

change by 3"!

Table 5.2 shows the scattering parameters and offered impedances at the device plane

when the amplifier is connected. Connecting the amplifier has two effects. First, the S1 and

Table 5.2: Scattering parameters of through with amplifier connected

Szl measurements, which were taken with power incident to port one, are only valid at

1.97 GHz. At other frequencies no power leaves the amplifier. Second, the waves sampled

at port one are not properly calibrated. The amplifier output offers a very reflective load at

any frequency but the fundamental, which partially invalidates the calibration. These

effects are seen in the measurements. The scattering parameters at 1.97 GHz are not as pre-

5.3 Transistor Measurements 83

cise as the ones without the amplifier. The trends of SI2 are correct, but due to the reflective

nature of the amplifier output, are not as good as the measurements taken without the ampli-

fier. The Su measurements are quite accurate, which is good since the most important part

of the MRF284 measurements will be the voltage and current at the drain. The errors in Su

are due to the reflection coefficient of the amplifier being ignored when calculating T,,,,,.

To conclude, the scattering parameter measurements of the through taken with no

amplifier match the predicted values well. The measurements taken with the amplifier are

not as good as those taken without it, as was to be expected due to the large mismatch the

amplifier adds at port one. The waveforms taken at the gate of the MRF284 will not be per-

fect, although the fundamental components will be measured accurately. The amplifier will

not affect the measurements taken at port two, where the interesting drain waveforms are.

5.3 Transistor Measurements

This section presents measurements of the MRF284 taken using the NNA. The goal was to

demonstrate the variety of measurements that can be taken, as we11 as to gather further evi-

dence that the NNA was working correctIy. Once the fixture parameters were extracted, the

device was soldered into the fixture. A single tone at 1.97 GHz was applied to the input port

and the NNA was used to measure the harmonics up to 11 -82 GHz. Above this frequency

the waveforms had IittIe power.

Section 5.3.1 compares the voltage and current measurements with predictions from a

model. Section 5.3.2 presents measurements of the drain waveforrns taken when the device

is matched for maximum output power. Section 5.3.3 further verifies that the NNA. is work-

ing correctIy by calculating the impedance offered to the drain from the measured current

and voltage waveforms.

5.3 Transistor Measurements 84 - - - - - -

53.1 Comparison with Model

For this measurement, no tuners were used so the fixture was transIating the 50 !2 offered

by the NNA to low impedances at the gate and drain. Around 3 Cl was offered at the odd

harmonic frequencies and around 50 S2 was offered at the even harmonic frequencies. The

gate was biased at 2 V and the drain at 26 V, resulting in a 200 rnA drain current, The gate

voltage was chosen so the device would be almost off with no input signal present. This

class-AB configuration produced many harmonics when the device was driven with a

36 dBm, or 4 W7 tone.

The MRF284 was modelled using a Root model and package parasitic parameters sup-

plied by Motorola. The simulation embedded this model between the scattering parameter

files which describe the two fixture halves. Figure 5.9 compares the measured and modelled

drain waveforms at the package edge. The model predicts the measured waveforms surpris-

ingly well. The measured and predicted drain voltage waveforms are both dipped at the

bottom. This asymmetrical clipping is caused by the high impedance offered to the drain at

even harmonics. Although the second harmonic current is significantly smaller than the cur-

rent at the fundamental, it results in a voltage of similar magnitude. This large second har-

monic voltage combines with the fundamental to produce the observed clipping.

Figure 5.10 compares the measured and modeled gate waveforms at the package edge.

The gate current was modelled correctly, but the measured gate voltage was 30% larger than

modelled. This is likeiy due to an error in the input fixture model. The TRL extraction afgo-

rithm did not take into account the large step from the transformer to the gate flange. The

source connection to the fixture ground was very near to this step which caused an

increased fringing capacitance. The voltage predicted by the model was found to be very

sensitive to any small change in input impedance. This sensitivity, combined with the step


Figure 5.9: Modelled and measured drain waveforms

15

Time (ps)

Figure 5.10: Modelled and measured gate waveforms

10 I I f

0 -2000

200 400 600 800 1000 Time (ps)

15 3000

. Q

,

I O e 0 3

i3 3 h

3 ' . . -1000 2 . .. . .

- . - _ - . . - - - . - -2000

-1 000 . - . - . . * * . - - . - -

-15-

-20

r

vdrain measured - vdrain simulated

0 4000

200 400 600 800 1000

! :

-3000

: ' 0 ' -0 -:

- - - - - - - - - idrain measured

- - - -o- - - - idrain simulated

- measured "gate - vgate simulated I I i

- - - - - - - - - igate measured . - - .O- - - - bate simulated

" . ' ' ' - . . - - ' - - ' ' -..

i -

-

5.3 Transistor Measurement. 86

that wasn't modelled, could explain the discrepancy between the measured and modelled

gate voltages. Another source of error at the input, is the assumption that the calibration

which must be performed without the 40 dB amplifier connected, is still valid when it is

connected.

Figure 5.11 shows that the measured and modelled load lines compare favourably. As

described in Section 2.2.1, a load line is simply a plot which shows the voltage on the hor-

izontal axis versus the current on the vertical axis. It is a useful tool to gain insight into how

a device is operating. The slope of each harmonic component in the load line is determined

by the impedance offered to the drain at that frequency. Increasing the resistance compo-

nent of the impedance will increase the voltage swing for a given current swing. Increasing

Figure 5.11: Load line at the package edge


the reactance portion of an offered impedance increases the hysteresis of the curves. This

will be seen in Section 5.3.2 and Section 5.3.3.

5.3.2 Matching with Tuners or Loadpull System

The gate bias voltage was adjusted to around 2 V to get a 200 rnA drain current. The input

was then matched using a tuner. Matching the input reduces the power reflected back from

the gate and maximizes the power entering the gate lead of the device. A tuner at the output

was used to load the drain to get maximum output power. The input power was increased

until the output power was L dB lower than it would be if the device was linear. This is the

1 dB compression point of the device. The output was then matched for maximum power.

This chaaged the 1 dB compression point, so the input power was swept to find it again.

The output was then tuned again for maximum power. This iterative procedure of tuning

the output, and finding the 1 dB compression point was repeated until the tuner setting did

not change. The input tuner was not changed throughout this procedure.

