Measurement result format and its relation to calibration matrix math

Hello all,

I have a question concerning the format of complex numbers and the math behind calculating the error matrix to calculate calibrated measurements.

I am using the above relationship to relate my actual measured values to calibrated values. My three standards are a delay match, and two delay shorts. (The match is on a delay because this work is being done in rect waveguide and i don't want to mess up my match's face, so its connected to a 3" section.)

My question: I told the VNA to save real and imaginary. However, in the above picture, isn't Γ_delayshort = -1*e^jβl magnitude and phase? I have a feeling using mixed complex formats Γ_measured in RL and Γ_expected in mag/phase will not work, is this true?

I know i can easily convert the format of one, but this is for my edification.

Thanks,
Sami