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Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 1
Prof. Luca Perregrini
Dept. of Electrical, Computer and Biomedical EngineeringUniversity of Pavia
e-mail: luca.perregrini@unipv.itweb: microwave.unipv.it
Course on Microwave Measurements
Vector Network Analyzer
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 2
Summary
• Vector network analyzer
• VNA calibration technique
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 3
Scattering parameters are typically measured, at microwavefrequencies, with a network analyzer (NA).
These instruments have found wide application since the mid tolate 1970’s.
Vector network analyzer: measurement of magnitudes andphases of the S-parameters
Scalar network analyzer: measurement of only the magnitudes ofthe S-parameters
Most NA’s measure 2-port parameters. Some measure 4 and 6ports.
Vector network analyzer
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 4
Vector network analyzer
Hewlett-Packard 8510
frequency generator
microwave test set
mm-wave test set
IF processing
digital processing
& instrument control
test cables
DUT
port 1port 2
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 5
Vector network analyzer
Hewlett-Packard 8510
test cables
DUT
port 1port 2
DUTb2
b1
a1
a2Attenuator (optional)
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 6
RFSource
LOSource
a0
b0 b3Port - 1 Port - 2
a3
DUTa2
a1
b1
b2Cable Cable
IF
IF
IF
IF
VNA Block Diagram
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 7
DUT
A/D
DSP
A/D
DSP
A/D
DSP
a2
a1
b1
b2
a0 b0 b3
LO LO
RFSource
Port - 1 Port - 2
IF IF
VNA Block Diagram: Forward Direction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 8
aS
NLa0 NLb0 NLb3
b0 b3
M2M1
L2-b3
1+Aa0+NHa0
a0
Port - 1 a1
a2b1
b2
S11
S21
S22
S12
DUTPort - 2
Cable &Connector
Cable &Connector
LC
MC
LC
LCLC
MC MCMC
Branches With No Label = 1
IF IF
MS
La0-b3
LS-1
L1-S
LS-a0 LS-b0 L1-a0L1-b0
1+Ab0+NHb0 1+Ab3+NHb3
VNA Error Model Forward Direction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 9
a1 = Incident Signal at Port-1b1 = Reflected Signal at Port-1a2 = Incident Signal at Port-2b2 = Transmitted signal at Port-2
aS = Source Porta0 = Measured Incident Portb0 = Measured Reflected Portb3 = Measured Transmitted Port
LS-1 = Loss from Source to Port-1L1-S = Loss from Port-1 to SourceLS-a0 = Loss from Source to a0LS-b0 = Loss from Source to b0 (Directivity)L1-a0 = Loss from Port-1 to a0 (Directivity)L1-b0 = Loss from Port-1 to b0L2-b3 = Loss from Port-2 to b3La0-b3 = Loss from a0 to b3 (Leakage)LC = Loss of Cables
S11 = Refl Coef of DUT at Port-1S21 = Forward Trans Coef of DUTS12 = Reverse Trans Coef of DUTS22 = Refl Coef of DUT at Port-2
M1 = Match at Port-1M2 = Match at Port-2MS = Match of SourceMC = Match of Cables
NLa0 = Low Level Noise at a0NLb0 = Low Level Noise at b0NLb3 = Low Level Noise at b3NHa0 = High Level Noise at a0NHb0 = High Level Noise at b0NHb3 = High Level Noise at b3
Aa0 = Dynamic Accuracy at a0 (Linearity)Ab0 = Dynamic Accuracy at b0 (Linearity)Ab3 = Dynamic Accuracy at b3 (Linearity)
VNA Error Model Forward Direction
Error Model Definitions
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 10
Branches With No Label = 1
a0
b0
Port - 1 a1
a2b1
b2
S11
S21
S22
S12
DUTPort - 2
b3
e30
e00 e11
e01
e10
e22
e32
There are also Six Terms in the Reverse Direction
Directivity
ReflectionTracking
Port-1 Match
Leakage
TransmissionTracking
Port-2 Match
There are also Errors caused by the Converter, IF, Cables and Connectors
e e L L
LL L L
LS b
S a
S a S b
S a10 01
1 1 0
0
1 1 0 0
02
e M L LL
S a
S a11 2
1 1 0
0
e LL
S b
S a00
0
0
e La b30 0 3
e e L LLS b
S a10 32
1 2 3
0
e M22 2
Reduced Error Model Forward Direction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 11
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
