Slide 1 Linear and Nonlinear Device Measurements Doug Rytting

Slide 1

Linear and Nonlinear Device Measurements

Doug Rytting

Slide 2

Agenda

Microwave Measurement Methods

Linear Measurements with a Vector Network Analyzer

Block Diagram

Error Correction

Nonlinear Measurements with a Large Signal Network Analyzer

Block Diagram

Error Correction

Examples

Slide 3

Microwave Measurement Methods

Power Meter

Oscilloscope

Spectrum Analyzer

Vector Network Analyzer

Slide 4

Linear Measurements with a Vector Network Analyzer

Slide 5

RFSource

LOSource

a0

b0 b3

Port - 1 Port - 2

a3

DUTa2

a1

b1

b2Cable Cable

IF

IF

IF

IF

Network Analyzer Block Diagram

Slide 6

Improvements with Correction

Slide 7

ERRORS REMOVED ERRORS REMAINING

Noise and Residuals

Receiver Linearity

Drift after Error-Correction

Stability after Error-Correction

Repeatability of Connectors, etc

Lower Lever Leakage Paths

Errors of Calibration Standards

Port Match

Directivity

Tracking

Main Leakage Paths

Improvements with Correction

Slide 8

ErrorAdapter

DUT

PerfectReflectometer

a0

b0

a0

b0

b1

a1

3 Error Terms

Port - 1

e00 e11

e10 e01

1

b1

a0

b0

DUT

a1

e00 =

e11 =

(e 10 e01 ) =

Directivity

Port Match

Tracking

One Port: 3-Term Error Model

Slide 9

For ratio measurements there are 3 error termsThe equation can be written in the linear form

Any 3 independent measurements can be used

e00 -e

1 - e 11M =

b0

a0

=M - e 00

Me11 - e

=

Measured Actual

e00 + Me11 - e = M

e = e 00 e11 - (e 10 e01 )

e00 + M1 e11 - e = M1

e00 + M2 e11 - e = M2

e00 + M3 e11 - e= M3

With 3 different known , measure the resultant 3 MThis yields 3 equations to solve for e 00 , e 11 , and e

One Port: 3-Term Error Model

Slide 10

DUTPerfectReflectometer

b0

b3

a0

b0

a3

b3

b1

a1

b2

a2

ErrorAdapter

a0,a 3

Forward

Reverse

12-Term Error Model

Slide 11

ReverseError

Adapter

ForwardError

Adapter

DUT[S]


b' 0

a' 3 b' 3

a' 0

b' 0

a' 3

b' 3

b' 1

a' 1

b' 2

a' 2

6 Error Terms

DUT[S]


a0

b0

b3

a0

b0

a3

b3

b1

a1

b2

a2

6 Error Terms

ForwardModel

ReverseModel

12-Term Error Model

Slide 12

a0

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

b3

e30

e00 e11

e10 e01

1

e22

e10 e32

e00 =

e11 =

(e 10 e01 ) =

(e 10 e32 ) =

e22 =

e30 =

Directivity

Port-1 Match

Reflection Tracking

Transmission Tracking

Port-2 Match

Leakage

S 11M =b0

a0

= e 00 + (e 10 e01 )S 11 - e 22 S

1 - e 11 S 11 - e 22 S 22 + e 11 e22 S

S 21M =b3

a0

= e 30 + (e 10 e32)S 21

1 - e 11 S 11 - e 22 S 22 + e 11 e22 S

S = S 11 S 22 - S 21 S 12

FORWARD MODEL

12-Term Error Model

Slide 13

b'0

Port - 1 a'1

a'2b'1

b'2

S 11

S 21

S 22

S 12

DUTPort - 2

b'3

e'11

e'23 e'01

e'22

e'23 e'32

1

e'33

a'3

e'03

REVERSE MODEL

e'33 =

e'11 =

(e' 23e'32) =

(e' 23e'01) =

e'22 =

e'03 =

Directivity

Port-1 Match

Reflection Tracking

Transmission Tracking

Port-2 Match

Leakage

= e' 33 + (e' 23e'32)S 22 - e' 11 S

1 - e' 11 S 11 - e' 22 S 22 + e' 11 e'22 S

S 22M =b'3a'3

= e' 03 + (e' 23e'01)S 12

1 - e' 11 S 11 - e' 22 S 22 + e' 11 e'22 S

S 12M =b'0a'3

S = S 11 S 22 - S 21 S 12

12-Term Error Model

Slide 14

S

S e

e e

S e

e ee e

S e

e e

S e

e e

D

S

S e

e e

S e

e ee

D

S

S e

e e

S e

e e

M M M M

M M

M M

11

11 00

10 01

22 33

23 3222 22

21 30

10 32

12 03

23 01

21

21 30

10 32

22 33

23 3222 22

22

22 33

23 32

11 00

10 01

1

1

1

'

