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

Máximo EA1DDO_HK1H ea1ddo at hotmail.com
Mon Jan 8 13:09:41 EST 2018

```Just test them.

All are same results. Three different ways to get same results.

Thank you again

73, Maximo

________________________________
De: Máximo EA1DDO_HK1H <ea1ddo at hotmail.com>
Enviado: lunes, 8 de enero de 2018 17:51
Para: jimlux; towertalk at contesting.com
Asunto: Re: [TowerTalk] S21 to Rp & Cp - Equivalent Circuit

Hi Jim,

Great stuff.

I´ll try later on.

By the way, I´ve found a similar formula but I am not sure if it is same results as yours;

http://www.dicks-website.eu/compleximp/enindex.htm#serpar

We have the complex series circuit Z=RS+JXS
RS and XS are the series components.

With the next formulas we can find the values for the parallel components RP en XP.
Rp = (RS²+XS²)/RS

Xp = J(RS²+XS²)/XS

And one more formula;

http://www.w5big.com/AIM_122212.htm

If the equivalent parallel load circuit is needed:

Rparallel=Zmag*Zmag/Rseries

Xparallel=Zmag*Zmag/Xseries

I guess all of them are same, just different ways to reach same point.

Thank you very much

73, Maximo

________________________________
De: TowerTalk <towertalk-bounces at contesting.com> en nombre de jimlux <jimlux at earthlink.net>
Enviado: domingo, 7 de enero de 2018 22:01
Para: towertalk at contesting.com
Asunto: Re: [TowerTalk] S21 to Rp & Cp - Equivalent Circuit

On 1/7/18 12:59 PM, Máximo EA1DDO_HK1H wrote:
> Hi all,
>
>
> I know there is a formula to get Rp and Cp from S21 or S11 data (LogMag and Phase, or R & I).
Convert S11 from logmag, angle to complex

Z = Z0 * ((1+gamma)/(1-gamma))
in Excel
gamma =
imcomplex(10^(S11mag/20)*cos(s11phase*pi()/180),10^(S11mag/20)*sin(s11phase*pi()/180))

Z= immult(50,imdivide(imsum(1,gamma),imsub(1,gamma))

that gives you R+jX series form R and C/L

You then have to convert to the parallel form

Rp = Xs*(Rs/Xs+Xs/Rs)
Xp = Rs*(Rs/Xs+Xs/Rs)

The Rs/Xs+Xs/Rs is common to both, so in excel, adding a column for that
makes it easier.

>
> Anyone know that formula?
>
> It is to use it in Excel and get Rp and Cp from the VNA´s exported data.
>
>
> Thank you very much
>
>
> 73, Maximo
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