Electrical Engineering Asked by KJ7LNW on September 7, 2020
Given a simple loaded-line shunt-capacitor phase shifter, how can I calculate the phase shift and insertion loss at S21 caused by the shunt capacitor (varicap in my case, but for any cap) assuming I know the capacitance value C1? I can model this in Sonnet (or perhaps some circuit theory program) but I want to put the calculations in a spreadsheet and see if my simulated model (nearly) matches the mathematical model.
At microwaves101.com they hint that "the reflection coefficient from a shunt capacitor" might be used to calculate phase shift, in which case I don’t need susceptence: $ {displaystyle Gamma ={1-j2pi fCZ_0 over 1+j2pi fCZ_0} } $ . But once I have $Gamma$, how do I calculate shift?
and Wikipedia:Reflection Coefficient says that "if that load, $Z_L$ were measured not directly but through a transmission line, then […] its phase will have shifted according to
$ {displaystyle Gamma ‘=Gamma e^{-i,2phi }}$ where ϕ [is phase]"—but I think thats the S11 reflection phase not the S21 phase. Even if it is the S21 phase, how do I calculate $phi$?
If you can help me understand what is right, what is irrelevant, and what other information I need to answer the question and how to calculate phase shift and insertion loss then I would greatly appreciate it!
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