' ''

'

' '

'

' ''

'

' '

e

e eS e

e e

S e

e e

D

S

S e

e e

S e

e ee e

D

DS e

e ee

S e

e ee

S e

e e

M M

M M

M M M

11 1121 30

10 32

12 03

23 01

12

12 03

23 01

11 00

10 0111 11

11 00

10 0111

22 33

23 3222

21 30

10 32

1

1 1

''

' '

'

' ''

'

' ''

S e

e ee eM12 03

23 0122 11

'

' ''

12-Term Error Model

Slide 15

CalibrationSTEP 1: Calibrate Port-1 using One-Port procedure

STEP 2: Connect Z 0 terminations to Ports 1 & 2

STEP 3: Connect Ports 1 & 2 together

Solve for e 11 , e 00 , & (e 10 e01 ), Calculate (e 10 e01 ) from e

Measure S 21M gives e 30 directly

S 11M - e 00

S 11M e11 - e

e22 =

e10 e32 = (S 21M - e 30 )(1 - e 11 e22 )

Use the same process for the reverse model

12-Term Error Model

Slide 16

16-Term Error Model

ErrorAdapter

DUT[S]


ImperfectSwitch

a0

b0

a3 b3

a0

b0

a3

b3

b1

a1

b2

a2

16 Error Terms

To remove the effects of an imperfect switch, use the procedure described later.

Slide 17

DUT

S 11

S 12

S 22

S 21

e20 e13

e10

e01

e00 e11

e30 e03

e23

e21 e12

e22e33

e32

e31 e02

a0

a0 a1

a1

b2

b1

a2

b2b3

b0

a3

b3

b0 b1

a3 a2

One of the 16 error terms can be normalized to yield 15 error terms

e00 , e 33 Directivitye11 , e 22 Port Matche10 , e 01 , e 32 , e 23 Trackinge30 , e03 Primary Leakage

All others are lower levelleakage paths

16-Term Error Model

Slide 18

Measured S-Parameters SM = (T 1S + T 2)(T 3S + T 4)-1

Actual S-Parameters S = (T 1 - S MT3)-1(S MT4 - T 2)

Linear-in-T Form T1S + T 2 - S MT3S - S MT4 = 0

Error Model

With 15 or more independent observations the linear matrixequation can be solved. TRL as well as TOSL calibrationmethods are possible.

b

b

a

a

a

a

b

b

0

3

0

3

1

2

1

2

T T

T T1 2

3 4

16-Term Error Model

Slide 19

8-Term Error Model

DUTPerfect

Reflectometer

ImperfectSwitch

a0

b0

a3 b3

a0

b0

a3

b3

b1

a1

b2

a2

8 Error Terms

XError

Adapter

YError

Adapter

To remove the effects of an imperfect switch, use the procedure described later.

Slide 20

DUT

S 11

S 12

S 22

S 21

e10

e01

e00 e11

e23

e22e33

e32

a0

a0 a1

a1

b2

b1

a2

b2b3

b0

a3

b3

b0 b1

a3 a2

One of the 8 error terms can be normalized to yield 7 error terms

X Error Adapter

Y Error Adapter

8-Term Error Model

Slide 21

233233220110110023

10

22

11

33

00

, ,

0

01

0

0

0

0

0

0

eeeeeeeee

ek

kke

e

ke

e

k

YX

Y

X

43

21

TT

TT

b

b

a

a

a

a

b

b

0

3

0

3

1

2

1

2

T T

T T1 2

3 4

8-Term Error Model

Slide 22

Measured S-Parameters SM = (T 1S + T 2)(T 3S + T 4)-1

Actual S-Parameters S = (T 1 - S MT3)-1 (S MT4 - T 2)

