slide 1 linear and nonlinear device measurements doug rytting
TRANSCRIPT
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]
PerfectReflectometer
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]
PerfectReflectometer
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]
PerfectReflectometer
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]
Thru (T) or Line (L) withknown S-parameters
[4 conditions]
Thru (T) or Line (L) withknown S-parameters
[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]
PerfectReflectometer
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
Accuracy of Error Correction
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
Accuracy of Error Correction
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
Model Verification & Improvement
Slide 69
Model Verification & Improvement
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
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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