TSD-160 Introduction to Network Analyzers and Error Correction

1

TSD-160 Introduction to

Network Analyzersand Error Correction

Doug Rytting

4804 Westminster PlaceSanta Rosa, CA 95405

[email protected]

2

Agenda

• Block Diagram

• Improvements with Error Correction

• 3-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


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


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]


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]


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]


[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

24

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

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


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

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31

Vector Network AnalyzerReferences

32

Doug RyttingBiography

Documents

TSD-160 Introduction to Network Analyzers and Error Correction