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% s_param_rf.m
%
% David Rowe Nov 2015
%
% Working for small signal VHF amplifier design using
% S-param techniques from "RF Circuit Design" by Chris Bowick
rfdesign; % library of helped functions
more off;
Ic = 0.014;
% BRF92 VCE=5V Ic=5mA 100MHz
if Ic == 0.005
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);
end
% BRF92 VCE=10V Ic=14mA 100MHz
if Ic == 0.02
S11 = 0.548*exp(j*(-56.8)*pi/180);
S12 = 0.020*exp(j*(67.8)*pi/180);
S21 = 20.43*exp(j*(133.7)*pi/180);
S22 = 0.796*exp(j*(-18.5)*pi/180);
end
% 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);
% Note different design procedures for different operating points
if Ic == 0.005
% Choose a gammaL on the gain circle
gammaL = 0.8 - 0.4*j;
% Caclulate gammaS and make sure it's stable by visual inspection
% compared to stability circle.
gammaS = conj(S11 + ((S12*S21*gammaL)/(1 - (gammaL*S22))));
end
if Ic == 0.014
% lets set zo (normalised Zo) based on Pout and get gammaL from that
Pout = 0.01;
Irms = 0.002;
Zo = Pout/(Irms*Irms);
zo = Zo/50;
[magL,angleL] = ztog(zo);
gammaL = magL*exp(j*angleL*pi/180);
% calculate gammaS
gammaS = conj(S11 + ((S12*S21*gammaL)/(1 - (gammaL*S22))));
end
[zo Zo] = gtoz(abs(gammaL), angle(gammaL)*180/pi,50);
[zi Zi] = gtoz(abs(gammaS), angle(gammaS)*180/pi,50);
scAddPoint(zi);
scAddPoint(zo);
% Transducer gain
Gt_num = (abs(S21)^2)*(1-abs(gammaS)^2)*(1-abs(gammaL)^2);
Gt_den = abs((1-S11*gammaS)*(1-S22*gammaL) - S12*S21*gammaL*gammaS)^2;
Gt = Gt_num/Gt_den;
if Ic == 0.005
% 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
% Lets make Xp a capacitor, so negative sign
Xp_match = -Xp - imag(Zip);
% Now convert to real component values
w = 2*pi*150E6;
Ls = Xs/w; diameter_mm = 6.25;
Ls_turns = design_inductor(Ls*1E6, diameter_mm);
Cp = 1/(w*(-Xp_match));
printf("Transducer gain: %3.1f dB\n", 10*log10(Gt));
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);
printf(" Ls can be made from %3.1f turns on a %4.2f mm diameter air core\n", Ls_turns, diameter_mm);
% Now Z match for output -------------------------------------
Lo = -imag(Zo)/w;
Lo_turns = design_inductor(Lo*1E6, diameter_mm);
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);
printf(" Lo can be made from %3.1f turns on a %4.2f mm diameter air core\n", Lo_turns, diameter_mm);
end
if Ic == 0.014
printf("Transducer gain: %3.1f dB\n", 10*log10(Gt));
% 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(Rl,Rs);
% Lets make Xs a capacitir to block DC, so Xp is an inductor.
% Modify Xs so transistor input sees conjugate match to Zi. Xs is a
% capacitor, so reactance is negative
Xs_match = -Xs - imag(Zip);
% Now convert to real component values
w = 2*pi*150E6; diameter_mm = 6.25;
Li = Xp/w;
Li_turns = design_inductor(Li*1E6, diameter_mm);
Ci = 1/(w*(-Xs_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 Xs a capacitor, and Xp and inductor Xs = %3.1fj Xp = %3.1fj\n", -Xs, Xp);
printf(" With a conj match to Zi Xs = %3.1fj Xp = %3.1fj\n", Xs_match, Xp);
printf(" matching components Li = %5.3f uH Ci = %4.1f pF\n", Li*1E6, Ci*1E12);
printf(" Li can be made from %3.1f turns on a %4.2f mm diameter air core\n", Li_turns, diameter_mm);
% Design output Z match ----------------------------------------------
Rs = real(Zo); Rl = 50;
[Xs Xp] = z_match(Rl,Rs);
% Lets make XP an inductor so it can double as a RF choke, and Xp as
% a capacitor will give us a convenient DC block
w = 2*pi*150E6; diameter_mm = 6.25;
Lo = Xp/w; Lo_turns = design_inductor(Lo*1E6, diameter_mm);
Co = 1/(w*Xs);
printf("Output: Zo = %3.1f + %3.1fj ohms\n", real(Zo), imag(Zo));
printf(" matching network Xp = %3.1f X = %3.1f ohms\n", Xp, Xs);
printf(" which is parallel Lo = %5.3f uH and series Co = %4.1f pF\n", Lo*1E6, Co*1E12);
printf(" Lo can be made from %3.1f turns on a %4.2f mm diameter air core\n", Lo_turns, diameter_mm);
end
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