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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: Steve Hunt <steve@karinya.net>
Date: Fri, 12 Jan 2018 13:47:16 +0000
List-post: <mailto:towertalk@contesting.com>
I thought Maximo was trying to derive R and X from S21 measurements, not S11 measurements - at least that's what his Subject line suggests.

Steve G3TXQ


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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