[TowerTalk] S11 to R+jX

[jimlux]

here's some Matlab/Octave code to calculate the series R+jX from S11 for 
a range of phases, with a constant return loss..
(-30dB as written), and the tabulated values for -20dB and -30dB.

(Now to convert to parallel form)


S11mag = -30;   % dB
S11phase = [-180:10:180];

gamma = 10^(S11mag/20)*complex(cos(S11phase/180*pi),sin(S11phase/180*pi));

Z0 = 50;

Z = Z0 * (1+gamma)./(1-gamma);

figure(1)
plot(S11phase,real(Z),'r',S11phase,imag(Z),'g')
legend('real','imag')
xlabel('degrees')
ylabel('Ohms')
grid on
title('|S11| = -30dB')

fprintf('deg  R    X\n');
for i=1:length(S11phase)
   fprintf('%5d %6.2f %6.2f\n',S11phase(i),real(Z(i)),imag(Z(i)));
end

For -20dB
deg  R    X
  -180  40.91  -0.00
  -170  41.01  -1.44
  -160  41.32  -2.86
  -150  41.84  -4.23
  -140  42.55  -5.53
  -130  43.48  -6.73
  -120  44.59  -7.80
  -110  45.90  -8.71
  -100  47.38  -9.43
   -90  49.01  -9.90
   -80  50.76 -10.10
   -70  52.57  -9.98
   -60  54.40  -9.52
   -50  56.16  -8.69
   -40  57.77  -7.50
   -30  59.15  -5.98
   -20  60.21  -4.16
   -10  60.88  -2.14
     0  61.11   0.00
    10  60.88   2.14
    20  60.21   4.16
    30  59.15   5.98
    40  57.77   7.50
    50  56.16   8.69
    60  54.40   9.52
    70  52.57   9.98
    80  50.76  10.10
    90  49.01   9.90
   100  47.38   9.43
   110  45.90   8.71
   120  44.59   7.80
   130  43.48   6.73
   140  42.55   5.53
   150  41.84   4.23
   160  41.32   2.86
   170  41.01   1.44
   180  40.91   0.00

For -30dB

deg  R    X
  -180  46.93  -0.00
  -170  46.98  -0.52
  -160  47.10  -1.02
  -150  47.31  -1.50
  -140  47.60  -1.94
  -130  47.95  -2.33
  -120  48.37  -2.65
  -110  48.84  -2.91
  -100  49.36  -3.08
   -90  49.90  -3.16
   -80  50.45  -3.15
   -70  51.00  -3.03
   -60  51.53  -2.83
   -50  52.01  -2.52
   -40  52.44  -2.13
   -30  52.79  -1.67
   -20  53.05  -1.15
   -10  53.21  -0.58
     0  53.27   0.00
    10  53.21   0.58
    20  53.05   1.15
    30  52.79   1.67
    40  52.44   2.13
    50  52.01   2.52
    60  51.53   2.83
    70  51.00   3.03
    80  50.45   3.15
    90  49.90   3.16
   100  49.36   3.08
   110  48.84   2.91
   120  48.37   2.65
   130  47.95   2.33
   140  47.60   1.94
   150  47.31   1.50
   160  47.10   1.02
   170  46.98   0.52
   180  46.93   0.00