smith_4.m

%% Using RF Toolbox Smith Chart for Impedance Matching.
%  Copywrite 2006-2010 The Mathworks, Inc.
%  Dick Benson
%  Topology:  Tapped C Match    source-> shunt L -> series C ->shunt C -> load
   clear all; close all; clc;
  
   f     = 14.1e6;       % frequency
   Zl    = 20 + j*10;    % given load
   Zin   = 500 + j*200;  % desired input Z
   Zo    = 50;           % characteristic impedance of system
   Q     = 8;            % desired matching circuitry Q

%% Normalize Impedances and compute reflection coefficients pl and pin
zl =  Zl/Zo;
pl = (zl-1)/(zl+1);
zin = Zin/Zo;
pin = (zin-1)/(zin+1);

%% Draw smith chart and mark normalized Zin and Zl (pin and pl)

[hls,hs]=smithchart;
set(hls,'Type','zy','Color',[1 0 0],'SubColor',[0 1 0],'SubLineWidth',2);  
set(gcf,'Name','Tapped C Match')
hold on
plot(real(pin), imag(pin),'o','MarkerSize',8,'markerfacecolor',[0 1  0]);
text(real(pin)+.05, imag(pin)+.05, 'z_{in}', 'FontSize', 12, 'FontUnits', 'normalized')
plot(real(pl), imag(pl),'o','MarkerSize',8,'markerfacecolor',[0 1  0]);
text(real(pl)+.05, imag(pl)+.05, 'z_{l}', 'FontSize', 12, 'FontUnits', 'normalized')

%% Plot Constant Q Contours 
%  keep X/R a constant
x = -5:.01:5;
z = Q*j*x + abs(x);
pcurveQ = (z-1)./(z+1);
hlQ     = plot(real(pcurveQ),imag(pcurveQ),'-','linewidth',2,'color',[1 0 0]);


%% Work back from Zin adding suseptance due to shunt L along constant
% conductance curve
ydelta  = (0:0.1:2)*j;
y       = 1/zin + ydelta;
pcurveL = (1-y)./(y+1);
hl3=plot(real(pcurveL),imag(pcurveL),'-','linewidth',2, 'color',[0 1 1]);

%%   Find intersection with Q curve
[xint1,yint1]=curveintersect(hl3,hlQ);
h = plot(xint1,yint1,'o','color',[1 0 0]);
set(h,'markerfacecolor',[1 0 0]);
pint1 = xint1+j*yint1;
zint1 = (pint1+1)/(1-pint1);   % map reflection coefficient back to impedance

%% Add -reactance from series C to follow constant resistance curve  
zdelta        = (0:0.01:2)*j; 
z             = zint1+zdelta;
pcurveCseries = (z-1)./(z+1);
hl2=plot(real(pcurveCseries),imag(pcurveCseries),'-','linewidth',2,'color',[0 1 0]); % green


%% Follow constant conductance curve from Zl by changing susceptance 
%  Parallel Cap adds susceptance
ydelta  = (0:0.1:8)*j;
y       = 1/zl + ydelta;
pcurveCl = (1-y)./(y+1);
hl1=plot(real(pcurveCl),imag(pcurveCl),'-','linewidth',2);


%% Find intersection of series capacitance and suseptance
[xint2,yint2]=curveintersect(hl2,hl1);
h = plot(xint2,yint2,'o','color',[1 0 0]);
set(h,'markerfacecolor',[1 0 0]);
pint2 = xint2 + j*yint2;      % 
zint2 = (pint2+1)/(1-pint2);   % map reflection coefficient back to impedance

%% Determine the element values 

yL   =  -imag(1/zin -1/zint1);   % shunt L 
L_nH = (Zo*(1/yL))/(2*pi*f)*1e9


zCseries         =  imag(zint2-zint1);  % series C
Cseries_pF = ((1/zCseries)*(1/Zo)/(2*pi*f))*1e12 


yC   = imag(1/zint2-1/zl);           % shunt C
Cl_pF = (yC*(1/Zo)/(2*pi*f))*1e12   


%% Use RF toolbox functions for a sanity check on the matching network

fs=f;
hL = rfckt.shuntrlc('R',inf,'L',1e-9*L_nH,'C',0);
hCseries = rfckt.seriesrlc('R',0,'L',0,'C',1e-12*Cseries_pF);
hCl  = rfckt.shuntrlc('R',inf,'L',inf,'C',1e-12*Cl_pF);
hnl= rfckt.cascade('Ckts',{hL,hCseries,hCl});
%                 Zl   Zs  Zo
analyze(hnl,fs,   Zl,  50, 50);     
h  =  smith(hnl,'GammaIn');
set(h,'Marker','o','markersize',8,'markerfacecolor',[0 0 1]);
legend([hl1,hl2,hl3],'Shunt C', 'Series C','Shunt L'); drawnow