You're over-Excelling the problem, Maximo. Best to go back to
fundamentals. A simple parallel resonant circuit looks like an inductor
below resonance and a capacitor above resonance. Go far enough away from
resonance and the other terms become increasing insignificant.
To find Lp, take one or more measured Z values well down in amplitude
and frequency from the resonant peak (say 1/20 of both) and use the
simple equation for X = 2 pi F L Far below resonance, Z becomes
approximately equal to XL, so use the measured value for Z at some low
frequency and solve that equation for L. Do that at 2-3 frequencies,
and you should get values for Lp that are quite close to each other.
73, Jim K9YC
On 1/11/2018 10:01 AM, Máximo EA1DDO_HK1H wrote:
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@contesting.com> en nombre de Jim Brown
<jim@audiosystemsgroup.com>
Enviado: martes, 9 de enero de 2018 17:53
Para: towertalk@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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