Introduction VNA Measurement Model Database Uncertainty Visualization Results
VNA Tools IIS-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
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.
Michael Wollensack 3 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 4 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 5 METAS
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.
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
Michael Wollensack 6 METAS
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.
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
Michael Wollensack 7 METAS
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 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′
Figure: VNA Measurement Model
Michael Wollensack 8 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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′
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 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′
Figure: VNA Measurement Model
Michael Wollensack 10 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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.
Michael Wollensack 11 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 12 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Database - VNA Device
There are three groups ofuncertainty definitions for a VNAdevice:
1. Noise
2. Linearity
3. Drift
Figure: DB VNA Device Settings
Michael Wollensack 13 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Database - VNA Device
Noise
I Noise Floor in dB (additive)
I Trace Noise in dB rms anddeg rms (multiplicative)
Figure: DB VNA Device Noise
Michael Wollensack 14 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Database - VNA Device
Linearity
I Linearity in dB and degdepends on power level(multiplicative)
Figure: DB VNA Device Linearity
Michael Wollensack 15 METAS
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 anddeg (multiplicative)
I Match Drift in dB (additive)
I Isolation Drift in dB(additive) Figure: DB VNA Device Drift
Michael Wollensack 16 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Database - Cable
Cable Stability
I Stability in dB and deg(multiplicative)
Figure: DB Cable
Michael Wollensack 17 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Database - Connector
Connector Repeatability
I Repeatability in dB(additive)
Figure: DB Connector
Michael Wollensack 18 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 19 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Database - Calibration Standard
Databased StandardUncertainties explicitly stated foreach data point.
Figure: DB Databased Standard
Michael Wollensack 20 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 21 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 22 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 23 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 24 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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
Michael Wollensack 25 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:
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.
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:
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.
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 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).
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 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).
Michael Wollensack 29 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Visualization - Graph
Figure: Data Explorer Graph
Michael Wollensack 30 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Visualization - Table
Figure: Data Explorer Table
Michael Wollensack 31 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Visualization - Point
Figure: Data Explorer Point
Michael Wollensack 32 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
Visualization - Info
Figure: Data Explorer Info
Michael Wollensack 33 METAS
Introduction VNA Measurement Model Database Uncertainty Visualization Results
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.
Michael Wollensack 34 METAS