VNA Tools II S-parameter uncertainty calculation · VNA Tools II S-parameter uncertainty calculation Michael Wollensack METAS 25. May 2011 Michael Wollensack 1 METAS. Introduction

Introduction VNA Measurement Model Database Uncertainty Visualization Results

VNA Tools IIS-parameter uncertainty calculation

Michael Wollensack

METAS

25. May 2011

Michael Wollensack 1 METAS


Outline

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results



Introduction

ProblemComputation of the uncertainties of S-parameter measurements.

SolutionSet up a measurement model for the Vector Network Analyzer andpropagate all uncertainties through the VNA measurement model.



Measurement Errors

Which non correctable influences affect the S-parametermeasurements?

I Noise floor and trace noise

I Linearity

I Drift of switch and calibration error terms

I Cable stability

I Connector repeatability

I Calibration standard definitions



VNA Measurement Model

The following equation describes the in VNA Tools II used N-portVNA measurement model. All bold variables are S-parametermatrices and i is the measurement index.

M(i) = R(i) +[(

W + V(i))⊕[(

E + D(i))⊕[C(i) ⊕ S(i)

]]]

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

N+1

N+2

2N

1

2

N

C

1

2

N

SM− R

SS′M′′M′

W′ E′

Figure: VNA Measurement Model



VNA Measurement Model - Raw Data

M denotes the raw data measured by the VNA.It changes from measurement to measurement.

R denotes the noise and linearity influences.It changes from measurement to measurement.

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

N+1

N+2

2N

1

2

N

C

1

2

N

SM− R

SS′M′′M′

W′ E′




VNA Measurement Model - Switch Terms

W denotes the switch terms.It’s constant during an entire calibration.

V denotes the drift of the switch terms.It changes from measurement to measurement.

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

N+1

N+2

2N

1

2

N

C

1

2

N

SM− R

SS′M′′M′

W′ E′




VNA Measurement Model - Calibration Error Terms

E denotes the calibration error terms.It’s constant during an entire calibration.

D denotes the drift of the calibartion error terms.It changes from measurement to measurement.

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

N+1

N+2

2N

1

2

N

C

1

2

N

SM− R

SS′M′′M′

W′ E′




VNA Measurement Model - Cable and Connector

C denotes the cable stability and connectorrepeatability influences. It changes for every newconnection or cable movement.

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

N+1

N+2

2N

1

2

N

C

1

2

N

SM− R

SS′M′′M′

W′ E′




VNA Measurement Model - Error Corrected Data

S denotes the error corrected data or the calibration kitstandard definitions. It changes if a new device isconnected.

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

N+1

N+2

2N

1

2

N

C

1

2

N

SM− R

SS′M′′M′

W′ E′




Database

I All influences that affect the measurements are definded asuncertainties in a database.

I There are two types of uncertainties:

1. Additive quantities2. Multiplicative quantities

I There are four types of database items:

1. VNA Device (noise, linearity, drift)2. Cable (stability)3. Connector (repeatability)4. Calibration Standard

I All influences are frequency dependent.

I VNA Tools II has a graphical user interface to edit items inthe database.



Database - Type of Uncertainties

Additive Quantity

The real and imaginary part isspecifed in dB.

Multiplicative Quantity

The magnitude is specifed in dBand the phase in deg.

(0, 0)

Real

Imag

Figure: Additive Quantity

(1, 0)

Mag

Ph

ase

Figure: Multiplicative Quantity



Database - VNA Device

There are three groups ofuncertainty definitions for a VNAdevice:

1. Noise

2. Linearity

3. Drift

Figure: DB VNA Device Settings




Noise

I Noise Floor in dB (additive)

I Trace Noise in dB rms anddeg rms (multiplicative)

Figure: DB VNA Device Noise




Linearity

I Linearity in dB and degdepends on power level(multiplicative)

Figure: DB VNA Device Linearity




Drift

I Switch Term Drift in dB(additive)

I Directivity Drift in dB(additive)

I Tracking Drift in dB anddeg (multiplicative)

I Match Drift in dB (additive)

I Isolation Drift in dB(additive) Figure: DB VNA Device Drift



Database - Cable

Cable Stability

I Stability in dB and deg(multiplicative)

Figure: DB Cable



Database - Connector

Connector Repeatability

I Repeatability in dB(additive)

Figure: DB Connector



Database - Calibration Standard

Agilent Model Standard

I Open and Short havespecified Phase Deviation indeg. Magnitude deviationassumed to be the same asthe phase deviation.(multiplicative)

I Load has specified ReturnLoss in dB. (additive)

Figure: DB Agilent Model Standard



Database - Calibration Standard

Databased StandardUncertainties explicitly stated foreach data point.

