VNA Tools II S-parameter uncertainty calculation

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

VNA Tools II S-parameter uncertainty calculation Michael Wollensack METAS

25. May 2011

Michael Wollensack

1

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Outline

Introduction VNA Measurement Model Database Uncertainty Visualization Results

Michael Wollensack

2

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Introduction

Problem Computation of the uncertainties of S-parameter measurements.

Solution Set up a measurement model for the Vector Network Analyzer and propagate all uncertainties through the VNA measurement model.

Michael Wollensack

3

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Measurement Errors

Which non correctable influences affect the S-parameter measurements? 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

Michael Wollensack

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METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

VNA Measurement Model The following equation describes the in VNA Tools II used N-port VNA measurement model. All bold variables are S-parameter matrices and i is the measurement index. h  h  h iii M(i) = R(i) + W + V(i) ⊕ E + D(i) ⊕ C(i) ⊕ S(i) W0

E0

1 2

M−R

1

N+2

2

W+V N

M0

N+1

N+1

1

N+2

2

M00

1

N+2

2

C

E+D 2N

N+1

N

2N

S0

S

N

2N

N

S

Figure: VNA Measurement Model Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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. W0

E0

1 2

M−R

1

N+2

2

W+V N

M0

N+1

N+1

1

N+2

2

E+D 2N

M00

N+1

1

N+2

2

C

N

2N

S0

S

N

2N

N

S

Figure: VNA Measurement Model Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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. W0

E0

1 2

M−R

1

N+2

2

W+V N

M0

N+1

N+1

1

N+2

2

M00

1

N+2

2

S

C

E+D 2N

N+1

N

2N

S0

N

2N

N

S

Figure: VNA Measurement Model Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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 calibration error terms. It changes from measurement to measurement. W0

E0

1 2

M−R

1

N+2

2

W+V N

M0

N+1

N+1

1

N+2

2

M00

1

N+2

2

S

C

E+D 2N

N+1

N

2N

S0

N

2N

N

S

Figure: VNA Measurement Model Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

VNA Measurement Model - Cable and Connector C denotes the cable stability and connector repeatability influences. It changes for every new connection or cable movement. W0

E0

1 2

M−R

1

N+2

2

W+V N

M0

N+1

N+1

1

N+2

2

M00

1

N+2

2

S

C

E+D 2N

N+1

N

2N

S0

N

2N

N

S

Figure: VNA Measurement Model

Michael Wollensack

9

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

VNA Measurement Model - Error Corrected Data S denotes the error corrected data or the calibration kit standard definitions. It changes if a new device is connected. W0

E0

1 2

M−R

1

N+2

2

W+V N

M0

N+1

N+1

1

N+2

2

M00

1

N+2

2

S

C

E+D 2N

N+1

N

2N

S0

N

2N

N

S

Figure: VNA Measurement Model

Michael Wollensack

10

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database I

I

All influences that affect the measurements are defined as uncertainties in a database. There are two types of uncertainties: 1. Additive quantities 2. Multiplicative quantities

I

There are four types of database items: 1. 2. 3. 4.

VNA Device (noise, linearity, drift) Cable (stability) Connector (repeatability) Calibration Standard

I

All influences are frequency dependent.

I

VNA Tools II has a graphical user interface to edit items in the database.

Michael Wollensack

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METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - Type of Uncertainties

Additive Quantity

Multiplicative Quantity

The real and imaginary part is specified in dB.

The magnitude is specified in dB and the phase in deg.

Real

Figure: Additive Quantity

Michael Wollensack

Phase

(1, 0)

Imag

(0, 0)

Mag

Figure: Multiplicative Quantity

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - VNA Device

There are three groups of uncertainty definitions for a VNA device: 1. Noise 2. Linearity 3. Drift Figure: DB VNA Device Settings

Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - VNA Device

Noise I

Noise Floor in dB (additive)

I

Trace Noise in dB rms and deg rms (multiplicative)

Figure: DB VNA Device Noise

Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - VNA Device

Linearity I

Linearity in dB and deg depends on power level (multiplicative)

Figure: DB VNA Device Linearity

Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - VNA Device

Drift I

Switch Term Drift in dB (additive)