Linear-in-T Form T1S + T 2 - S MT3S - S MT4 = 0

Expanding Yields:

e00 + S 11 S 11M e11 - S 11X + 0 + S 21 S 12M (ke 22 ) + 0 + 0 = S 11M

0 + S 12 S 11M e11 - S 12X + 0 + S 22 S 12M (ke 22 ) + 0 - S 12M k = 0

0 + S 11 S 21M e11 + 0 + 0 + S 21 S 22M (ke 22 ) - S 21 (kY) + 0 = S 21M

0 + S 12 S 21 Me11 + 0 + (ke 33 ) + S 22 S 22M (ke 22 ) - S 22 (kY) - S 22M k = 0

8-Term Error Model

Slide 23

Using the cascade parameters in matrix form yields

MEASURED

TM = T XT T Y

ACTUAL

T = T X-1 TM TY

-1

ATBTT

TT

TT

M

YX

M

321033

22Y

11

00X

3210

23323322Y01101100X

33

22Y

3211

00X

10

M21M12M22M11M21122211S

M22

M11M

M2122

11S

21

ee

1

1e

e

1e

e

ee

1

eeeeeeee

1e

e

e

1

1e

e

e

1

SSSSSSSS

1S

S

S

1

1S

S

S

1

8-Term Error Model

Slide 24

TRL & LRL

TRM & LRM

TraditionalTOSL

(Overdetermined)

LRRM

UXYZ

TXYZ & LXYZ

Thru (T) or Line (L) withknown S-parameters

[4 conditions]

Unknown Line (U) withS 12 = S 21

[1 condition]

Line (L) with knownS 11 and S 22

[2 conditions]

Known Match (M)on port-1 and port-2

[2 conditions]

3 known Reflects (XYZ)on port-1 or port-2

[3 conditions]

3 known Reflects (OSL)on port-1

[3 conditions]

Known match (M)on port-1

[1 condition]

3 known Reflects (XYZ)on port-1

[3 conditions]

2 unknown equal Reflects(RR) on port-1 and port-2

[2 conditions]

3 known Reflect (OSL)on port-2

[3 condition]

Unknown equal Reflect (R)on port-1 and port-2

[1 condition]

Seven or more independent known conditions must be measuredA known impedance (Z 0) and a port-1 to port-2 connection are required

Line (L) with knownS-parameters[4 conditions]


[4 conditions]


[4 conditions]

Thru (T) withknown S-parameters

[4 conditions]

Unknown equal Reflect (R)on port-1 and port-2

[1 condition]

3 known Reflects (XYZ)on port-2

[3 conditions]

8-Term Calibration Examples

Slide 25

ErrorAdapter

DUT[S]


a0

b0

a3 b3

a0

b0

a3

b3

b1

a1

b2

a2

Forward

Reverse

Forward

b0 = S 11M a0 + S 12M a3b3 = S 21M a0 + S 22M a3

Reverse

b' 0 = S 11M a' 0 + S 12M a' 3b' 3 = S 21M a' 0 + S 22M a' 3

Measuring S-parameters

Slide 26

Measuring S-parameters

213

0

0

3

13

0

0

3

3

3

M22

20

3

3

3

0

3

M21

13

0

0

0

3

0

M12

20

3

3

0

0

0

M11

'a

'b

a

b1d

d

'a'b

ab

'a'b

Sd

ab

'a'b

ab

S

d

'a'b

ab

'a'b

Sd

ab

'a'b

ab

S

By defining

3

32

0

01 b

a and

b

a

Slide 27

Multiport Error Model

S M = (T 1S + T 2)(T 3S + T 4)-1

S = (T 1 - S MT3)-1(S MT4 - T 2)