Figure 5.12 shows the external load line for measurements with the un-tuned output and

the optimally loaded output. The tuners were characterised using a linear network andyser,

and their scattering parameters chained with those of the fixture and blocking capacitors.

These combined models were used to de-embed the effect of the tuners, the capacitors and

the fixture from the measurements to obtain the load line at the device edge.

The tuned load line has a much greater current swing than the un-tuned line. The power

in the fundamental of the output wave was 30 W, the rated power for the device. The tuned

load line is closer to a linear, oval shape than the un-tuned line for two reasons. First, the

tuned impedance offered at the fundamental frequency resulted in a large fundamental com-

ponent in the voltage. Second, the un-tuned fixture offers around 50 i2 at the even harmon-

ics, whereas the tuner offers essentially random impedances at the harmonic frequencies.

53 Transistor Measurements 88

Figure 5.12: Tuned and un-tuned external load lines


In this case, the magnitude of the impedance offered at the second harmonic frequency was

around 10 Cl which produced a small second harmonic component in the voltage for the

tuned measurement.

Figure 5.13 shows the tuned and un-tuned internal load lines. The MRF284 package

was assumed to have no coupling between the gate and the drain. With this assumption,

input and output scattering parameter models were generated from Motorola's models

which described the gate and drain parasitics respectively. These parasitic models were

chained with the fixture, the tuner and the capacitor models and used to de-embed the rneas-

ured waves up to the chip substrate.

The drain to source parasitics for the MRF284 are quite small. Because of this, not

much current should be lost between the internal and the external drain connection. Indeed,

the current swing of the external measurement is only very slightly smaller than the internal

measurement. As would be expected for a transistor tuned for maximum power and driven

into compression, the voltage is clipped at the left where the device leaves the saturation

region. The current is not clipped hard at the bottom of the load line became the impedances

offered at the drain are not red. This means that when the channel stops conducting, and

the voltage at the drain is pulled up by the inductance of the DC bias supply, the capacitive

load will draw current to try and keep the voltage the same. Positive current is defined as

entering the drain, so the current which charges the capacitor will be negative.

The effects seen when the output was matched for maximum power are consistent with

those predicted by a model. These effects are also consistent with the theoretical operation

of amplifiers, and are further indicators that the NNA is working correctly.


5.3.3 Verification of Waveforms with Ohm's Law

To further confirm that the NNA was operating correctly the voltage, current and imped-

ance at the drain were investigated. Figure 5.14 is a simplified schematic showing the drain

connections. The Vdrain parameter is the DC drain bias voltage, vg;, is the input gate volt-

Figure 5.14: Simplified diab0ram showing the drain voltage, current, and load

age, vdrain is the drain voltage, idrain is the drain current, and zload is the impedance offered

to the drain. From the diagram, Ohm's law

should be valid at each multiple of the fundamental frequency. The negative sign is

required because iMn is defined as leaving the load.

The MRF284 was biased with 4 V at the gate and 26 V at the drain. No tuners were used

in the measurement. The load impedance was estimated from B22, the reflection coefficient

seen by the device looking into the output fixture using


where B22 is defined in Figure 5.3. A 1.97 GHz tone was swept from 10 dBm to 36 dBm.

The six harmonic components of v h - n and idrain were extracted and qoad was estimated at

each frequency using (5-3). Table 5.3 compares the values of qOad extracted from the fix-

ture model using (5-4) with the values from the measurements calculated using (5-3). The

Table 53: Extracted ZIoad and measured Zload at different power levels

Frequency Fl 1.970

3 -940

5.9 10

7.880

9.850

1 1.820

extracted and the measured impedances agree well. The small error between the two is due

to the way zlOad was calculated from the extracted output future model. It is assumed in

(5-4) that the impedance offered to port one of the output fixture half at the calibration plane

is exactly 50 a. In reality, the return loss of the 100 W, 10 dB attenuator is only specified

to be greater than 15 dB.

The measured z l , d values are very consistent as the power is swept. The gain of the

oscilloscope inputs was increased for the smaller input signals to minimize the effect of

dynamic range limitations. The only differences between the measured impedances at dif-

ferent powers is for the higher harmonics. When the input power is low, the drain and volt-

age waveforms have almost no higher harmonic frequency components. The effect of

random errors in the measurement begin to effect the accuracy of the calculated values.

However, even these very low power measurements are quite consistent.

(Extracted) 1 %ad cn)

(36 dBm) (30 dBm) (20 dBm) (10 dBm)

3.3053ij0.0510

49.253-j2.4757

3.2426-jO.6532

45.665-j 1.8636

3.8404-jO.2310

26.821-tj8.0560

3.0691-j0.0426

49.975-j7.0602

3.3907-j0.6396

45.932-j5.0364

2.8626-j0.0297

27.735ij10.859

3.0682-j0.0421

49.974-j7.0043

3.3897-j0.6393

45.936-j5.0562

2-8659-jO.0337

27.748ijL0.862

3.0680-3'0.0423

49.976-j7.0209

3.3944-j0.6407

46.0 18-j5.0633

2.8426-jO.0521

27.854+j101857

3.0686-j0.0424

49.966-j7.0 184

3.3917-j0.6136

48.55 l+j 1.4925

3.1275-j0.0476

27.534+j10.097

5.4 Proposed Amplifier Tuning Technique 92

5.4 Proposed AmpMer M g Technique

The capability to measure the load line right at the chip substrate is one of the most power-

ful things the NNA can be used for. The shape of the load line at the device channel, which

is very close to the chip edge, determines the efficiency, gain, output power and linearity

of an amplifier.

