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

Fri Jan 12 11:13:06 EST 2018

```On 1/12/18 7:50 AM, Máximo EA1DDO_HK1H wrote:
>
> Is a different formula to convert LogMag(dB) & Phase from S11 than from S21?
>

No, it's the same. But calculating Z from S11 (a one port measurement)
is different than calculating it from S21 (a two port measurement) - if
you've got the Z in series between the ports it's different than if you
have something like the Z and a resistor in series, or something like that.

> ________________________________
> De: TowerTalk <towertalk-bounces at contesting.com> en nombre de Steve Hunt <steve at karinya.net>
> Enviado: viernes, 12 de enero de 2018 13:47
> Para: towertalk at contesting.com
> Asunto: Re: [TowerTalk] S21 to Rp & Cp - Equivalent Circuit
>
> 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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