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

Máximo EA1DDO_HK1H ea1ddo at hotmail.com
Thu Jan 11 13:01:37 EST 2018

```Hi Jim, Steve, all,

Playing with those formulas I´ve got an inconsistency.

To get R and jX from LogMag and Phase I can use two different formulas, one from Steve and one from Jim, but the results are not same, so I don´t know where the mistake is.

Example from Excel;

LogMag -29.601925

Phase  -77.10851

Steve´s formula:

Rx = (100*10^(-LogMag/20))/(SQRT(1+(TAN(Phase/57.29578))^2))-100  =  573.916

X = -(Rx+100)*TAN(Phase/57.29578)  =  2944.484

Jim´s formula:

R = COMPLEX(10^((LogMag/20)*(COS((Phase*PI())/180))),10^((LogMag/20)*(SIN((Phase*PI())/180))))

then Rx+jX = IMPRODUCT(50,IMDIV(IMSUM(1,R),IMSUB(1,R)))  =  -49.930  +3.606

As you can see, 573 is not same as -49 OHm

And 2944 is not 3.606

Anyone know where the error is?

Thank you

73, Maximo

________________________________
De: TowerTalk <towertalk-bounces at contesting.com> en nombre de Jim Brown <jim at audiosystemsgroup.com>
Enviado: martes, 9 de enero de 2018 17:53
Para: towertalk at contesting.com
Asunto: Re: [TowerTalk] S21 to Rp & Cp - Equivalent Circuit

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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>>
>>
>>
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>>
>
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