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Network Analyzer Error Models and Calibration Methods by Doug Rytting. Presentation Outline. Network Analyzer Block Diagram and Error Model System Error Model for Error-Correction One-Port Error Model and Calibration Two-Port Error Models and Calibration 12-Term Method - PowerPoint PPT Presentation
Citation preview
Slide 1
Network Analyzer
Error Modelsand
Calibration Methods
byDoug Rytting
Slide 2
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 3
RFSource
LOSource
a0
b0 b3
Port - 1 Port - 2
a3
DUTa2
a1
b1
b2Cable Cable
IF
IF
IF
IF
Network Analyzer Block Diagram
Slide 4
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
Block Diagram – Forward Direction
Slide 5
aS
N La0 N Lb0N Lb3
b0 b3
M 2M 1
L2-b3
1+A a0 +N Ha0
a0
Port - 1a1
a2b1
b2
S 11
S 21
S 22
S 12
DUT
Port - 2Cable &
ConnectorCable &
Connector
LC
M C
LC
LCLC
M C M CM C
Branches With No Label = 1
IF IF
M S
La0-b3
LS-1
L1-S
LS-a0 LS-b0 L1-a0
L1-b0
1+A b0 +N Hb0 1+A b3 +N Hb3
Error Model – Forward Direction
Slide 6
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 a 0LS-b0 = Loss from Source to b 0 (Directivity)L1-a0 = Loss from Port-1 to a 0 (Directivity)L1-b0 = Loss from Port-1 to b 0L2-b3 = Loss from Port-2 to b 3La0-b3 = Loss from a 0 to b 3 (Leakage)LC = Loss of Cables
S 11 = Refl Coef of DUT at Port-1S 21 = Forward Trans Coef of DUTS 12 = Reverse Trans Coef of DUTS 22 = Refl Coef of DUT at Port-2
M 1 = Match at Port-1M 2 = Match at Port-2M S = Match of SourceM C = Match of Cables
N La0 = Low Level Noise at a 0N Lb0 = Low Level Noise at b 0N Lb3 = Low Level Noise at b 3N Ha0 = High Level Noise at a 0N Hb0 = High Level Noise at b 0N Hb3 = High Level Noise at b 3
A a0 = Dynamic Accuracy at a 0 (Linearity)A b0 = Dynamic Accuracy at b 0 (Linearity)A b3 = Dynamic Accuracy at b 3 (Linearity)
Error Model Definitions
Slide 7
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 8
Branches With No Label = 1
a0
b0
Port - 1a1
a2b1
b2
S 11
S 21
S 22
S 12
DUTPort - 2
b 3
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
L
L L L
LS b
S a
S a S b
S a
10 011 1 0
0
1 1 0 0
0
2
e ML L
LS a
S a11 2
1 1 0
0
eL
LS b
S a00
0
0
e L a b30 0 3
e eL L
LS b
S a10 32
1 2 3
0
e M22 2
System Model – Forward Direction
Slide 9
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 10
Improvements with Correction
Slide 11
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 12
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 13
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 14
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 15
DUTPerfectReflectometer
b0
b3
a0
b0
a3
b3
b1
a1
b2
a2
ErrorAdapter
a0,a 3
Forward
Reverse
12-Term Error Model
Slide 16
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 17
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 18
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 19
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 20
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 21
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 22
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 23
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 24
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 25
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 26
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 27
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 28
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 29
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 30
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 31
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 32
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 12-Term: Forward
12-term model if add 2 crosstalk
terms
Slide 33
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
e33
b3
a3
e22
e32
e23
e33
b3
a3
8-Term to 12-Term: Reverse
12-term model if add 2 crosstalk
terms
Slide 34
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 35
Example: TRL
Slide 36
Example: TRL
Slide 37
Example: TRL
Slide 38
Example: TRL
Slide 39
Example: TRL
Slide 40
Example: TRL
Slide 41
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 42
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 43
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 44
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-parametersRemoving Switch Errors
Slide 45
Measuring S-parametersRemoving Switch Errors
Slide 46
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 47
Electronic Calibration Standards
Dave Blackham& Ken Wong
Slide 48
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.
Dave Blackham& Ken Wong
Slide 49
First Generation Solid State Electronic Calibrator
Transmission Line
PIN Diodes
Dave Blackham& Ken Wong
Slide 50
Second Generation Solid State Electronic Calibrator
Z1
Z4
Z3
Z2
Z1
Z4
Z3
Z2
ATTN
Discrete FET Switches
PORT A PORT B
Dave Blackham& Ken Wong
Slide 51
Second Gen E-Cal Impedance States
Dave Blackham& Ken Wong
Slide 52
Third Generation E-Cal
MMICPORT B
PORT A
Dave Blackham& Ken Wong
Slide 53
Typical E-Cal Calibration Set-Up
Dave Blackham& Ken Wong
Slide 54
1 1 1
2 2 2
1
2
1
1
1
m m
m m
mn
a
b
c
n mnn
H H
H
1 H
A E M
A A E A M
let C A A ;
then E C A M
[C] is also the covariance matrix-1
[A] *[E] = [M]
H = conjugate transpose(31)
1-Port Calibration: E-Cal Case
Dave Blackham& Ken Wong
Slide 55
Differences of Calculated System Error Terms
Delta Directivity
Delta Source Match
|Ref Cal – ECal|
Dave Blackham& Ken Wong
Slide 56
Differences of Calculated System Error Terms
Delta Transmission Tracking
Delta Reflection Tracking
|Ref Cal - ECal|
Dave Blackham& Ken Wong
Slide 57
Noninsertable Calibration Using E-Cal
Noninsertable ECal Module
Insetable ECal Module + Unknown Thru or Adapter Removal
User Characterization
Dave Blackham& Ken Wong
Slide 58
Noninsertable E-Cal Module
SAME GENDER
MIX CONNECTOR
Dave Blackham& Ken Wong
Slide 59
Insertable E-Cal + Unknown Thru
VNA
Cal Port-1
Dave Blackham& Ken Wong
Slide 60
Insertable E-Cal + Unknown Thru
VNA
Cal Port-2
Dave Blackham& Ken Wong
Slide 61
Insertable E-Cal + Unknown Thru
VNA
Connect Unknown Thru
Dave Blackham& Ken Wong
Slide 62
Fixture Embedding
PNA
P1 P2
PNA
P1 P2
Port1Coaxial Access
Point Fixtures
Ecal ModuleConnected to Coaxial
Access Points
Port2Coaxial Access
Point
Full 2-port Cal Characterize E-Cal
Dave Blackham& Ken Wong
Slide 63
Fixture Embedding – alternate set up
SPDT
PNA
P1 P2
SwitchDriver
Dave Blackham& Ken Wong
Slide 64
Insitu Calibration – 2-port E-Cal
VNA
MEASUREMENTPORTS
Requires External Software
Dave Blackham& Ken Wong
Slide 65
• Network Analyzer Block Diagram and Error Model• System Error Model for Error-Correction• One-Port Error Model and Calibration• Two-Port Error Models and Calibration
• 12-Term Method• 16-Term Method• 8-Term Method• 8-Term Examples
• Measuring S-parameters• E-Cal• Accuracy of Error-Correction
Presentation Outline
Slide 66
Accuracy of Error Correction
Slide 67
Accuracy of Error Correction
Slide 68
Accuracy of Error Correction
Slide 69
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 70
Accuracy of Error Correction
Slide 71
Vector Network AnalyzerReferences