The shapes of the voltage and current waveforms at the drain can be manipulated to

make different kinds of amplifiers. For example, to make a class-F amplifier, the gate bias

is changed to get a 180" current conduction angle, so the current is a rectified sinusoid. The

voltage waveform is made square so that when the current is high the voltage is low, and

when the current is low the voltage is high. This reduces the power dissipated by the device

as waste heat. The tuned load line shown in Figure 5.13 could be from a prototype amplifier

on the bench. To create a class-F amplifier, the impedance offered to the channel at the fun-

damental frequency should be made red, so that the current does not go negative and the

device turns off completely. The impedances offered at the hannonic frequencies must be

changed to produce a square voltage wave which is low when the device is conducting cur-

rent. For an ideal device with no parasitics, the odd harmonics should be offered an open

and the even harmonics should be shorted. The fundamental should be matched for maxi-

mum power or gain. Obviously for a real device, these theoretical impedances will have to

be changed a littIe. The NNA can be used to look at the voltage and current waveforms to

determine how the impedances should be changed,

Assuming the device is ided, changing the load impedance will not affect the drain cur-

rent The device can be thought of as supplying a current which produces a voltage across

the output load. In this case, Ohm's law can be used at each frequency to calculate the

impedance required to produce the desired voltage from the given current.


The assumption that the drain current is not affected by changing the load impedance

was tested. The input was matched with a tuner on the input. The drain bias Vdrain was set

to 26 V, the gate bias to 4 V and the input power was set to 20 dBm. The output was

tuned for maximum gain. Measurements were then taken with and without the output tuner.

Fi,me 5.15 and Figure 5.16 show the drain and gate waveforms for the tuned and un-

tuned measurements. The gate current and voltage did not change greatly by changing the

load impedance. The drain current advanced by about 30" and increased in amplitude by

about 10% when the load impedance was changed. As would be expected, the drain voltage

changed quite dramatically-

The change in drain current is larger than expected, and appears to slightly disprove the

hypothesis that the drain current is not a function of load impedance for the MRF284. How-

ever, the fundamental of the load impedance was changed from 3.0743-j0.0651 Q to

2.0984-j3.7896 i2; a very large change. It is proposed that for smaller changes, the hypoth-

esis is valid to a certain degree.

The marginal truth to the assumption that the drain current is not a function of the load

impedance, suggests that an iterative design approach may be valid. A first cut of an arnpli-

fier would be built using nonlinear models if available, or by assuming the device 'is ideal.

The voltage and current waveforms at the drain would be measured with the NNA. Assum-

ing the drain current will not be affected, new load impedances are calculated at each fre-

quency of interest to obtain the desired voltage shape. This new amplifier would then be

built and again measured on the NNA. The amplifier will likely not behave exactly as pre-

dicted, so a new set of impedances would be calculated to get the desired voltage waveform

at the drain. On this second design iteration, the impedance changes should be much


Time (ps)

Figure 5.15: Drain waveforms with two different load impedances

Time (ps)

Figure 5.16: Gate waveforms with two different load impedances


smaller than for the first iteration, so the drain current should change less. A new amplifier

would be built and another design iteration performed if the waveforms were not shaped as

desired.

This iterative approach initially seems wasteful in terms of the number of prototypes

that may need to be built. However, when building a high power amplifier, it is normal to

go through several design prototypes until everything works correctly. The proposed itera-

tive technique could likely be performed with each prototype that is built. By understanding

exactly how the device is operating, and making changes based on this knowledge, better

amplifiers can be built in less time than it currently takes.

Chapter 6

Conclusion

This thesis described a Nonlinear Network Analyser (NNA), and some tests that verified

that it works correctly. The NNA excites either port of a device under test with a microwave

signal. It measures the amplitude and phase of the harmonics in the travelling waves inci-

dent to, reflected by, and transmitted by a network. The NNA has a measurement band-

width of about 18 GHz. Above this frequency an assumption used to calibrate the NNA,

that the oscilloscope inputs have flat group delays, begins to cause phase errors. The system

has a graphical user interface that controls the measurement hardware. The work presented

in this thesis is summarised in Section 6.1 and some ideas for future work related to the

NNA are presented in Section 6.2.

6.1 Thesis Summary

In Chapter 2 it was explained what an NNA does, how it works, and why it is useful.

Because the wavelength of microwaves is on the same order as the circuit size, it is quite

difficult to measure the voltage and current waveforms at the ports of a network. Direc-

6.1 Thesis Summary 97

tiond couplers separate the forward and reverse travelling voltage waves without affecting

the operation of the network under test. A calibration is used to estimate the waves at the

network edge from these waves which are sampled a distance away from the network. The

voltage and current waveforms can be calculated from the travelling waves.

The NNA samples the forward and reverse waves at two measurement ports using a

50 GHz bandwidth sampling oscilloscope. Since, in the frequency domain, the phases of

different frequency tones rotate with respect to each other, a phase measurement must be

defined at a certain time. This reference time is defined by the oscilloscope's input trigger.

For the phase measurements to be repeatable, every tone to be measured must be at a muI-

tiple of the trigger frequency. The start and end of the sampled waveforms must be contin-

uous so they do not need to be windowed before their spectra are estimated using an FFT.

This is guaranteed by making the time window Iength a multiple of the trigger period.

The NNA measures the amplitude and phase of all the tones generated by a nonlinear

network, essentially providing the shape of the waveforms. This information will be useful

for characterising most nonlinear microwave networks. It will be especially useful for look-

ing at the current and voltage waveforms in a transistor, to determine how an amplifier is

working, or to improve device models.

Unfortunately, to operate efficiently, power amplifiers must be driven into compression,

\ and offered loads and biased so that they behave nonlinearly. Increased efficiency lengthens

the battery life in mobile power amplifiers, and reduces the cost of building and maintaining

power amplifiers in base stations. It is very difficult to amplify some digitaI communication

signals with high peak to average power ratios linearly. These factors mean that amplifiers

must often work in nonlinear ways, resulting in signal distortion. Intermodulation distortion

causes a signal to spread in frequency. This distortion causes adjacent channel interference

which limits how efficiently spectrum can be used. The NNA is the only tool that fully char-


acterise this nonlinear behaviour by measuring the waveforms entering and leaving a non-

linear network directly.

The NNA implementation was described in detail in Chapter 3. There are a number of

sources of error in measurements taken with the NNA. Noise and jitter are the biggest

causes of random error and are reduced by averaging many waveforms together in the oscil-

loscope. Systematic linear distortion introduced by the NNA is removed with a calibration.

