% vcvs_tol.m - effects of component tolerances in second-order
%   VCVS LP filter - Fig 5.16, p. 274 in H&H
% HJSIII - 98.07.09

clear
clf

% component tolerance - 10%
pct = 0.1;

% cutoff frequency (Hz) fc = 1 / (2*pi*R*C)
% capacitor (Farads)

fc = 15;
C1C2_des = 0.1E-6;

% single-stage second-order passband gain
%		K	fn
% Butterworth	1.586	1
% Bessel	1.268	1.272
% 2dB Chebyshev	2.114	0.907

K_des = 1.586;
R_des = 10000;
RKm1_des = (K_des - 1) * R_des;

fn = 1;
R1R2_des = 1 / (2*pi*fc*C1C2_des*fn);

% use 0.01 Hz <= f      <= 1 MHz
%          -2 <= log(f) <= 6
lf = -2:0.01:6;
f = 10 .^ lf;

% initialize max/min
npts = 51;
dB_max = -1000 * ones( size(f) );
dB_min =  1000 * ones( size(f) );
phi_max = -1000 * ones( size(f) );
phi_min =  1000 * ones( size(f) );

% repeat 1000 times
nrep = 1000;
for irep = 1:nrep,
  irep
  if irep == nrep,
    pct = 0;
  end
  
% add random tolerance to components
  R = R_des * ( 1 + pct*(2*rand-1) );
  RKm1 = RKm1_des * ( 1 + pct*(2*rand-1) );
  K = 1 + (RKm1 / R);
  R1 = R1R2_des * ( 1 + pct*(2*rand-1) );
  R2 = R1R2_des * ( 1 + pct*(2*rand-1) );
  C1 = C1C2_des * ( 1 + pct*(2*rand-1) );
  C2 = C1C2_des * ( 1 + pct*(2*rand-1) );

% capacitor impedance
  ZC1 = -j ./ ( 2 * pi * f * C1 );
  ZC2 = -j ./ ( 2 * pi * f * C2 );

% gain
  G  =  K.*ZC1.*ZC2 ./ ( ( R1+ZC1).*( R2+ZC2) +  R1*(ZC1- K*ZC2) );

% gain in dB and phase in degrees
  dB = 20 * log10( abs( G ) );
  phi = angle( G ) * 180 / pi;

% find max/min
  dB_max = max( dB_max, dB );
  dB_min = min( dB_min, dB );
  phi_max = max( phi_max, phi );
  phi_min = min( phi_min, phi );
  
% next irep
end

% set up plots
subplot(2,1,1)
  Kplot = 20*log10(K)*ones( size(f) );
  plot( lf,dB, lf,dB_max, lf,dB_min, lf,Kplot,'--' )
  axis( [ -1 3 -40 10 ] )
  title('VCVS LP filter - 10% component variation')
  xlabel('log f')
  ylabel('Gain (dB)')

subplot(2,1,2)
  plot( lf,phi, lf,phi_max, lf,phi_min )
  axis( [ -1 3 -190 10 ] )
  xlabel('log f')
  ylabel('Phase (deg)')
  hold on