Figure: DB Databased Standard



Metas.UncLib

Metas.UncLib is a measurementuncertainty calculator.

The user specifies

I input quantities X withinput covariance matrix VX

I measurement model f

Metas.UncLib computes

I output quantities Y = f (X)

I Jacobi matrix JYX of f usingautomatic differentiation

I output covariance matrixVY = JYXVXJYX

′

X1 X2 X3

f1

corr

Input quantities

Output quantities

Measurement model

f2

Y1 Y2

corr

Figure: Metas.UncLib



Uncertainty Generators

I Uncertainty Generators are used to generates Metas.UncLibinput uncertain quantities.

I The value of an uncertain quantity is zero for additivequantities or one for multiplicative quantities.

I The standard uncertainty of an uncertain quantity comes fromthe database.

I The uncertainty generator decides if the uncertain quantitygets a new (uncorrelated) or an existing (correlated) uncertaininput id.

I There are three groups of uncertainty generators:

1. Noise and linearity influences2. Drift of switch and error terms3. Cable stability and connector repeatability



Uncertainty Generators - Noise and Linearity

Noise

I Uncorrelated for eachmeasurement.

I Depends on the VNA devicenoise floor and trace noisedefinition.

Linearity

I Correlated for eachmeasurement.

I Depends on the VNA devicelinearity definition.

1

2

N

R

Figure: Noise and linearity influences



Uncertainty Generators - Drift of Switch and Error Terms

Drift

I Uncorrelated for eachmeasurement.

I Depends on the VNA devicedrift definition.

N+1

N+2

2N

1

2

N

W + V

N+1

N+2

2N

1

2

N

E + D

W′ E′

Figure: Drift of switch and errorterms



Uncertainty Generators - Cable and Connector

Cable

I Uncorrelated for each newcable position.

I Depends on the cablestability definition.

Connector

I Uncorrelated for each newconnection.

I Depends on the connectorrepeatability definition.

21Cable

21Conn.

0 0

Cp

Cp

Rp,1 Rp,2

1

1

p p̄

Figure: Cable stability andconnector repeatability 2-port



Uncertainty Propagation

The uncertainty generators are represented by R, V, D and C.

I Vna measurement model:

M(i) = R(i)+[(

W + V(i))⊕[(

E + D(i))⊕[C(i) ⊕ S(i)

]]]I Calibration and error correction are based on the above

equation.

I Linear uncertainty propagation is done with Metas.UncLib.

I The complexity is hidden from the user and from the VNATools II programmer.

I Metas.UncLib takes care about correlations.



Uncertainty Propagation

The uncertainty generators are represented by R, V, D and C.

I Vna measurement model:

M(i) = R(i)+[(

W + V(i))⊕[(

E + D(i))⊕[C(i) ⊕ S(i)

]]]I Calibration and error correction are based on the above

equation.

I Linear uncertainty propagation is done with Metas.UncLib.

I The complexity is hidden from the user and from the VNATools II programmer.

I Metas.UncLib takes care about correlations.



Visualization

VNA Tools II supports different view modes:

Graph shows a graphical visualization of multiple files.

Table shows a tabular visualization of a single file.

Point shows an uncertainty budget for one frequency pointand one parameter of a single file.

Info shows file information including MD5 checksum ofmultiple files.

There are three different uncertainty modes:

None hides the uncertainty.

Standard shows the standard uncertainty (67% coveragefactor, k = 1).

U95 shows the expanded uncertainty (95% coveragefactor, k = 2).



Visualization

VNA Tools II supports different view modes:

Graph shows a graphical visualization of multiple files.

Table shows a tabular visualization of a single file.

Point shows an uncertainty budget for one frequency pointand one parameter of a single file.

Info shows file information including MD5 checksum ofmultiple files.

There are three different uncertainty modes:

None hides the uncertainty.

Standard shows the standard uncertainty (67% coveragefactor, k = 1).

U95 shows the expanded uncertainty (95% coveragefactor, k = 2).



Visualization - Graph

Figure: Data Explorer Graph



Visualization - Table

Figure: Data Explorer Table



Visualization - Point

Figure: Data Explorer Point



Visualization - Info

Figure: Data Explorer Info



Results

I New VNA measurement model for a N-port Vector NetworkAnalyzer.

I Definition of all influences that affect the measurements.

I Linear propagation of all uncertainties through the VNAmeasurement model.

I Visualization of S-parameter data with uncertainties.


VNA Tools II S-parameter uncertainty calculation · VNA Tools II S-parameter uncertainty calculation Michael Wollensack METAS 25. May 2011 Michael Wollensack 1 METAS. Introduction

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