An eight parameter error model at each frequency of interest describes the measurement

system. A linear calibration, similar to that performed in a linear network analyser, deter-

mines seven of the error parameters. An absolute calibration at each frequency of interest

determines the last parameter in order to correct the shape of the measured waveforms in

the time domain. The absolute phase calibration assumes the oscilloscope inputs have flat

group delays. This reduces the phase calibration problem to that of characterising the NNA

between the port one calibration plane and the osciIloscope inputs. The NNA is always cal-

ibrated to connectors. To measure a device that is in a fixture, the NNA is caIibrated up to

the edges of the fixture, and the effect of the fixture on the measurements is de-embedded.

In Chapter 4 experiments were described that demonstrate the NNA works correctly.

The flat group delay assumption, used to simplify the absolute phase calibration routine,

was examined. A measurement taken by Jan Verspecht, working for Hewlett-Packard, indi-

cates that the phase error of an earlier version of the oscilIoscope used in the NNA was only

&.75O up to 18 GHz. The magnitude of this phase error is very small, and is not an issue

affecting the accuracy of the NNA.

A measurement of the oscilIoscope's time base distortion, a systematic error in the

timing of the samples, was taken. For single tone measurements, or measurements where

the bandwidth around each harmonic is less than 250 MHz, this distortion can be ignored

since its effect is removed by the caIibration routine. For measurements where this error is


a problem, it can be reduced by using a modified Fourier transform which takes into

account the timing of the samples.

The Linear part of the calibration was tested by measuring a splitter with a linear net-

work analyser and with the NNA. The results agreed very well, indicating that the linear

part of the calibration routine works correctly.

To verify the entire operation of the NNA, measurements taken of a Schottky diode

were compared with predictions from a model. The measurements agreed well, but some

discrepancies indicated that the simuIations did not take into account a resistance or induct-

ance in the fixture. Because the diode fixture was essentially a 50 R Line, the voltage across

the diode is approximately the same as the voltage travelling wave leaving the fixture. The

oscilloscope was used to measure this wave directly. This measurement lined up exactly

with a measurement taken using the NNA, where the effects of the cables and directional

couplers were removed using a calibration. This verified that the absolute calibration rou-

tine works correctly.

In Chapter 5 measurements taken of an MRF284 were discussed. The MRF284 is an

LDMOS transistor which must be offered low impedances at the gate and drain to operate

correctly. The NNA was modified to operate with the 30 W signals required to test the tran-

sistor. A fixture was built which supplied the device with bias voltage and also had quarter

wave transformers which translated the impedances from tuners into low impedances. A

TRL extraction technique determined the fixture half models, but left two signs for root

choices unknown. A new technique was used to determine these signs. The extracted fixture

models agreed well with simulations used to design the fixture.

Measurements of the through fixture taken with the NNA verified that the calibration

and deembedding processes work as expected. Because the calibration must be performed

6.2 Future Work 100

without the driver amplifier at port one, measurements at port one were only valid at the

fundamental. The drain measurements at port two were not affected by the amplifier.

The drain voltage and current measured with the NNA agreed well with predictions

made using a simulator. The gate voltage was 30% larger than predicted; likely due to

capacitive fringing in the fixture not included in the extracted fixture models. A tuner was

used to match the device for maximum output power. The load lines at the device edge, and

at the chip subsAmte edge, were measured with and without the output tuner. All the effects

seen were consistent with the theoreticaI operation of amplifiers.

The measurement accuracy was further confirmed by calculating the load impedance

from the measured voltage and current waves. At each frequency of interest, these meas-

ured impedances agreed very well with the load impedance calculated from the output fix-

ture half model.

6.2 Future Work

There are a number of research topics that could be investigated, either to improve the oper-

ation of the NNA or to demonstrate that the NNA is a useful design tool. In this section a

number of them are discussed.

In Section 5.4 a technique for building amplifiers was proposed, based on the assump-

tion that a small change in load impedance effects the drain voltage substantially more than

the drain current. An iterative approach could be used to tune the drain waveforms for a

desired shape. After a few iterations of changing the load to get a desired voltage waveform,

the impedance changes will be small and any deviation from the assumption will be negli-

gible. It is proposed that this technique could be tested by building a highly efficient class-

F amplifier.

6.2 Future Work 101 - - - - --

The NNA provides a lot of information that would be useful for generating device mod-

els. This could be a very fruitfkl area of research. The NNA should also be a useful tool for

system-level, black-box modelling. System level models could be used for simulating lin-

earization techniques or could be included in simulations of proposed systems that predict

bit error rate curves and other system properties.

In Section 3.2.1 an approximation made while developing the error model was

described. A calibrated measurement returns what the waves at a port would be if the NNA

offered exactly 50 52 to that port. The technique it uses to remove the effect of the deviation

from 50 i2 is only strictly valid for linear networks. This effect was ignored because the

NNA actually offered very close to 50 Q. A technique was developed to remove the effect

of this error, but it has not been tested so was not discussed in this thesis. This work could

improve the routines used to calibrate NNAs.

Appendix A

NNA LabView Software Guide

This appendix is a guide to the software that runs the NNA measurement system. The NNA

software controls most aspects of the measurement process from calibration to displaying

results. It is written using the National Instruments LabView programming language. This

language was chosen because of its excellent support of the National Instruments GPIB

card used to interface with the NNA's components, and the tools it provides for developing

graphical user interfaces.

Overview of Software

Figure A.1 shows the hierarchy of panels visible to the user. Each box gives the panel's

name at the top and a summary of the inputs required from the user underneath. The panels

are shown vertically in the order in which they would first be used. This section gives a

brief overview of how these panels are used. The section after will give precise details of

how the panels work and what they do.

NNA LabView Software Guide 103

Figure A.1: NNA interface hierarchy showing panel names and describing inputs

Open calibration panel

Set cal powers / scope

Set GPIB addresses

Choose folders Choose fixture files

- - ., - J ; ;<> : ; .~y$ : *y ;a>e~ , :~ -L ; ;~~ - *:

:>;?? M & ~ ~ ~ e m e n ~ ~ ~ , G . : ~ - ~ ~ ~ r ~ ~ : - ~ 3 - ~ ; < < g i ~ ~ ~ ~ ~ ~ f < i ~ . ? ; .--

' -~;-2~~firact10~r,:L~~f~T$ -.--La- r, --..<,*. ,-. . ,,,-. - - ,. . ~ ~ ~ - ~ : ~ - - = ~ ~ s ? & ~ $ ~ ~ - ~

,.-- .-... r-*- -p!&;; &;*y!~ zhy$$-c$;:,. :;- < .. .: ,z23;-p;- & 5 q r q 9 4 ~ : ~ ~ ~ ~ ~ -z..:8-::

a- - -/-- :* .. 2&$$%i$in~le~~ne:~,..~ .-:: LG~..~~J%~Y~ . - i;F [email protected]~ * :-*:, , *a-.:- .-~:d%- 5: <..,:2z,,: .-A,%- firr~&*~:-~Y7~. ;;'.;'.,: Choose frequency

Set meas power / scope

Set scales

Write data files

- Choose frequencies

Set meas power / scope

- ;.;-;;z; :y.. .<i.:< - ,A , : -. -

"?