T1S + T 2 - S MT3S - S MT4 = 0

Slide 28

Accuracy of Error Correction

Slide 29


Residual Errors

OSL Fixed Load

OSL Sliding Load

TRL TRM

Directivity -40 dB -52 dB -60 dB -40 dB

Match -35 dB -41 dB -60 dB -40 dB

Reflection Tracking

± .1 dB ± .05 dB ± .01 dB ± .01 dB

APC-7 (7 mm Coax) at 18 GHz

Slide 30


Slide 31

Other Network Analyzer Topics

Amplifier Measurements

Mixer Measurements

Pulse Measurements

Non-Insertable Measurements

Fixture and Probe Calibration

Two-Tier Calibration

Multiport Measurements

Balanced & Differential Measurements

Slide 32

Nonlinear Measurements with a Large Signal Network

Analyzer

Slide 33

Vector Network Analyzer

Linear Theory

S-parameters

H

MEAS FORMATSCALE

REF

DISPLAY AVG CAL

MKRFCTN

MKR

CH 1 CH 2

MENU

START STOP

CENTER SPAN

SYSTEM LOCALUSER

PRESET

COPYSAVE

RECALL SEQ

7 8 9

4 5 6

1 2 3

0 . -

@

n

M

k

m

x1ENTRY

OFF

ACTIVE CHANNEL

RESPONSE

STIMULUS

ENTRY

INSTRUMENT STATE R CHANNEL

OUTR L T S

HP-IB STATUS

IN

PROBE POWER FUSED

PORT 1 PORT 2

TRANS FWDREFL FWD

TRANS REVREFL REV

+26 dBm RF 30 VDC MAX PORTS 1&2 AVOID STATIC DISHCARGE

8753DNETWORK ANALYZER

30 KHz-3GHz

50 Ohm

Acquisition (VNA)

Stimulus

Response

Slide 34

Complete SpectrumWaveforms

Harmonics and Modulation

Large Signal Network Analyzer

Acquisition (LSNA)

Stimulus

Response

ESG 50 Ohmor

Tuner

Slide 35

Large Signal Network Analyzer

Measures magnitude and phase of incident and reflected waves at fundamental, harmonic, and modulation frequencies.Calibrated for relative and absolute measurements for both linear and nonlinear components at the device under test.Calculate calibrated voltage and current in both the time and frequency domains.

Combination of a vector network analyzer, sampling scope, spectrum analyzer and power meter.

Slide 36

LSNA System Block DiagramSampler Front End

Requires high BW IFRequires Harmonic LO

Slide 37

Sampling Converter Fundamentals

LP

Freq. (GHz)1 2 3

50 fLO 100 fLO 150 fLO

Freq. (MHz)1 2 3

RF

IF

fLO=19.98 MHz = (1GHz-1MHz)/50

IF Bandwidth: 4 MHz

Slide 38

Periodic Modulation

IF Bandwidth: 4 MHz

1 2 3

50 fLO 100 fLO 150 fLO

Freq. (MHz)1 2 3

RF

IF

fLO=19.98 MHz = (1GHz-1MHz)/50

Slide 39

LSNA System Block DiagramMixer Front End

Requires harmonic syncCan use high BW IF for modulationOr low BW IF if no modulation

Slide 40

Nonlinear Calibration - Model

Measured wavesActual waves at DUT

7 relative error termssame as a VNAAbsolute magnitude

and phase error term

50 Ohmor

Tuner

AcquisitionStimulus

Response

ModulationSource

0a 0b 3a 3b

1a 2a

1b 2b

Slide 41

Relative Calibration

50 Ohm

Acquisition

50 Ohm

LoadOpenShort

50 Ohm

Acquisition

50 Ohm Thru

{1 GHz, 2 GHz, …, 20 GHz}

22

22

11

1

00

00

00

001

K

Slide 42

Power Calibration

50 Ohm

Acquisition

Power Meter

{1 GHz, 2 GHz, …, 20 GHz}

22

22

11

1

00

00

00

001

K

Amplitude

Slide 43

Phase Calibration

50 Ohm

Acquisition

Harmonic PhaseReference Generator

1 GHz

...1 GHz

50 Ohm

22

22

11

1

00

00

00

001

K

Phase

Slide 44

Characterization of the Harmonic Phase Reference

Generator

Sampling oscilloscopeHarmonic Phase Reference generator

Slide 45

Nose-to-Nose Calibration Procedure

Slide 46

Nose-to-Nose Measurement

Slide 47

3 Oscilloscopes are Needed

1

2

1

3

3

2

Slide 48

Electro-Optic Sampling*

* The schematic that is shown is “U.S. Government work not subject to copyright.”D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, "Calibrating electro-optic sampling systems,“Int. Microwave Symposium Digest, Phoenix, AZ, pp. 1527-1530, May 20-25, 2001.

