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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: [email protected]: microwave.unipv.it

Course on Microwave Measurements

Vector Network Analyzer


Summary

• Vector network analyzer

• VNA calibration technique


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



Hewlett-Packard 8510

frequency generator

microwave test set

mm-wave test set

IF processing

digital processing

& instrument control

test cables

DUT

port 1port 2



Hewlett-Packard 8510

test cables

DUT

port 1port 2

DUTb2

b1

a1

a2Attenuator (optional)


RFSource

LOSource

a0

b0 b3Port - 1 Port - 2

a3

DUTa2

a1

b1

b2Cable Cable

IF

IF

IF

IF

VNA Block Diagram


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


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


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


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


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


Improvements with Correction


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


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


DUTPerfectReflectometer

b0

b3

a0

b0

a3

b3

b1

a1

b2

a2

ErrorAdapter

a0,a3

Forward

Reverse

12-Term Error Model


ReverseError

Adapter

ForwardError

Adapter

DUT[S]


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]


a0

b0

b3

a0

b0

a3

b3

b1

a1

b2

a2

6 Error Terms

ForwardModel

ReverseModel

12-Term Error Model


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


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


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


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


Slide 21Dave Blackham& Ken Wong

Electronic Calibration Standards




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.



Accuracy of Error Correction






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


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