.. - , - 7.,-- ,- --? ..-,<.- 54 2,. .4.c?$;:,;; : . . --.. ..:s---r:r.wo dTo.ne . ., . . I.-- . -+-:>:- , .<.* . - -

;;-:,,-;,;*.:T .. I , , . -peV .--. '.?.c.+-,-' .:.. -- -..--r,--.FH T... =.:;:.-, r.-..;: .-. . ~. .

.- . - - ' . < - . ...-. ~ .,-. - . -,. 2; -22.: ---= ..-> L.-Ty;;, -* ;. - .-

'- ' " - -- ' -. - , '-.'. ';;,.-;a; >-.T;+:. s,7'. . ,-, ,,, .. . ,. . . .-.. ".: -.:. . - - ., .. ,2 ...-.-;+-.. ..- -... .. . -.:::, -*-y 5 zc :2t/-+&:,m.;-~,--. ,c-.- '.

'..

,.-;:::V~~ew:Wavefo~s::~ 7.-~+k~.;-z:u~~7-;~+~:,-~~7~-~z~~c ,.. . ,-,. .-,&z-y-. .,<- /a.s-'... -4 ,- -4. &SV>.. -... " i .-&w.z1.z. -.-- 2 -

Prompted for file name Choose display type


The Front panel is used to set some parameters and to open sub-panels. When using the

NNA for the first time, the GPIB addresses of the equipment should be set on this panel.

The directories used to store calibration and measurement information are aIso selected

here. There is an option to de-embed the effects of a fixture from the measurements. Press-

ing the run button will start the main panel running. Once the panel is running, pressing

one of the large buttons will bring up the corresponding sub-panel. Pressing the STOP

button will halt the program.

Before the NNA can be used the Set-up Equipment panel should be run by pressing the

SETUP button on the Front panel. It will reset the oscilloscope and the GPIB bus so that

everything is in a predictable state. The oscilloscope timebase is set here and the Calibrate

Power Meter panel can be called to load the power meter head's calibration data into the

power meter. On this panel, and all other sub-panels, the required fields should be filled in

and the run button pressed to start the panel. When the panel has completed, pressing

+ -&-- L..++-" rn ..,:,I ~ G L U I I I V U L I V ~ ~ - nlll g~ b ~ c k to the next panel up in the hierarchy.

Before a measurement can be taken the NNA must be calibrated. The Acquire Calibra-

tion Data panel is first used to measure the standards, and the Extract Calibration Param-

eters panel then used to extract the calibration parameters from this data,

The Acquire Calibration Data panel is opened by pressing the CAL DATA button on

the Front panel. It gives the option of selecting either a linear or nonlinear calibration. The

resulting SOLT Linear and SOLT Nonlinear panels have fields to enter the calibration fre-

quencies. The selected panel will prompt the user to connect standards and it will record

the waveforms from each measurement it takes in the calibration data directory.

Pressing the CAL EXTRACT button on the Front panel will bring up the Extract Cal-

ibration Parameters panel. It takes the raw data from the calibration data directory and


generates the error correction matrixes which are saved in the calibration parameters direc-

tory

After connecting the DUT the Acquire Measurement Data panel should be opened with

the MEAS DATA button on the Front panel in order to take a measurement. From here

either the Frequency Sweep, Single Tone, or Two Tone panels can be opened. The Frequency

Sweep panel will perform a frequency sweep measurement similar to that performed by a

linear network analyser. The Single Tone or Two Tone panels will take a single measurement

with power incident to a specified port. These panels record uncorrected data in the meas-

urement data directory. The Measurement Extraction panel removes the systematic errors

from the measurement and de-embeds the effects of a fixture from the measurement if

required,

The waveforms that result from a single tone or two tone test can now be viewed with

the View Wmefonns panel by pressing the VIEW WAVEFORMS button on the Front panel.

Various time-domain or frequency-domain modes can be selected to display the results in.

The Cascade Fixture Files panel is opened by pressing the CASCADE FILES button

on the Front panel. It chains a number of Touchstone format scattering parameter files into

a single file. This is useful for generating a deembedding file describing a number of com-

ponents connected between the calibration plane and the Device Under Test PUT).

Panel Details

This section gives a detailed explanation of the panels shown in Figure A- 1. Many of the

sections refer to Touchstone format scattering parameter files. For this reason, these files

are described first.


Touchstone Scattering Parameter Files

This standard file forrnat contains a number of header lines followed by a number of data

lines:

! <comments>

# <frequency units> <parameter> <fonnat> R <n>

<data line>

.-.

<data line>

where

! = delimiter indicating a comment line

# = delimiter indicating the line that specifies the data format

frequency units = units of frequency: Hz, kHz, MHz or GHz

parameter = parameter type of data: S, Y, 2, G or H; normally S

format = parameter format of data:

DB for dB-angle

MA for magnitude-angle

RI for real-imaginary

n = real reference impedance in ohms; normally 50

Although Touchstone format files can contain different kinds of parameters, the NNA uses

only scattering parameters so the parameter type will always be S. Each data line contains

numbers separated by some form of white space. The first column gives the frequency in

the units indicated byfreqccency units. The eight columns that follow are organised into four


pairs normally describing the S, S2*, S12, and Su parameters in the format indicated by

format. For example, if the file contains scattering parameters in the red-imaginary format

a single data line would be:

f WSI I 1 ~ ( S I I J Re{S21} Im(S21 J Re{S12J h{S121 Re{S22} Im{S22}

Front Pane1

The Front panel is automatically opened when the NNA software is started. It has a number

of buttons which bring up sub-panels. There are also fields that determine the operation of

the NNA.

