# [TowerTalk] S11 to R+jX

Fri Jan 12 11:28:09 EST 2018

```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
```