Slide 49

Example # 1

Complete device measurement capability using a Large Signal Network Analyzer (LSNA).

Slide 50

Device Measurement

)(1 ta )(1 tb

)(2 ta )(2 tb

)(1 tv

)(1 ti

)(2 tv

)(2 ti dsv

dsi

-1.2 V

-0.2 V

MHzf 9000

50 Ohm loadOpen port

gv

Slide 51

Breakdown Current

Time (ns)

(Transistor provided by David Root, Agilent Technologies - MWTC)

Slide 52

Forward Gate Current

Time (ns)

Slide 53

Example # 2

Resistive mixer with all waveforms available.

Slide 54

Resistive Mixer Schematic

(Transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC)

HEMT transistor (no drain bias applied)

Slide 55

Time Domain Waveforms

Slide 56

Example # 3

Modulation envelope measurements shows harmonic distortion effects.

Slide 57

A1

Carrier Modulation

Carrier Modulation

B2

Carrier Modulation

3rd harmonicModulation

Harmonic DistortionCompression

Modulation Trans Characteristics

Slide 58

A1

Carrier Modulation

Carrier Modulation

B1

3rd harmonicModulation

Harmonic Distortion

Carrier Modulation

2nd harmonicModulation

Expansion

Modulation Trans Characteristics

Slide 59

Example # 4

Mismatch effects can be measured and shows contamination of the modulated signal from the source.

Slide 60

Acquisition

ESG

Acquisition

ESG

50 ohms

A1

A1

A1

SpectralRegrowth

Effect of Source Mismatch

Slide 61

Example # 5

Error corrected waveform measurements improves digital signal integrity results.

Slide 62

High-Speed Digital Signal Integrity

Calibrated Eye Measurement On Wafer (@10GB/sec)

Oscilloscope Data

(Courtesy of Jonathan Scott, Agilent Technologies)

Slide 63

Improved device and system design using waveform

measurements

Slide 64

Present Nonlinear Design Approach

Measured S-parameters, spectrum and power insufficient to provide complete verification of design.Nonlinear models are inaccurate and difficult to use.Cut and try design approach.

Measure (VNA)S-parameters

SimulateNonlinearModel Build

Can’t Easily Adjust Model to

Match Measurements

Measure (SA)Spectrum

Measure (PM)Power

Slide 65

New Nonlinear Design Approach

Measured nonlinear waveforms provides complete verification of design.New types of nonlinear models extracted to match application (CDMA, GSM, etc).Easy to couple measured data through a model and simulate much faster.

Measure (LSNA)Complete

Nonlinear Waves

Simulate(Modified)

ImprovedNonlinear

ModelBuild

Adjust Model to

Match Measurements

MeasureModel

Simulate

NEW NEW

Slide 66

Example # 6

Device measurement verification and measurement-based model improvement.

Slide 67

MODEL TO BE OPTIMIZED

generators apply LSNA measured waveforms

“Chalmers Model”

“Power swept measurements under mismatched conditions”

GaAs pseudomorphic HEMTgate l=0.2 um w=100 um

Parameter Boundaries

Model Verification & Improvement

Slide 68

During OPTIMIZATION

Time domain waveforms Frequency domaingate drain

voltage

current

gate drain

Voltage - Current State Space


Slide 69


Time domain waveforms Frequency domaingate drain

voltage

current

gate drain

Voltage - Current State Space

After OPTIMIZATION

Slide 70

Example # 7

Power amplifier PAE optimization using waveform measurements and improved model developed from these measurements.

Slide 71

IRCOM & Thompson Example34% better PAE performance through waveform engineering1

Verified Model

with traditional tools•Load Pull System•Spectrum Meas.

Designed Virtual PA

Expected 80% PAE2

MeasuredMesFET #1

w/prototypeLSNA plusImpedanceTuner

Modified Model

Designed Model for MesFET #1

Built PA Measured PA #1

50% PAEMeasured ≠ Simulated

Re-designed PA

w/Waveform Analysis

Built PAMeasured

PA #2Achieved84% PAE!!

