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APPENDIX
TO
AN ANALYSIS
OF
VECTOR MEASUREMENT
ACCURACY ENHANCEMENT
TECHNIQUES
DOUG RYTTING
NETWORK MEASUREMENTS DIVISION
1400 FOUNTAIN GROVE PARKWAY
SANTA ROSA, CALIFORNIA 95401
RF L Microwave
Measurement
Symposium
And
Exhibition
FIJP'I
HEWLETT
a:~ PACKARD
www.HPARCHIVE.com
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Appendix I: One-Port Accuracy Enhancement
MEASURED DATA (rM)
~~ I UNKNOWN
(Sj I X X I
ONE-PORT
IMPER~ECT
SWEEP REFLECTOMETER
OSCILLATOR
MEASURED DATA (rM)
~~
-=-b:-I :D~~:R~
UNKNOWN
(
(Sj-+I-...::..X....::pc-E-R-FE-.:;:...-T-=------+-I rA I
ONE-PORT
SWEEP REFLECTOMETER 4 ERROR
OSCILLATOR TERMS
Figure 1
One-Port Measurement System Block-Diagram
The equations for the error adapter from Fig. 1 are
The equation for the unknown one-port is
(
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Substitutions (3) into (1) and (2) yields
(4) bo = eaoa o + e01 f A 1
b
(5) b
1 = e 10 aO + e 11 f Ab1
Solving for b1 from (5)
(6) b = e 10 a
1
1-e ll f A
o
Substituting (6) into (4)
(7) bo = (e oo + e 1Oe 01 fA ) ao
l-ellfA
b
Defi ne r 6 0
m= a:-
a
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.
f
Appendix II: Circle Fitting Procedure
A modified least square error criterion is
N 2 2 2 2
(1) I
. 1
[(x.-A)
1
+ (y .