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

Jim Brown jim at audiosystemsgroup.com
Tue Jan 9 12:53:12 EST 2018

```This, of course, is classic circuit analysis that we learned in our
first EE year. If, however, you have a plot of data vs frequency that
you can identify as a parallel resonant circuit, there's a relatively
easy way to find Rp, Lp, and Cp. Rp is the peak value of Z at resonance.
Lp is the value that yields Z far below resonance, and Cp is the value
that resonates with Lp.  Graphical techniques like this, by the way,
were taught in another course in that first year of EE.

When I was doing the point by measurements on the first ferrite chokes
using a signal generator and voltmeter, I put the raw data into a
Quattro Pro spreadsheet, computed Z magnitude, and plotted it. To find
the equivalent circuit, I used the method above, plotted the result on
the same axes as the raw data, and tweaked the three values so that the
plot of the equivalent circuit matched the measured data. These tweaks
are necessary because mu' and mu'' vary with frequency. Mu' is the value
that defines the series inductance, mu'' is the value that defines the
series equivalent resistance.

73, Jim K9YC

On 1/7/2018 2:01 PM, jimlux wrote:
> 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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```