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

[jimlux <jimlux@earthlink.net>]

On 1/12/18 5:47 AM, Steve Hunt wrote:
> 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
I'd have to go back and look - maybe that's the hiccup
I'm still curious about the Excel/Octave variance though.



> > 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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