Building Complex Differential Error Regions

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Antennas Research Group RGA at DUTh Democritus
University of Thrace
Nikolitsa Yannopoulou and Petros Zimourtopoulos
Building Complex Differential Error Regions
30th ANAMET Club Meeting 24/10/2008
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Error Models
One-Port
Two-Port
? Reflection Coefficient m Measurement of ?
D Directivity M Source Match R Frequency
Response
L Load Match T Transmission Tracking X
Isolation or Crosstalk m Measurement of S
One-Port
Two-Port
1 Unknown 3 Errors
4 Unknowns 12 Errors
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Typical Differential Errors
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Enumeration
Full One-Port Calibration 4 Measurements gt 4
Inaccuracies . 3 Standard Loads gt 3
Uncertainties .
7 Complex Variables gt 7 Complex Differential
Errors
14 Real Parameters14 Real Differential Errors
Full Two-Port Calibration 16 Measurements gt 16
Inaccuracies . 6 Standard Loads gt 6
Uncertainties
. 22 Complex Variables gt 22 Complex
Differential Errors
44 Real Parameters 44 Real Differential Errors
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Differential Error Regions
If z measurement or standard
load, dz inaccuracy or uncertainty, W
partial derivative of ? or S, then Wdz
partial differential error of ? or S,
represents a z-DER Differential Error Region on
the complex plane.
We discriminate 3 basic DERs within the unit
circle
Orthogonal i-DER at any Interior
point
Half-Orthogonal c-DER at any Contour point
Circular o-DER at the Origin
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Example - Building DERs - Step 1/4
c-DER goes to 4 i-DER vertices
c-DER overlays i-DER
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Example - Building DERs - Step 2/4
DER with 8 vertices
i-DER c-DER
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Example - Building DERs - Step 3/4
o-DER overlays DER
o-DER goes to 8 DER vertices Each circle gives
2 vertices
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Example - Building DERs - Step 4/4
DER contour with 8 line segments and 8 circular
arcs
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Example - Real Uncertainties Estimation
Polar and Rectangular Uncertainties
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Typical DERs
Any DER is built from a number of basic DERs
General Calibration
DER contour ?-DER 7
Orthogonals x 4 vertices gt 28
vertices S-DER 22 Orthogonals x 4 vertices
gt 88 vertices SLO/SLOdT Calibration
DER
contour ?-DER SLO 6 Orthogonals 1
Circle gt 48 vertices S-DER SLOdT 20
Orthogonals 2 Circles gt 160 vertices
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Conclusions
It is impossible to analytically estimate real
uncertainties directly from complex
differential errors. Real rectangular
uncertainties are estimated from the orthogonal
circumscribed about the complex DER. Real
polar uncertainties are estimated from the
annular sector circumscribed about the complex
DER. The proposed method of uncertainty
estimation, by building complex DERs, can be
applied to any VNA calibration technique.
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Applications
SLO or SLOdT Calibration
Antenna SWR
Antenna Amplitude Pattern
Antenna Impedance
Antenna Phase Pattern
Two Antennas S-Matrix
T-Network Z-Matrix
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30th ANAMET Club Meeting 24/10/2008
. Building Complex Differential Error
Regions . References, Computer
Animations, Updated Material www.antennas.gr/anam
et/30/
Thank you for your attention
Antennas Research Group RGA at DUTh Democritus
University of Thrace