% RF small signal amplifier design, using equations from "RF Cicruit
% Design" by Chris Bowick
+1;
+
+% 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. Note Xp and Xs
+% must be implemented as opposite sign, ie one a inductor, one
+% a capacitor (your choice).
+%
+% /--Xs--+---\
+% | | |
+% Rlow Xp Rhigh
+% | | |
+% \------+---/
+%
+
+function [Xs Xp] = z_match(Rlow, Rhigh)
+ assert(Rlow < Rhigh, "Rlow must be < Rhigh");
+ Q = sqrt(Rhigh/Rlow -1);
+ Xs = Q*Rlow;
+ Xp = Rhigh/Q;
+endfunction
+
+
+% Design an air core inductor, Example 1-5 "RF Circuit Design"
+
+function Nturns = design_inductor(L_uH, diameter_mm)
+ Nturns = sqrt(29*L_uH/(0.394*(diameter_mm*0.1/2)));
+endfunction
+
more off;
+Ic = 0.014;
+
% 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);
+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
D2 = abs(S22)^2-abs(Ds)^2;
C2 = S22 - Ds*conj(S11);
-GdB = 20; Glin = 10^(GdB/10); % lets shoot for 20dB gain
+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
+% 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
-gammaL = 0.8 -j*0.4;
+ Pout = 0.01;
+ Irms = 0.002;
+ Zo = Pout/(Irms*Irms);
+ zo = Zo/50;
+ [magL,angleL] = ztog(zo);
+ gammaL = magL*exp(j*angleL*pi/180);
-% Caclulate gammaS and make sure it's stable by visual inspection
-% compared to stability circle.
+ % calculate gammaS
+
+ gammaS = conj(S11 + ((S12*S21*gammaL)/(1 - (gammaL*S22))));
+
+end
-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
+% 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
[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);
+ Xp_match = -Xp - imag(Zip);
% Now convert to real component values
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(" 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
+ % Now Z match for output -------------------------------------
Lo = -imag(Zo)/w;
Lo_turns = design_inductor(Lo*1E6, diameter_mm);
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
-% Helper functions -------------------------------------------------
+if Ic == 0.014
+ printf("Transducer gain: %3.1f dB\n", 10*log10(Gt));
-% convert a parallel R/X to a series R/X
+ % Lets design the z match for the input ------------------------------
-function Zs = zp_to_zs(Zp)
- Xp = j*imag(Zp); Rp = real(Zp);
- Zs = Xp*Rp/(Xp+Rp);
-endfunction
+ % put input impedance in parallel form
+ Zip = zs_to_zp(Zi);
-% convert a series R/X to a parallel R/X
+ % first match real part of impedance
-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
+ 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);
-% Design a Z match network with a parallel and series reactance
-% to match between a low and high resistance:
-%
-% /--Xs--+---\
-% | | |
-% Rlow Xp Rhigh
-% | | |
-% \------+---/
-%
+ % Now convert to real component values
-function [Xs Xp] = z_match(Rlow, Rhigh)
- Q = sqrt(Rhigh/Rlow -1);
- Xs = Q*Rlow;
- Xp = -Rhigh/Q;
-endfunction
+ 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 an air core inductor, Example 1-5 "RF Circuit Design"
+ % 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
-function Nturns = design_inductor(L_uH, diameter_mm)
- Nturns = sqrt(29*L_uH/(0.394*(diameter_mm*0.1/2)));
-endfunction
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