Customer predicted best case results (the old way) would have been mid-70% PAEafter numerous design iterations

1 MesFET Class F PA f0=1.8 GHz2 Power Added Efficiency

Slide 72

Waveform Engineering Block Diagram

DUTTestSet Da

ta-A

cqui

sitio

n

Source

PC

Sampling Converter

Filter

Filter

Filter

Filter

f0

f0

2f0

3f0IRCOM Setup

LO

Slide 73

IRCOM & Thompson Example

MesFET Class Ff0=1.8 GHzIds0=7 mAVds0= 6 V

Z(f0)=130+j73 Z(2f0)=1-j2.8 Z(3f0)=20-j97

PAE=84%

PAE50%

WaveformEngineering

Slide 74

Example # 8

Nonlinear model for two individual amplifiers used to predict performance of the combined cascade configuration.

Slide 75

Modeling - Two Separate Amps

Slide 76

Modeling - Cascaded Amplifiers

Slide 77

Example # 9

Nonlinear model of a communications channel enables the inverse model to accurately pre-distort the signal to improve performance.

Slide 78

Inverse Model Compensation

Slide 79

Pre-Distortion of 16 QAM Channel

Slide 80

Acknowledgments

Agilent Technologies

NIST

NMDGMarc Vanden Bossche

Jan Verspecht

And Team

Slide 81

Appendix

Slide 82

Example: TRL

Slide 83

Example: TRL

Slide 84

Example: TRL

Slide 85

Example: TRL

Slide 86

Example: TRL

Slide 87

Example: TRL

Slide 88

T T ATB

T ATB

T ATB

T AB T

A B

T

M

M

M

M

M

11 1

1

1

10 32

00

11

22

33 10 32

10 32

10 32

10 32

2

21 12

10 32

e e

e

e

e

e e e

e e

e e

e e S

e e

X Y

det det

det det , since det because S

Therefore

det det

det

,

Example: Unknown T, Known A & B

Slide 89

T T ATB

B T A T D D

M

1 1M

11 1

1

1

1

1

10 32

00

11

22

33 10 32

10 32

10 32

22

10 32

33

10 32 10 32

11 12

21 22

10 3222

2212

2233

21

22

11

22

e e

e

e

e

e e e

e e

e e

e

e ee

e e e e

D D

D D

e eD

eD

De

D

D

D

D

X Y

Y

Y

, and is completely known

Therefore

Example: Unknown B, Known A & T

Slide 90

a0

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

b3

e00 e11

e10 e01

1e' 22

e10 e' 32

a0

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

b3

e00 e11

e01

e10

e22

e32

a0

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

b3

e00 e11

e01

e10

e22

e32

a3

e23

e33

e23

e33 3

3

33 b

a

333

3232

333

323322222

e1

ee

e1

eeee

8-Term to 10-Term -Forward

Slide 91

0

00 b

a

000

0101

000

001101111

e1

ee

e1

eeee

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

e' 11

e23 e' 01

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

e00 e11

e01

e10

e22

e23 e32

a0

b0

Port - 1 a1

a2b1

b2

S 11

S 21

S 22

S 12

DUTPort - 2

b3

e00 e11

e01

e10

e22

e32

a3

e23

e33

1

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Slide 92

Calibration and Error Correction Techniques for Network Analysis

The accuracy of Vector-Network-Analyzer (VNA) measurements depends critically on calibration and error correction techniques. This talk will cover the evolution of conventional VNA calibration methods from the start of network

analysis through the development of new calibration methods for waveform and large-signal analysis. Included will be the original SOLT (Short-Open-Load-Through) methods, the newer self-calibration techniques like TRL, LRL and Unknown-Thru, and the strengths and weaknesses of these various VNA

calibration approaches. The talk will conclude with a discussion of new state-of-the-art extensions of the traditional VNA calibration strategy for calibrated

waveform measurements at microwave frequencies capable of capturing the both the temporal and large-signal behavior of microwave and digital devices.

Abstract

Slide 93

Vector Network AnalyzerReferences

Slide 94Copyright 2003Jan Verspecht bvba

Large Signal Network Analyzer References

Slide 95

Doug RyttingBiography

Documents

Slide 1 Linear and Nonlinear Device Measurements Doug Rytting