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 12
Improvements with Correction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 13
ErrorAdapter DUT
PerfectReflectometer
a0
b0
a0
b0
b1
a1
3 Error Terms
Port - 1
e00 e11
e10e01
1
b1
a0
b0
DUT
a1
e00 =
e11 =
(e10e01) =
Directivity
Port Match
Tracking
One Port: 3-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 14
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 - e11M =
b0
a0
=M - e00
Me11 - e
=
Measured Actual
e00 + Me11 - e = M
e = e00e11 - (e10e01)
e00 + M1e11 - e = M1
e00 + M2e11 - e = M2
e00 + M3e11 - e= M3
With 3 different known , measure the resultant 3 MThis yields 3 equations to solve for e00, e11, and e
One Port: 3-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 15
DUTPerfectReflectometer
b0
b3
a0
b0
a3
b3
b1
a1
b2
a2
ErrorAdapter
a0,a3
Forward
Reverse
12-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 16
ReverseError
Adapter
ForwardError
Adapter
DUT[S]
PerfectReflectometer
b'0
a'3 b'3
a'0
b'0
a'3b'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
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 17
a0
b0
Port - 1 a1
a2b1
b2
S11
S21
S22
S12
DUTPort - 2
b3
e30
e00 e11e10e01
1e22
e10e32
e00 =e11 =
(e10e01) =
(e10e32) =e22 =e30 =
DirectivityPort-1 MatchReflection Tracking
Transmission TrackingPort-2 Match
Leakage
S11M =b0
a0
= e00 + (e10e01)S11 - e22 S
1 - e11S11 - e22S22 + e11e22 S
S21M =b3
a0
= e30 + (e10e32)S21
1 - e11S11 - e22S22 + e11e22 S
S = S11S22 - S21S12
FORWARD MODEL
12-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 18
b'0
Port - 1 a'1
a'2b'1
b'2
S11
S21
S22
S12
DUTPort - 2
b'3e'11
e'23e'01
e'22
e'23e'32
1e'33
a'3
e'03
REVERSE MODEL
e'33 =e'11 =
(e'23e'32) =(e'23e'01) =
e'22 =e'03 =
DirectivityPort-1 MatchReflection Tracking
Transmission TrackingPort-2 MatchLeakage
= e'33 + (e'23e'32)S22 - e'11 S
1 - e'11S11 - e'22S22 + e'11e'22 S
S22M =b'3a'3
= e'03 + (e'23e'01)S12
1 - e'11S11 - e'22S22 + e'11e'22 S
S12M =b'0a'3
S = S11S22 - S21S12
12-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 19
S
S ee e
S ee e
e e S ee e
S ee e
D
S
S ee e
S ee e
e
D
S
S ee e
S ee 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 e S ee e
S ee e
D
S
S ee e
S ee e
e e
D
D S ee e
e S ee e
e S ee 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 ee e
e eM12 03
23 0122 11
'' '
'
12-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 20
CalibrationSTEP 1: Calibrate Port-1 using One-Port procedure
STEP 2: Connect Z0 terminations to Ports 1 & 2
STEP 3: Connect Ports 1 & 2 together
Solve for e11, e00, & (e10e01), Calculate (e10e01) from e
Measure S21M gives e30 directly
S11M - e00
S11Me11 - e
e22 =
e10e32 = (S21M - e30)(1 - e11e22)
Use the same process for the reverse model
12-Term Error Model
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 21
Slide 21Dave Blackham& Ken Wong
Electronic Calibration Standards
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 22
Electronic Calibration Standards
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 23
Electronic Calibration Standards are Transfer Standards
Definition:
Devices that derived their characteristics from measured data relative to primary or physical standards or other transfer standards.
Electronic Calibration Standards
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 24
Accuracy of Error Correction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 25
Accuracy of Error Correction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 26
Accuracy of Error Correction
Microwave Measurements 2015/16 Prof. Luca Perregrini Vector Network Analyzer, pag. 27
Slide 27
Residual Errors
OSLFixed Load
OSLSliding Load TRL TRM
Directivityd -40 dB -52 dB -60 dB -40 dB
Matchm -35 dB -41 dB -60 dB -40 dB
Reflection Tracking
t± .1 dB ± .05 dB ± .01 dB ± .01 dB
Accuracy of Error Correction
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