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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: jimlux <jimlux@earthlink.net>
Date: Fri, 12 Jan 2018 05:38:39 -0800
List-post: <mailto:towertalk@contesting.com>
On 1/11/18 10:48 AM, jimlux wrote:
On 1/11/18 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




working in Octave (free version of Matlab), which is a bit easier than Excel

>> s11mag = -29.6
s11mag = -29.600
>> s11ph = -77.1
s11ph = -77.100
>>
>> gamma = 10^(s11mag/20)
gamma =  0.033113
>> gamma = gamma*complex(cos(s11ph/180*pi),sin(s11ph/180*pi))
gamma =  0.0073925 - 0.0322774i
>> z = 50* ( 1+gamma)/(1-gamma)
z =  50.6383 -  3.2725i

This is the series form, and close to 50 ohms, as expected (a return loss of 30dB is a good match)
Convert to parallel form

>> rs = real(z)
rs =  50.638
>> xs = imag(z)
xs = -3.2725
>> comterm = (rs/xs+xs/rs)
comterm = -15.538
>> rp=xs*comterm
rp =  50.850
>> xp = rs*comterm
xp = -786.84
>>

Which matches *neither* of the other versions.

And using a different way to convert series to parallel
>> Q = xs/rs
Q = -0.064626

>> xp = xs*(Q^2+1)/Q^2
xp = -786.84
>> rp=rs/(Q^2+1)
rp =  50.428
>>

Slightly different R - maybe it's a numerical precision thing Q^2 is small


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