first pass at designing RF anps with S params

git-svn-id: https://svn.code.sf.net/p/freetel/code@2495 01035d8c-6547-0410-b346-abe4f91aad63

diff --git a/codec2-dev/octave/s_param_rf.m b/codec2-dev/octave/s_param_rf.m
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+% s_param_rf.m
+%
+% David Rowe Nov 2015
+%
+% RF small signal amplifier design, using equations from "RF Cicruit
+% Design" by Chris Bowick
+
+more off;
+
+% BRF92 VCE=5V Ic=5mA 100MHz
+ 
+S11 = 0.727*exp(j*(-43)*pi/180);
+S12 = 0.028*exp(j*(69.6)*pi/180);
+S21 = 12.49*exp(j*(147)*pi/180);
+S22 = 0.891*exp(j*(-16)*pi/180);
+
+% Stability
+
+Ds = S11*S22-S12*S21;
+Knum = 1 + abs(Ds)^2 - abs(S11)^2 - abs(S22)^2;
+Kden = 2*abs(S21)*abs(S12);
+K = Knum/Kden                                    % If > 1 unconditionally stable
+                                                 % If < 1 panic
+figure(1);
+clf
+scCreate;
+
+if K < 1
+  C1 = S11 - Ds*conj(S22);
+  C2 = S22 - Ds*conj(S11);
+  rs1 = conj(C1)/(abs(S11)^2-abs(Ds)^2);           % centre of input stability circle
+  ps1 = abs(S12*S21/(abs(S11)^2-abs(Ds)^2));       % radius of input stability circle
+  rs2 = conj(C2)/(abs(S22)^2-abs(Ds)^2);           % centre of input stability circle
+  ps2 = abs(S12*S21/(abs(S22)^2-abs(Ds)^2));       % radius of input stability circle
+
+  s(1,1)=S11; s(1,2)=S12; s(2,1)=S21; s(2,2)=S22;
+  plotStabilityCircles(s)
+end
+
+% Gain circle
+
+D2 = abs(S22)^2-abs(Ds)^2;
+C2 = S22 - Ds*conj(S11);
+GdB = 20; Glin = 10^(GdB/10);                     % lets shoot for 20dB gain
+G = Glin/(abs(S21)^2);
+r0 = G*conj(C2)/(1+D2*G);                                             % centre of gain circle
+p0 = sqrt(1 - 2*K*abs(S12*S21)*G + (abs(S12*S21)^2)*(G^2))/(1+D2*G);  % radius of gain circle
+
+scAddCircle(abs(r0),angle(r0)*180/pi,p0,'g')
+printf("Green is the %3.1f dB constant gain circle for gammaL\n",GdB);
+
+% Choose a gammaL on the gain circle
+
+gammaL = 0.8 -j*0.4;
+
+% Caclulate gammaS and make sure it's stable by visual inspection
+% compared to stability circle.
+
+gammaS = conj(S11 + ((S12*S21*gammaL)/(1 - (gammaL*S22))));
+[zo Zo] = gtoz(abs(gammaL), angle(gammaL)*180/pi,50);
+[zi Zi] = gtoz(abs(gammaS), angle(gammaS)*180/pi,50);
+scAddPoint(zi);
+scAddPoint(zo);
+
+% Lets design the z match for the input
+
+  % put input impedance in parallel form
+
+  Zip = zs_to_zp(Zi);
+
+  % first match real part of impedance
+
+  Rs = 50; Rl = real(Zip);
+  [Xs Xp] = z_match(Rs,Rl);
+  
+  % Modify Xp so transistor input sees conjugate match to Zi
+
+  Xp_match = Xp - imag(Zip);
+
+  % Now convert to real component values
+
+  w = 2*pi*150E6;
+  Ls = Xs/w;
+  Cp = 1/(w*(-Xp_match));
+
+  printf("Input: Zi = %3.1f + %3.1fj ohms\n", real(Zi), imag(Zi));
+  printf("       In parallel form Rp = %3.1f Xp = %3.1fj ohms\n", real(Zip), imag(Zip));
+  printf("       So for a conjugate match transistor input wants to see:\n         Rp = %3.1f Xp = %3.1fj ohms\n", real(Zip), -imag(Zip));
+  printf("       Rs = %3.1f to Rl = %3.1f ohm matching network Xs = %3.1fj Xp = %3.1fj\n", Rs, Rl, Xs, Xp);
+  printf("       with conj match to Zi Xs = %3.1fj Xp = %3.1fj\n", Xs, Xp_match);
+  printf("       matching components Ls = %5.3f uH Cp = %4.1f pF\n", Ls*1E6, Cp*1E12);
+
+% Now Z match for output
+
+  Lo = -imag(Zo)/w;
+  printf("Output: Zo = %3.1f + %3.1fj ohms\n", real(Zo), imag(Zo));
+  printf("        So for a conjugate match transistor output wants to see:\n          Rl = %3.1f Xl = %3.1fj ohms\n", real(Zo), -imag(Zo));
+  printf("        Which is a series inductor Lo = %5.3f uH\n", Lo*1E6);
+
+% Helper functions -------------------------------------------------
+
+% convert a parallel R/X to a series R/X
+
+function Zs = zp_to_zs(Zp)
+  Xp = j*imag(Zp); Rp = real(Zp);
+  Zs = Xp*Rp/(Xp+Rp);
+endfunction
+
+% convert a series R/X to a parallel R/X
+
+function Zp = zs_to_zp(Zs)
+  Xs = imag(Zs); Rs = real(Zs);
+  Q = Xs/Rs;       
+  Rp = (Q*Q+1)*Rs;
+  Xp = Rp/Q;
+  Zp = Rp + j*Xp;
+endfunction
+
+% Design a Z match network with a parallel and series reactance
+% to match between a low and high resistance:
+%
+%  /--Xs--+---\
+%  |      |   |
+% Rlow   Xp  Rhigh
+%  |      |   |
+%  \------+---/
+%        
+
+function [Xs Xp] = z_match(Rlow, Rhigh)
+  Q = sqrt(Rhigh/Rlow -1);
+  Xs = Q*Rlow;
+  Xp = -Rhigh/Q; 
+endfunction
+