Calibration
My career began when calibration for a gain measurement meant plotting a reference line from a "Thru" measurement on a pen and ink XY recorder before attaching the device to be measured. Using a grease pencil on an oscilloscope display was not unheard of. It was a great day in the late '70s when we were given the data normalizer from Hewlett-Packard, the HP 8750A Storage Normalizer as in the above image from ebay. It stored the trace shown on a Scalar Analyzer's display. Select "Store Input" to save the trace to Memory, then select "Input minus Memory" when the Device Under Test is being measured. It was great. See it in the article on p. 17 of the HP Journal for January 1978 here . One of the authors is Mark Roos, founder of Roos Instruments.
Calibration for the complex impedance ( R + jX ) of a one-port device measured with a Vector Network Analyzer (or high frequency LCR Meter) requires more than the simple subtraction used in the Scalar Analyzer. The measurement of 3 known impedances, traditionally a Short, an Open, and a Load, provide what is needed. Year after year, calibrating with the Short-Open-Load, it seemed to me it must just involve solving a system of 3 equations and 3 unknowns. In retirement, I satisfied myself with a derivation. It is only slightly complicated, in that the 3 linear equations are not the linear equations we learned in high school, but the bi-linear equations of complex variables. The steps are essentially the same.
I have not seen this approach taken elsewhere. It makes a nice pedagogical example.
Before jumping into the Short-Open-Load problem, two similar applications provide a review of for solving a system of 3 equations by the Method of Determinants and Cramer's Rule.
The third application details the analogous solution for the Short-Open-Load application.
The last presentation has a QucsStudio simulation of a hypothetical calibration. Note the Short, Open, and Load "standards" do not need to be ideal, but only of a known (or assumed) impedance.
