% vcvs_2_4.m - complex numbers to compute gain and phase for
%  second-order and fourth-order VCVS LP filter
% HJSIII - 07.10.17

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 = 1.586;
fn = 1;

R = 1 / (2*pi*fc*C*fn);
R1 = R;
R2 = R;

% two-stage fourth-order passband gains and normalizing factors
%		KA	fnA	KB	fnB
% Butterworth	1.152	1	2.235	1
% Bessel	1.084	1.432	1.759	1.606
% 2dB Chebyshev	1.924	0.471	2.782	0.964

KA = 1.152;
fnA = 1;

KB = 2.235;
fnB = 1;

RA = 1 / (2*pi*fc*C*fnA);
R1A = R;
R2A = R;

RB = 1 / (2*pi*fc*C*fnB);
R1B = R;
R2B = R;

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

% 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) );
GA = KA.*ZC1.*ZC2 ./ ( (R1A+ZC1).*(R2A+ZC2) + R1A*(ZC1-KA*ZC2) );
GB = KB.*ZC1.*ZC2 ./ ( (R1B+ZC1).*(R2B+ZC2) + R1B*(ZC1-KB*ZC2) );
G4 = GA .* GB;

% save log of gain and phase in degrees
dB = 20 * log10( abs( G ) );
dB4 = 20 * log10( abs( G4 ) );

phi = angle( G ) * 180 / pi;
phi4 = unwrap( angle( G4 ) ) * 180 / pi;

% plot
subplot(2,1,1)
  plot( lf,dB,'-', lf,dB4,'--' )
  axis( [ -2 6 -160 20 ] )
  title('VCVS 100 Hz LP filters')
  xlabel('log f')
  ylabel('Gain (dB)')
  legend( 'Second-order', 'Fourth-order' )

subplot(2,1,2)
  plot( lf,phi,'-' , lf,phi4,'--' )
  axis( [ -2 6 -360 90 ] )
  xlabel('log f')
  ylabel('Phase (deg)')
  legend( 'Second-order', 'Fourth-order' )