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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
(
    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




(


                                                            www.HPARCHIVE.com
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




                                           WWWHPARC~IVEcom
.
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 .



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