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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