# [TowerTalk] S21 to Rp & Cp - Equivalent Circuit

Steve Hunt steve at karinya.net
Fri Jan 12 08:47:16 EST 2018

```I thought Maximo was trying to derive R and X from S21 measurements, not
S11 measurements - at least that's what his Subject line suggests.

Steve G3TXQ

> working in Octave (free version of Matlab), which is a bit easier than
> Excel
>
> >> s11mag = -29.6
> s11mag = -29.600
> >> s11ph = -77.1
> s11ph = -77.100
> >>
> >> gamma = 10^(s11mag/20)
> gamma =  0.033113
> >> gamma = gamma*complex(cos(s11ph/180*pi),sin(s11ph/180*pi))
> gamma =  0.0073925 - 0.0322774i
> >> z = 50* ( 1+gamma)/(1-gamma)
> z =  50.6383 -  3.2725i
>
> This is the series form, and close to 50 ohms, as expected (a return
> loss of 30dB is a good match)
> Convert to parallel form
>
> >> rs = real(z)
> rs =  50.638
> >> xs = imag(z)
> xs = -3.2725
> >> comterm = (rs/xs+xs/rs)
> comterm = -15.538
> >> rp=xs*comterm
> rp =  50.850
> >> xp = rs*comterm
> xp = -786.84
> >>
>
> Which matches *neither* of the other versions.
>
> And using a different way to convert series to parallel
> >> Q = xs/rs
> Q = -0.064626
>
> >> xp = xs*(Q^2+1)/Q^2
> xp = -786.84
> >> rp=rs/(Q^2+1)
> rp =  50.428
> >>
>
> Slightly different R - maybe it's a numerical precision thing Q^2 is
> small
>
>
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```