Vector Network Analyzer

Prof. Luca Perregrini

Dept. of Electrical, Computer and Biomedical Engineering

University of Pavia

e-mail: luca.perregrini@unipv.it

web: microwave.unipv.it

Course on Microwave Measurements

Summary

• Vector network analyzer

• VNA calibration technique

Scattering parameters

are typically measured, at microwave

frequencies, with a network analyzer (NA).

These instruments have found wide application since the mid to

late 1970’s.

Vector network analyzer

:

measurement of magnitudes and

phases of the S-parameters

Scalar network analyzer

: measurement of only the magnitudes of

the S-parameters

Most NA’s measure 2-port parameters. Some measure 4 and 6

ports.

Vector network analyzer

Hewlett-Packard 8510

frequency

microwave

test set

mm-wave

test set

IF

processing

digital

processing

& instrument

control

test cables

DUT

port 1

port 2

Vector network analyzer

Hewlett-Packard 8510

test cables

DUT

port 1

port 2

DUT

b

₂

b

₁

a

₁

a

₂ Attenuator (optional)

RF Source LO Source a₀ b₀ b₃ Port - 1 Port - 2 a₃ DUT a₂ a₁ b₁ b₂ Cable Cable IF IF IF IF

DUT A/D DSP A/D DSP A/D DSP a₂ a₁ b₁ b₂ a₀ b₀ b₃ LO LO RF Source Port - 1 Port - 2 IF IF

a_S N_{La0 N} Lb0 NLb3 b₀ b₃ M₂ M₁ L_2-b3 1+A_a0+N_Ha0 a₀ Port - 1 a₁ a₂ b₁ b₂ S₁₁ S₂₁ S₂₂ S₁₂ DUT Port - 2 Cable & Connector Cable & Connector L_C M_C L_C L_C L_C M_C M_C M_C

Branches With No Label = 1

IF IF M_S L_a0-b3 L_S-1 L_1-S L_S-a0 L_S-b0 L_1-a0 L_1-b0 1+A_b0+N_Hb0 1+A_b3+N_Hb3

a₁ = Incident Signal at Port-1 b₁ = Reflected Signal at Port-1 a₂ = Incident Signal at Port-2 b₂ = Transmitted signal at Port-2 a_S = Source Port

a₀ = Measured Incident Port b₀ = Measured Reflected Port b₃ = Measured Transmitted Port L_S-1 = Loss from Source to Port-1 L_1-S = Loss from Port-1 to Source L_S-a0 = Loss from Source to a₀

L_S-b0 = Loss from Source to b₀ (Directivity) L_1-a0 = Loss from Port-1 to a₀ (Directivity)

L_1-b0 = Loss from Port-1 to b₀ L_2-b3 = Loss from Port-2 to b₃

L_a0-b3 = Loss from a₀ to b₃ (Leakage) L_C = Loss of Cables

S₁₁ = Refl Coef of DUT at Port-1 S₂₁ = Forward Trans Coef of DUT S₁₂ = Reverse Trans Coef of DUT S₂₂ = Refl Coef of DUT at Port-2 M₁ = Match at Port-1

M₂ = Match at Port-2 M_S = Match of Source M_C = Match of Cables

N_La0 = Low Level Noise at a₀ N_Lb0 = Low Level Noise at b₀ N_Lb3 = Low Level Noise at b₃ N_Ha0 = High Level Noise at a₀ N_Hb0 = High Level Noise at b₀ N_Hb3 = High Level Noise at b₃

A_a0 = Dynamic Accuracy at a₀ (Linearity) A_b0 = Dynamic Accuracy at b₀ (Linearity) A_b3 = Dynamic Accuracy at b₃ (Linearity)

VNA Error Model Forward Direction

Branches With No Label = 1 a₀ b₀ Port - 1 a₁ a₂ b₁ b₂ S₁₁ S₂₁ S₂₂ S₁₂ DUT Port - 2 b₃ e₃₀ e₀₀ e₁₁ e₀₁ e₁₀ e₂₂ e₃₂

Directivity

Reflection

Tracking

Port-1 Match

Leakage

Transmission

Tracking

Port-2 Match

There are also Errors caused by the Converter, IF, Cables and Connectors





e e

L

L

L

L

L

L

L

S b S a S a S b S a 10 01 1 1 0 0 1 1 0 0 0 2



 