When using the NNA for the first time the GPIB addresses of the equipment should be

set on this panel. After setting this information, or any other permanent information, the

'Make Current Values DefauIt' option from the 'Operate' menu should be selected so that

the information does not have to be re-entered when LabView is restarted. Note that this

option is only available when the software is stopped.

The MAIN SOURCE ADDRESS field sets the GPIB address of the main source used

for calibration and for taking measurements. The MAIN SOURCE TYPE field selects the

type of the main source. It is a list of the three sources which were available in the lab at

the time of writing: the W-83650, the HP-8780A and the HP-865x series. The M A .

SOURCE POWER LIMIT field is used to limit the power from the source; if a request is

sent to the source for a power higher than this limit, an alarm will sound and the software

will stop. This is to reduce the likelihood of accidentally applying too much power to either

the DUT or the NNA measurement system.

The 437B ADDRESS field sets the GPIB address of the HP-437B power meter used in

the absolute calibration routine. The 437B SENSOR NUMBER specifies the memory posi-

tion in the power meter that holds the calibration table for the connected power meter head.


Finally, the 1 17 13A ADDRESS field sets the GPIB address of the HP-117 13 switch con-

troller and the 54750A ADDRESS field sets the GPIB address of HP-54750A oscilloscope.

This panel contains four fields under the header of DIRECTORIES for specifying the

directories used by the main parts of the software. These are changed by clicking on the

button above them while the panel is running, opening a dialogue box from which a folder

can be chosen. The calibration data directory stores the waveforms that the NNA measures

during the calibration routine. The calibration parameters directory stores parameters

extracted from this data to model the errors in the NNA system. Note that a directory can

only contain one set of either calibration data or calibration There is an indica-

tor on the front panel that describes the calibration parameters that will be used for correct-

ing a measurement. The measurement data directory is used to store the uncorrected

waveforms acquired by the NNA when taking a measurement. The measurement results

directory stores the results obtained by using the parameters in the calibration parameters

directory and the specified de-embedding files to remove the errors from the raw data in the

measurement data directory. The measurement data and measurement results directories

can both contain a number of different measurements. The measurements in the measure-

ment data directory are listed under the heading MEASUREMENTS. The name of the

measurement that wilI be either taken or corrected should be entered in the SELECTED

MEASUREMENT field under this list.

If measurement de-embedding is to be performed, the FIXTURE DE-EMBEDDING

box should be selected and the names of the input and output fixture files specified in the

INPUT FIXTURE and OUTPUT FIXTUEE fields. Note that these fields are hidden unless

the box is on. The diagram above the input fields indicates that port two of the fixture halves

is the port that connects to the DUT.


Set-up Equipment

This panel should be run when the NNA is first turned on. It will reset the GPIB bus and

the GPIB buffers of the equipment connected to it, so that everything is in a known state.

There are fields to set the oscil~oscope timebase, acquisition type and triggering. Notice

that there are no fields to set the vertical settings of the oscilloscope; these are set individ-

ually for each part of the calibration and measurement process. The TIMEBASE SCALE

is normally set to I0 ns per division. This gives a total measurement time window of 0.1 ps

which is long enough to capture any tone which is a multiple of the 10 MHz reference

which is normally used for triggering the oscilloscope. The RECORD LENGTH, which is

the number of samples stored by the oscilloscope, should normally be set to its maximum

value of 4096 points. The AVERAGING field should normally be on. For the experiments

performed in this thesis, the NUMl3ERAVERAGES field was set to 64 to reduce the noise

floor to -65 dB without resulting in too long a measurement time.

The TRIGGER SLOT field is used to select which one of the two trigger inputs is active.

The input on the 20 GHz module is in slot two and the input in the 50 GHz module is in slot

four. The trigger LEVEL and SLOPE settings are the same as those in most other osciIlo-

scopes. When the trigger either increases or decreases past the trigger level, a trigger

occurs. To minimize jitter the level should be set so that the trigger occurs during the fastest

changing part of the trigger waveform. In the case of a typicd sinusoid this is at zero volts.

The trigger slope can normally be set as either positive or negative. The BW LIMIT switch.

limits the trigger input bandwidth to LOO MHz. If the trigger input is less than 100 MHz this

option should be enabled to reduce noise on the trigger signal and the resulting jitter.

The FLATNESS button turns on the flatness calibration in a HP-54750A sweeper. This

assumes that the sweeper has already been calibrated for flatness as described in its manual.

NNA LabView Software Guide 110 - - -

This option keeps the amplitude of the signal applied to the DUT constant as the frequency

of the sweeper is swept. It essentially accounts for any frequency dependent loss in the

NNA cables and directional couplers. The LOAD CAL TABLE button opens the Power

Meter Table panel.

Power Meter Table

This panel is used to load the calibration data shipped with a power meter head into the

power meter. This needs only be performed if the data has not aIready been entered. The

calibration data is essentially a list of percentages given at a number of frequencies that

describe the response of the power meter head. Power meter heads are shipped with a

detailed printout showing this calibration data. An abbreviated version of this data is also

shown on a sticker attached to the power meter head. The calibration data pairs are entered

in the FREQ and CAL FACTOR columns. The REF CAL FACTOR gives the response of

the power meter head at the 50 MHz calibration frequency.

The power meter has ten sensor positions that can each hold a different table of calibra-

tion factors. The SENSOR NUMBER field determines which of these is to be loaded, and

the SENSOR NAME field can be used to give a seven-character name for the table. The

SENSOR NUMBER and GPIB ADDRESS fields are initially the values set on the front

panel, but can be overridden. Tables 0-7 can contain up to 40 entries and tables 8 and 9 can

each contain up to 80 entries. Note that this panel does not calibrate the power meter; this

must be done manually before the power meter is used.


Acquire Calibration Data

This panel is used to take measurements of standards which will be used to generate the

error correction matrixes. The CAC TYPE fieId can be used to select either a linear or non-

linear calibration. When run, this panel will open either the SOLT Linear or SOLT Nonlin-

ear panels. The linear calibration does noes not include the absolute calibration routine

included in the more complete nodinear calibration. The linear calibration is useful when

only a frequency sweep measurement is to be performed to verify that a set of calibration

standards is working correctly or that de-embedding is being performed correctly.

