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%------------------------------------------------------------------------------
% Oscillation gm calculation
%
% ---------------------------------------------------------------------------------------
% | | | | | | | |
% | | | | | | | |
% C | | | | | | |
% Ls C | | | | | | |
% C | | | | | | |
% | | | | | | | |
% | | | < | | | |
% Cs ----- Cp ----- C3 ----- > Cgd ----- | | |
% ----- ----- ----- Rgd < ----- | | |
% | | | > | | | |
% | | | | | | | |
% < | | | | | | |
% > | | | | | | |
% Rs < | | | | | | |
% > | | | | | | |
% | | | | | | < |
% | | | | | ||--- > |
% ------------------------------------------------------------|| gm Rds < |
% | ||--- > |
% | | | |
% C1 ----- | | C2 -----
% ----- | | -----
% | | | |
% | | | |
% ----------------------------------
%
%------------------------------------------------------------------------------
clear j pi end
gm=logspace(-10,6,10000);
%Crystal parameter
Q=4e4;
Cp=2e-12;
Cs=2e-15;
Ls=88e-3;
Rs=300;
fs=12e6;
C1=15e-12;
C2=15e-12;
C3=0.01e-12;
%Rds=1e12;
Rds=(100*1)./gm;
%Rds=(10*1)./gm;
Rgd=10e6;
Cgd=0.1e-12;
w=2*pi*fs;
s=j*w;
z1=1/(s*C1);
zc2=1/(s*C2);
zc3=1/(s*(C3+Cgd+Cp));
z2=(Rds*zc2)./(Rds+zc2);
z3=(Rgd*zc3)/(Rgd+zc3);
zc=(z1*z3+z2*z3+gm.*z1.*z2.*z3)./(z1+z2+z3+gm.*z1.*z2);
rs_line=[-Rs, max(imag(zc))*0.98;
-Rs, min(imag(zc))*1.02];
%find the gm_opt, gm_a and gm_b
zcr_gm=[real(zc)',gm'];
[rc_opt,gm_opt_idx]=min(zcr_gm(:,1));
gm_opt=gm(gm_opt_idx);
tao_opt=-2*Ls/(rc_opt+Rs);
gm_a_idx=find(zcr_gm(:,1)<=-Rs,1,'first');
gm_a=gm(gm_a_idx);
gm_b_idx=find(zcr_gm(:,1)<=-Rs,1,'last');
gm_b=gm(gm_b_idx);
y0=imag(zc(1));
yend=imag(zc(end));
phi=abs(yend-y0);
%Print the optimized gm and the critical gm
rc_opt
tao_opt
gm_opt
gm_a
gm_b
y0
yend
phi
%Plot the zc vs gm locus
h=figure(1);clf;
set(h,'Name','zc vs gm locus')
plot(zc);
axis equal;
grid on;
hold on;
plot(rs_line(:,1), rs_line(:,2), '-r'); |
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