I

Directivity Drift in dB (additive)

I

Tracking Drift in dB and deg (multiplicative)

I

Match Drift in dB (additive)

I

Isolation Drift in dB (additive)

Michael Wollensack

Figure: DB VNA Device Drift

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - Cable

Cable Stability I

Stability in dB and deg (multiplicative)

Figure: DB Cable

Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - Connector

Connector Repeatability I

Repeatability in dB (additive)

Figure: DB Connector

Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - Calibration Standard

Agilent Model Standard I

Open and Short have specified Phase Deviation in deg. Magnitude deviation assumed to be the same as the phase deviation. (multiplicative)

I

Load has specified Return Loss in dB. (additive) Figure: DB Agilent Model Standard

Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Database - Calibration Standard

Databased Standard Uncertainties explicitly stated for each data point.

Figure: DB Databased Standard

Michael Wollensack

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METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Metas.UncLib Metas.UncLib is a measurement uncertainty calculator.

Input quantities corr

The user specifies I

input quantities X with input covariance matrix VX

I

measurement model f

X1

X2

X3

Measurement model f1

f2

Metas.UncLib computes I

output quantities Y = f (X)

I

Jacobi matrix JYX of f using automatic differentiation

I

output covariance matrix VY = JYX VX JYX 0

Michael Wollensack

Output quantities corr Y1

Y2

Figure: Metas.UncLib 21

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Uncertainty Generators I

Uncertainty Generators are used to generates Metas.UncLib input uncertain quantities.

I

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

I

The standard uncertainty of an uncertain quantity comes from the database.

I

The uncertainty generator decides if the uncertain quantity gets a new (uncorrelated) or an existing (correlated) uncertain input id. There are three groups of uncertainty generators:

I

1. Noise and linearity influences 2. Drift of switch and error terms 3. Cable stability and connector repeatability Michael Wollensack

22

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Uncertainty Generators - Noise and Linearity Noise I

Uncorrelated for each measurement.

I

Depends on the VNA device noise floor and trace noise definition.

1 2

R N

Linearity I

Correlated for each measurement.

I

Depends on the VNA device linearity definition.

Michael Wollensack

Figure: Noise and linearity influences

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METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Uncertainty Generators - Drift of Switch and Error Terms

W0 1

Drift

2

I

I

Michael Wollensack

N+1

1

N+2

2

W+V

Uncorrelated for each measurement. Depends on the VNA device drift definition.

E0

N

N+1 N+2

E+D 2N

N

2N

Figure: Drift of switch and error terms

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Uncertainty Generators - Cable and Connector Cable I

Uncorrelated for each new cable position.

I

Depends on the cable stability definition.

p

1

I

Depends on the connector repeatability definition.

Michael Wollensack

Conn.

2

p¯

1

0 Cp

Connector Uncorrelated for each new connection.

1

Cp

0

I

2

Cable

Rp,1

Rp,2 1

Figure: Cable stability and connector repeatability 2-port

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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

Vna measurement model: h  h  h iii 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.

Michael Wollensack

26

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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

Vna measurement model: h  h  h iii 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 VNA Tools II programmer.

I

Metas.UncLib takes care about correlations.

Michael Wollensack

27

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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 point and one parameter of a single file. Info shows file information including MD5 checksum of multiple files.

Michael Wollensack

28

METAS

Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

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 point and one parameter of a single file. Info shows file information including MD5 checksum of multiple files. There are three different uncertainty modes: None hides the uncertainty. Standard shows the standard uncertainty (67% coverage factor, k = 1). U95 shows the expanded uncertainty (95% coverage factor, k = 2). Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Visualization - Graph

Figure: Data Explorer Graph Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Visualization - Table

Figure: Data Explorer Table Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Visualization - Point

Figure: Data Explorer Point Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Visualization - Info

Figure: Data Explorer Info Michael Wollensack

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Introduction

VNA Measurement Model

Database

Uncertainty

Visualization

Results

Results

I

New VNA measurement model for a N-port Vector Network Analyzer.

I

Definition of all influences that affect the measurements.

I

Linear propagation of all uncertainties through the VNA measurement model.

I

Visualization of S-parameter data with uncertainties.

Michael Wollensack

34

METAS