    

e

M

L

L

L

S a S a 11 2 1 1 0 0





  

e

L

L

S b S a 00 0 0



 

e

₃₀



L

_a0b3

e e

L L

L

S b S a 10 32 1 2 3 0



 

e

₂₂



M

₂

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

Error Adapter DUT Perfect Reflectometer 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

For ratio measurements there are 3 error terms The equation can be written in the linear form

Any 3 independent measurements can be used e₀₀ -_e 1 - e₁₁ _M = 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 _M

This yields 3 equations to solve for e₀₀, e₁₁, and _e

DUT Perfect Reflectometer b₀ b₃ a₀ b₀ a₃ b₃ b₁ a₁ b₂ a₂ Error Adapter a₀,a₃ Forward Reverse

Reverse Error Adapter Forward Error Adapter DUT [S] Perfect Reflectometer b'₀ a'₀ b'₀ a'₃ b'₃ b'₁ a'₁ b'₂ a'₂ DUT [S] Perfect Reflectometer a₀ b₀ b₃ a₀ b₀ a₃ b₃ b₁ a₁ b₂ a₂ 6 Error Terms

Forward

Model

Reverse

Model

a₀ b₀ Port - 1 _a 1 a₂ b₁ b₂ S₁₁ S₂₁ S₂₂ S₁₂ DUT Port - 2 b₃ e₃₀ e₀₀ e₁₁ e₁₀e₀₁ 1 e₂₂ e₁₀e₃₂ e₀₀ = e₁₁ = (e₁₀e₀₁) = (e₁₀e₃₂) = e₂₂ = e₃₀ = Directivity Port-1 Match Reflection Tracking Transmission Tracking Port-2 Match Leakage S_11M = b0 a₀ = e00 + (e10e01) S₁₁ - e₂₂ _S 1 - e₁₁S₁₁ - e₂₂S₂₂ + e₁₁e₂₂ _S S_21M = b3 a₀ = e30 + (e10e32) S₂₁ 1 - e₁₁S₁₁ - e₂₂S₂₂ + e₁₁e₂₂ _S _S = S₁₁S₂₂ - S₂₁S₁₂ FORWARD MODEL

b'₀ Port - 1 a'₁ a'₂ b'₁ b'₂ S₁₁ S₂₁ S₂₂ S₁₂ DUT Port - 2 b'₃ e'₁₁ e'₂₃e'₀₁ e'22 e'₂₃e'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) S22 - e'11 S 1 - e'₁₁S₁₁ - e'₂₂S₂₂ + e'₁₁e'₂₂ _S S_22M = b'3 a'₃ = e'₀₃ + (e'₂₃e'₀₁) S12 1 - e'₁₁S₁₁ - e'₂₂S₂₂ + e'₁₁e'₂₂ _S S_12M = b'0 a'₃





S S e e e S e e e e e S e e e S e e e D S S e e e S e e e e 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 32 22 22 21 30 10 32 12 03 23 01 21 21 30 10 32 22 33 23 32 22 22 22 22 33 23 32 11 00 10 01 1 1 1                                                                      ' ' ' ' ' ' ' ' ' ' ' ' ' ' e





                                                                              e e S e e e S e e e D S S e e e S e e e e e D D S e e e e S e e e e S e e e M M M M M M M 11 11 21 30 10 32 12 03 23 01 12 12 03 23 01 11 00 10 01 11 11 11 00 10 01 11 22 33 23 32 22 21 30 10 32 1 1 1 ' ' ' ' ' ' ' ' ' ' ' '         S e e e e e M 12 03 23 01 22 11 ' ' ' '

Calibration

STEP 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 S_21M gives e₃₀ directly

S_11M - e₀₀ S_11Me₁₁ - _e

e₂₂ =

e₁₀e₃₂ = (S_21M - e₃₀)(1 - e₁₁e₂₂) Use the same process for the reverse model

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.

Residual

Errors

OSL

Fixed Load

OSL

Sliding Load

TRL

TRM

Directivity

d

-40 dB

-52 dB

-60 dB

-40 dB

Match

m

-35 dB

-41 dB

-60 dB

-40 dB

Reflection

Tracking

t

± .1 dB

± .05 dB

± .01 dB

± .01 dB