VNA Tools II S-parameter uncertainty calculation
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1 VA Tools II S-parameter uncertainty calculation Michael Wollensack METAS 5. May 0 Michael Wollensack METAS
2 Outline Introduction VA Measurement Model Database Uncertainty Visualization Results Michael Wollensack METAS
3 Introduction Problem Computation of the uncertainties of S-parameter measurements. Solution Set up a measurement model for the Vector etwork Analyzer and propagate all uncertainties through the VA measurement model. Michael Wollensack 3 METAS
4 Measurement Errors Which non correctable influences affect the S-parameter measurements? oise floor and trace noise Linearity Drift of switch and calibration error terms Cable stability Connector repeatability Calibration standard definitions Michael Wollensack 4 METAS
5 VA Measurement Model The following equation describes the in VA Tools II used -port VA measurement model. All bold variables are S-parameter matrices and i is the measurement index. M (i) = R (i) + [( W + V (i)) [( E + D (i)) [C (i) S (i)]]] W E M R W + V + E + D + C + S M M S S Figure: VA Measurement Model Michael Wollensack 5 METAS
6 VA Measurement Model - Raw Data M denotes the raw data measured by the VA. It changes from measurement to measurement. R denotes the noise and linearity influences. It changes from measurement to measurement. W E M R W + V + E + D + C + S M M S S Figure: VA Measurement Model Michael Wollensack 6 METAS
7 VA 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. W E M R W + V + E + D + C + S M M S S Figure: VA Measurement Model Michael Wollensack 7 METAS
8 VA 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. W E M R W + V + E + D + C + S M M S S Figure: VA Measurement Model Michael Wollensack 8 METAS
9 VA Measurement Model - Cable and Connector C denotes the cable stability and connector repeatability influences. It changes for every new connection or cable movement. W E M R W + V + E + D + C + S M M S S Figure: VA Measurement Model Michael Wollensack 9 METAS
10 VA 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. W E M R W + V + E + D + C + S M M S S Figure: VA Measurement Model Michael Wollensack 0 METAS
11 Database All influences that affect the measurements are defined as uncertainties in a database. There are two types of uncertainties:. Additive quantities. Multiplicative quantities There are four types of database items:. VA Device (noise, linearity, drift). Cable (stability) 3. Connector (repeatability) 4. Calibration Standard All influences are frequency dependent. VA Tools II has a graphical user interface to edit items in the database. Michael Wollensack METAS
12 Database - Type of Uncertainties Additive Quantity The real and imaginary part is specified in db. Multiplicative Quantity The magnitude is specified in db and the phase in deg. Real Mag (0, 0) Imag (, 0) Phase Figure: Additive Quantity Figure: Multiplicative Quantity Michael Wollensack METAS
13 Database - VA Device There are three groups of uncertainty definitions for a VA device:. oise. Linearity 3. Drift Figure: DB VA Device Settings Michael Wollensack 3 METAS
14 Database - VA Device oise oise Floor in db (additive) Trace oise in db rms and deg rms (multiplicative) Figure: DB VA Device oise Michael Wollensack 4 METAS
15 Database - VA Device Linearity Linearity in db and deg depends on power level (multiplicative) Figure: DB VA Device Linearity Michael Wollensack 5 METAS
16 Database - VA Device Drift Switch Term Drift in db (additive) Directivity Drift in db (additive) Tracking Drift in db and deg (multiplicative) Match Drift in db (additive) Isolation Drift in db (additive) Figure: DB VA Device Drift Michael Wollensack 6 METAS
17 Database - Cable Cable Stability Stability in db and deg (multiplicative) Figure: DB Cable Michael Wollensack 7 METAS
18 Database - Connector Connector Repeatability Repeatability in db (additive) Figure: DB Connector Michael Wollensack 8 METAS
19 Database - Calibration Standard Agilent Model Standard Open and Short have specified Phase Deviation in deg. Magnitude deviation assumed to be the same as the phase deviation. (multiplicative) Load has specified Return Loss in db. (additive) Figure: DB Agilent Model Standard Michael Wollensack 9 METAS
20 Database - Calibration Standard Databased Standard Uncertainties explicitly stated for each data point. Figure: DB Databased Standard Michael Wollensack 0 METAS
21 Metas.UncLib Metas.UncLib is a measurement uncertainty calculator. The user specifies input quantities X with input covariance matrix V X measurement model f Metas.UncLib computes output quantities Y = f (X) Jacobi matrix J YX of f using automatic differentiation output covariance matrix V Y = J YX V X J YX Input quantities corr X X X 3 Measurement model f f Output quantities corr Y Y Figure: Metas.UncLib Michael Wollensack METAS
22 Uncertainty Generators Uncertainty Generators are used to generates Metas.UncLib input uncertain quantities. The value of an uncertain quantity is zero for additive quantities or one for multiplicative quantities. The standard uncertainty of an uncertain quantity comes from the database. 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:. oise and linearity influences. Drift of switch and error terms 3. Cable stability and connector repeatability Michael Wollensack METAS
23 Uncertainty Generators - oise and Linearity oise Uncorrelated for each measurement. Depends on the VA device noise floor and trace noise definition. Linearity R Correlated for each measurement. Depends on the VA device linearity definition. Figure: oise and linearity influences Michael Wollensack 3 METAS
24 Uncertainty Generators - Drift of Switch and Error Terms W E Drift Uncorrelated for each measurement. Depends on the VA device drift definition. + + W + V E + D + + Figure: Drift of switch and error terms Michael Wollensack 4 METAS
25 Uncertainty Generators - Cable and Connector Cable Uncorrelated for each new cable position. Depends on the cable stability definition. Connector Uncorrelated for each new connection. Depends on the connector repeatability definition. p Cable C p Conn. 0 0 R p, R p, C p Figure: Cable stability and connector repeatability -port p Michael Wollensack 5 METAS
26 Uncertainty Propagation The uncertainty generators are represented by R, V, D and C. Vna measurement model: M (i) = R (i) + [( W + V (i)) [( E + D (i)) [C (i) S (i)]]] Calibration and error correction are based on the above equation. Michael Wollensack 6 METAS
27 Uncertainty Propagation The uncertainty generators are represented by R, V, D and C. Vna measurement model: M (i) = R (i) + [( W + V (i)) [( E + D (i)) [C (i) S (i)]]] Calibration and error correction are based on the above equation. Linear uncertainty propagation is done with Metas.UncLib. The complexity is hidden from the user and from the VA Tools II programmer. Metas.UncLib takes care about correlations. Michael Wollensack 7 METAS
28 Visualization VA 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 8 METAS
29 Visualization VA 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: one hides the uncertainty. Standard shows the standard uncertainty (67% coverage factor, k = ). U95 shows the expanded uncertainty (95% coverage factor, k = ). Michael Wollensack 9 METAS
30 Visualization - Graph Figure: Data Explorer Graph Michael Wollensack 30 METAS
31 Visualization - Table Figure: Data Explorer Table Michael Wollensack 3 METAS
32 Visualization - Point Figure: Data Explorer Point Michael Wollensack 3 METAS
33 Visualization - Info Figure: Data Explorer Info Michael Wollensack 33 METAS
34 Results ew VA measurement model for a -port Vector etwork Analyzer. Definition of all influences that affect the measurements. Linear propagation of all uncertainties through the VA measurement model. Visualization of S-parameter data with uncertainties. Michael Wollensack 34 METAS
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