% vcvs_typ.m - VCVS LP filter types - Fig 5.16, p. 274 in H&H
% HJSIII - 98.07.09

clear
clf

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

fc = 15;
C = 0.1E-6;
C1 = C;
C2 = C;

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

K_but = 1.586;
K_bes = 1.268;
K_che = 2.114;

fn_but = 1;
fn_bes = 1.272;
fn_che = 0.907;

R_but = 1 / (2*pi*fc*C*fn_but);
R_bes = 1 / (2*pi*fc*C*fn_bes);
R_che = 1 / (2*pi*fc*C*fn_che);

% use 0.1 Hz <= f <= 1000
lf = -1:0.01:3;
f = 10 .^ lf;

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

% gain

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

K = K_bes;
R1 = R_bes;
R2 = R_bes;
G_bes  =  K.*ZC1.*ZC2 ./ ( ( R1+ZC1).*( R2+ZC2) +  R1*(ZC1- K*ZC2) );

K = K_che;
R1 = R_che;
R2 = R_che;
G_che  =  K.*ZC1.*ZC2 ./ ( ( R1+ZC1).*( R2+ZC2) +  R1*(ZC1- K*ZC2) );

% gain in dB and phase in degrees
dB_but = 20 * log10( abs( G_but ) );
dB_bes = 20 * log10( abs( G_bes ) );
dB_che = 20 * log10( abs( G_che ) );

phi_but = angle( G_but ) * 180 / pi;
phi_bes = angle( G_bes ) * 180 / pi;
phi_che = angle( G_che ) * 180 / pi;


% plots
subplot(2,1,1)
  plot( lf,dB_but, lf,dB_bes,'--', lf,dB_che,':' )
  axis( [ -1 3 -40 10 ] )
  title( 'VCVS 100 Hz LP filter types' )
  xlabel( 'log f' )
  ylabel( 'Gain (dB)' )
  legend( 'Butterworth', 'Bessel', '2dB Chebyshev' )

subplot(2,1,2)
  plot( lf,phi_but, lf,phi_bes,'--', lf,phi_che,':' )
  axis( [ -1 3 -190 10 ] )
  xlabel( 'log f' )
  ylabel( 'Phase (deg)' )
  hold on