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Re: [TowerTalk] S21 to Rp & Cp - Equivalent Circuit

To: towertalk@contesting.com
Subject: Re: [TowerTalk] S21 to Rp & Cp - Equivalent Circuit
From: Jim Brown <jim@audiosystemsgroup.com>
Reply-to: jim@audiosystemsgroup.com
Date: Tue, 9 Jan 2018 09:53:12 -0800
List-post: <mailto:towertalk@contesting.com>
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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