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TSD-160 Introduction to Network Analyzers and Error Correction. Doug Rytting 4804 Westminster Place Santa Rosa, CA 95405 707-539-1631 rytting@sbcglobal.net. Agenda. Block Diagram Improvements with Error Correction 3-Term Error Model 12-Term Error Model 16-Term Error Model - PowerPoint PPT Presentation
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1
TSD-160 Introduction to
Network Analyzersand Error Correction
Doug Rytting
4804 Westminster PlaceSanta Rosa, CA 95405
707-539-1631rytting@sbcglobal.net
2
Agenda
• Block Diagram
• Improvements with Error Correction
• 3-Term Error Model
• 12-Term Error Model
• 16-Term Error Model
• 8-Term Error Model
• Switch Correction
• Miltiport Error Model
• Accuracy of Error Correction
3
RFSource
LOSource
a0
b0 b3Port - 1 Port - 2
a3
DUTa2
a1
b1
b2Cable Cable
IF
IF
IF
IF
Network Analyzer Block Diagram
4
Improvement with Correction
5
Improvement with Correction
6
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
Improvement with Correction
7
ErrorAdapter
DUTPerfect
Reflectometer
a0
b0
a0
b0
b1
a1
3 Error Terms
Port - 1
e00 e11
e10 e01
1
b1
a0
b0
DUT
a1e00 =
e11 =
(e 10 e01 ) =
Directivity
Port Match
Tracking
One Port: 3-Term Error Model
8
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 11 M =
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
9
DUTPerfectReflectometer
b0
b3
a0
b0
a3
b3
b1
a1
b2
a2
ErrorAdapter
a0,a 3
Forward
Reverse
12-Term Error Model
10
ReverseError
Adapter
ForwardError
Adapter
DUT[S]
PerfectReflectometer
b' 0
a' 3b' 3
a' 0b' 0
a' 3
b' 3
b' 1
a' 1
b' 2
a' 2
6 Error Terms
DUT[S]
PerfectReflectometer
a0
b0
b3
a0b0
a3
b3
b1
a1
b2
a2
6 Error Terms
ForwardModel
ReverseModel
12-Term Error Model
11
a0
b0
Port - 1 a1
a2b1
b2
S 11
S 21
S 22S 12
DUTPort - 2
b3
e30
e00 e11e10 e01
1e22
e10 e32
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
e00 =
e11 =
(e 10 e01 ) =
(e 10 e32 ) =
e22 =
e30 =
Directivity
Port-1 Match
Reflection Tracking
Transmission Tracking
Port-2 Match
Leakage
12-Term Error Model
12
b' 0
Port - 1 a' 1
a' 2b' 1
b' 2
S 11
S 21
S 22S 12
DUTPort - 2
b' 3
e' 11e' 23 e' 01
e' 22
e' 23 e' 32
1
e' 33
a' 3
e' 03
REVERSE MODEL
= 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' 3
a' 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' 0
a' 3
S = S 11 S 22 - S 21 S 12
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
12-Term Error Model
13
S
S ee e
S ee e
e eS e
e eS e
e 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 eS e
e eS e
e e
D
S
S ee e
S ee e
e e
D
DS e
e ee
S ee e
eS 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 ee e
e eM12 03
23 0122 11
'' '
'
12-Term Error Model
14
STEP 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 - ee22 =
e10 e32 = (S 21M - e 30 )(1 - e 11 e22 )
Use the same process for the reverse model
12-Term Error Model
15
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.
16
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
17
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
18
8-Term Error Model
DUTPerfectReflectometer
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.
19
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
XError
Adapter
YError
Adapter
8-Term Error Model
202332332201101100
23
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
21
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 11 X + 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
22
Using the cascade parameters in matrix form yields
MEASURED
TM = T XT T Y
ACTUAL
T = T X-1 TM T Y
-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
11e
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
23
TRL & LRL
TRM & LRM
TraditionalTOSL
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
24
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
Switch Correction
25
Switch Correction
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
26
Multiport Error Model
SM = (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
27
Accuracy of Error Correction
28
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
29
Accuracy of Error Correction
30
Accuracy of Error Correction
31
Vector Network AnalyzerReferences
32
Doug RyttingBiography
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