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

Fri Jan 12 09:24:43 EST 2018

```On 1/12/18 5:47 AM, Steve Hunt wrote:
> 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
>

I'd have to go back and look - maybe that's the hiccup
I'm still curious about the Excel/Octave variance though.

>
>> 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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