SOLT Linear

This panel will prompt the user to connect a number of standards. It will then record raw

measurements of these standards into the calibration data directory. The FREQUENCIES

field is used to enter a fist of calibration frequencies. The two power settings, SOURCE

POWER PORT 1 and SOURCE POWER PORT 2, control the source power independently

when the power is incident to port one and port two. This is useful when taking high power

measurements with driver amplifiers and attenuators included in the calibration. There are

also two sets of vertical osciIloscope settings, VERTICAL PORT 1 and VERTICAL

PORT 2, for when power is applied to poa one and poa two by the NNA respectively. As

is the case for any of the NNA measurements, the oscilloscope should be set to get the max-

imum swing on the screen without clipping. If the oscilloscope clips while the NNA is

taking calibration measurements, the resulting error parameters will be invalid. Averaging

should be turned off to visualy verify that the data is not clipped for any of the calibration

frequencies. Selecting the BW LIMIT fields reduces the bandwidth of the 20 GHz inputs

to 12.4 GHz, and the bandwidth of the 50 GHz inputs to 26.5 GHz when power is incident

to both port one and port two. It is recommended that for most measurements under


15 GHz, the 20 GEfi modules be left unlimited, and the 50 GHz modules be limited. When

run, the panel will ask for a short, an open, and a load to be connected to port one and then

to port two, followed by a zero length through connecting the two calibration planes.

SOLT Nodinear

This panel behaves exactly the same as the SOLT Linear panel, having the same input

fields, but also takes measurements to implement the absolute portion of the calibration

routine. It will ask for a calibrated power meter to be connected poa one. It will then prompt

the user to put two files in the calibration data directory before the Extract Calibration

Parameters panel is run. The ' !pea 1-al-phase' and ' !port 1-b 1-phase' files are Touch-

stone format scattering parameter files taken using a linear network analyser. They describe

the response of the measurement system from the port one calibration plane to the cables

that enter the channel one and channel two oscilloscope inputs respectively.

Extract Calibration Parameters

This panel has no inputs and will run automatically when opened. It takes the raw calibra-

tion data from the calibration data directory and calculates an error correction matrix at

each calibration frequency. These are stored in the calibration parameters directory. Indi-

cators describe the calibration details, show the progress the calculations, and display the

calculated correction matrixes.

Acquire Measurement Data

This panel is used to open either the Frequency Sweep, Single Tone or Two Tone measure-

ment panels in order to take a measurement. The MEAS TYPE field is used to select the

measurement type. The measurement name from the Front panel is passed to the opened


panel as the default measurement name. However, this measurement name can be changed

within the panels so that a number of measurements can be taken without returning to the

Front panel every time.

Frequency Sweep

This panel will perform a single tone frequency sweep measurement putting the raw data

into the measurement data directory. The main source, specified in the Front panel, is used

for this measurement. The FREQUENCIES field sets the frequencies to take measurements

at. The two power settings, SOURCE POWER PORT 1 and SOURCE POWER PORT 2,

control the source power independently when the power is incident to port one and port two

of the DUT. There are also two sets of vertical oscilloscope settings, VERTICAL PORT 1

and VERTICAL PORT 2, for when power is appIied to poa one and port two respectively.

When the Measurement Extraction panel is run it creates a Touchstone format scattering

parameter file with the name 'uneasurement_name>.freqswp'.

Single Tone

This panel will perform a single tone, single power measurement putting the raw data into

the measurement data directory. The main source specified in the Front panel is used for

this measurement. The incident power level, frequency, and pea can be specified with the

POWER, FREQUENCY, and PORT fields respectively. The vertical oscilloscope settings

can also be set for the measurement using the VERTICAL fields. The measurement name

is set using the MEAS NAME field. When the Measurement Ernaction panel is run it cre-

ates a Touchstone format scattering parameter file with the name 'aneas_name>.single'.

This file does not contain scattering parameter data however. It contains a single row for


each frequency of interest. The first column gives the frequency. The next four pairs of col-

umns give the real and imaginary parts of the a ~ , bl , a ~ , and b2 peak voltage phasors at that

frequency.

Two Tone

This panel will perform a two tone measurement, putting the raw data into the measurement

data directory. It assumes that the outputs from two microwave sources are combined

together and connected to the switch. There is a set of five fields to control each of the two

sources, SOURCE 1 and SOURCE 2. The frequency and power are controlled using the

FREQUENCY and POWER fields respectively. Both of the sources have a PHASE BUMP

field. This will advance the phase of the source's output by a given angle. This is useful to

line up the phases of the incident tones so the results are easier to visuaIise. This is actually

equivalent to changing the reference time of the measurement, but is more intuitive to use.

The GPIB address and the type of source are specified using the ADDRESS and SOURCE

TYPE fields. To aid in specifying the source details, an indicator displays the address and

type of the main source specified on the front paneI. The vertical oscilloscope settings are

set with the fields in the VERTICAL box. The measurement name is set using the MEAS

NAME field. When the Measurement Extraction panel is run it creates a Touchstone format

scattering parameter file with the name '<measurement-name>.2tone7. This fde does not

contain scattering parameter data however. It contains a single row for each frequency of

interest. The first column gives the frequency. The next four pairs of columns give the real

and imaginary parts of the a I, b a2, and b2 peak voltage p hasors at that frequency.

NNA LabView Software Guide I15

Measurement Extraction

This panel wiU run automatically when opened. It takes a measurement from the calibra-

tion data directory, specified on the Front panel and uses the calibration parameters from

the calibration parameters directory and the specified de-embedding information to

remove the systematic errors. The result is placed in the meastirernent results directory. The

result's format is described in either the Frequency Sweep, Single Tone or Two Tone section

depending on the measurement type. Indicators on this panel show the details of the meas-

urement and calibration,

View Waveforms

This panel will show the results of either a single tone or two tone test- Pressing the LOAD

RESULTS button will bring up a fde selection box used to select a single file from the

measurement results directory. The PLOT switch selects either a four plot overlay or four

individual plots. The DISPLAY TYPE switch selects one of the following results to view:

the time domain waves, the time domain voltage and currents, the power of the waves at

each harmonic, or the phase of the waves at each harmonic. Underneath the main display

is a plot that shows the load line at port two when the voltage and current are being dis-

played. The MAX TIME field sets the time that the time domain results are showed up to,

and the POINTS field sets the number of points displayed in time domain waveforms. The

GROUP DELAY COMPENSATION slider adds group delay to or removes group delay

from the measurement. In the time domain this simply moves the waveforms to the left or

the right. In the frequency domain, this can be used to change the slope of the phase

response, or to set the incident tone phase to a desired reference value. The AUTOSCALE

button turns autoscale on or off. With autoscale off, a number of fields control the time

domain and frequency domain scales independently. Since the NNA does not measure the

NNA LabView Software Guide 116 - - -

DC components of a signal, there are vertical offset fields for the time domain displays.

