Hi Jeff;
I agree that the proof is certainly terse as you say. Likely an additional and serendipitous artifact of the elegance of the approach. :-)
The use of ideal -1, 0, and +1 standards in the proof simply serve to define them as ideal. Keep in mind also that all variables are complex values; hence the ideal standards all have imaginary components of zero. While these values can, and in many, if not most, cases will be defined as ideal in practice, it is the objective of calibration to normalize the measured standards to those boundaries. They are and will be set to the value and accuracy defined by the user based on their knowledge of the test standards used in their application, and the accuracy to which they wish to have them defined whether through published manufacturing tolerance specifications, or through elaborate laboratory characterization and comparison to certified industry reference standards.
The defined or "given" values as well as the computed result are upper case, and all lower case variables represent raw data measurements, with G being equal to the corrected reflection coefficient of a DUT exhibiting a measured reflection coefficient of g.
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73
Gary, N3GO