These are most useful when displaying the voltage and current waveforms: the DC bias

voltage and current from the DC supply can be entered, so that the waveforms are offset

correctly.

The SAVE TD WAVES button saves the time domain data to a text file who's name is

selected from a file selection box that pops up. The first column of this file contains the time

of each sample in ns. If displaying the voltage waves, the following columns contain the a*,

bl, a ~ , and b2 samples. If displaying voltage and current, the columns contain the vl, v2, il,

and samples. The SAVE FD WAVES button, saves frequency domain data to a text file

who's name is selected from a file selection box that pops up. No matter which format is

set to display, a Touchstone format file is created where each row represents a single fre-

quency. The first column gives the frequency in MHz. The next four pairs of columns give

the magnitude in dBm and the angle in degrees of the a*, bl, a2, and b2 waves respectively.

Cascade Fixture Files

This panel is used to help create scattering parameter files for de-embedding the effect of a

fixture combined with other devices such as tuners. It takes one or more Touchstone format

scattering parameter files, picks out a set of desired frequencies and chains them together

to produce a single scattering parameter file. If only one file is specified, the panel creates

a new file containing only the desired frequencies. The FREQUENCIES field describes the

frequencies which will be picked out of the input files. The NUMBER FILES field speci-

fies the number of files to cascade together. When the panel is run, file selection boxes will

prompt for the input file and output file names. The diagram on the panel indicates that the

files are numbered from the DUT outwards. The files are all defined with port two oriented

toward the DUT.

References

[IT Markku Sipilq Kari Lehtinen and Veikko Porra, "High-Frequency Periodic Time-

Domain Waveform Measurement S y s tern", IEEEE Transactions on Micro wave The-

ory and Techniques, Vo1.36, No. 10, pp. 1397- 1405, October 1988.

[2] Urs Lott, "Measurement of Magnitude and Phase of Harmonics Generated in Non-

linear Microwave Two-Ports", IEEE Transactions on Microwave Theory and Tech-

niques, Vo1.37, No. 10, pp. 1506-15 1 1, October 1989.

[3] Giinter Kompa and Friedbert van Raay, "Error-Corrected Large-Signal Waveform

Measurement System Combining Network Analyzer and Sampling OscilIoscope

Capabilities", IEEEE Transactions on Microwave Theory and Techniques, VoI.38,

No.4, pp. 358-365, April 1990.

141 Tom Van den Broeck and Jan Verspecht, "Calibrated Vectorial Nonlinear-Network

Analyzers", Conference Record of the IEEE Microwave Theory and Techniques

Symposium 1994, San Diego, California, USA, pp. 1069-1072, May 1994.

References 118

[5] T. Michael Souders, Donald R. Flach, Charles Hagwood and Grace L. Ymg, "The

Effects of Timing Jitter in Sampling Systems", IEEE Transactions on Instrumenta-

tion and Measurement, Vo1.M-39, pp. 80-85, February 1991.

[6] W.L. Gans, "The Measurement and Deconvolution of Time Jitter in Equivalent-

Time Waveform Samplers", IEEE Transactions on lnstrurnentation and Measure-

ment, Vo1.M-32, pp. 126-1 33, March 1983.

171 Stephan Adam, "A New Precision Automatic Microwave Measurement System",

IEEE Transactions on Instrumentation and Measurement, Vol.IM-17, No.4, pp.

308-3 13, December 1968.

[8] Jan Verspecht, "Calibration of a Measurement System for High Frequency Nonlin-

ear Devices", Doctoral Dissertation, Vrije Universiteit, Brussel, September 1995.

[9] "Specifying Calibration Standards for the KP-85 10 Network Analyzer", Hewlett-

Packard product note 85 10-5A.

[lo] Ken Rush and Jan Verspecht, 'bIndividual Characterization of Broadband Sampling

OsciIloscopes with a 'Nose-to-Nose' Calibration Procedure", IEEE Transactions on

Instrumentation and Measurement, Vol.IM-43, No.2, pp. 347-354, April 1994.

[I 11 "HP-54120B Digital Oscilloscope Mainframe - Service ManuaI", HewIett-Packard

Part No. 54120-90908, 1989.

1121 Jan Verspecht, "Accurate Spectral Estimation Based on Measurements With a Dis-

torted-Timebase Digitizer", IEEE Transactions on Instrumentation and Measure-

ment, Vo1.M-43, No.2, pp. 210-2 15, April 1994.

References 119

[13] E. Van der Oudera and J. Renneboog, "Some Formulas and Applications of Nonuni-

form Sampling of B andwidth-lirnited Signals", IEEE Transactions on Instrumenta-

tion and Measurement, Vo1.37, No.3, pp. 353-357, September 1988.

[14] Raymond Waugh, Hewlett-Packard WSD Diode Applications, personal correspond-

ence, November 1998

[15] "Fixture Characterization and S-Parameter Measurement Using Maury's MT956D

Software", Maury Microwave Application Note 5C-038, May 1998-

[16] Glenn F. Engen and Cletus A. Hoer, '"Thru-Reflect-Line': An Improved Technique

for Calibrating the Dual Six-Port Automatic Network Analyser", IEEE Transactions

on Microwave Theory and Techniques, Vol. M1T-27, No. 12, pp. 987-993, Decern-

ber 1979.

[I73 "Applying the Agilent 8510 TRL Calibration for Non-coaxial Measurements",

Hewlett-Packard Product Note 85 10-8A, Part No. 509 1-3645E.

Documents

A Microwave Nonlinear Network Analyser