The Control System Toolbox bandwidth function will work in some situations, but in others it’s necessary to take a less direct approach to calculate the -3 dB points.
Example —
s = tf('s');
sys = s^2/(s^3 - 2*s^2 - 2*s + 5);
[mag, phase, wout] = bode(sys);
mag = squeeze(mag);
phase = squeeze(phase);
mag_max = max(mag);
dB_3 = 10^(-3/20)*mag_max;
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0); % Returns Approximate Zero-Crossing Indices Of Argument Vector
zx = zci(mag-dB_3);
for k1 = 1:length(zx)
dB3w(k1) = interp1(mag(zx(k1):zx(k1)+1), wout(zx(k1):zx(k1)+1), dB_3, 'linear','extrap');
dB3p(k1) = interp1(wout(zx(k1):zx(k1)+1), phase(zx(k1):zx(k1)+1), dB3w(k1), 'linear','extrap');
end
figure(1)
subplot(2,1,1)
plot(wout, 20*log10(mag))
hold on
plot(dB3w, 20*log10([1 1]*dB_3), 'pg')
hold off
xlabel('Frequency')
ylabel('Amplitude (dB)')
grid
subplot(2,1,2)
plot(wout, phase)
hold on
plot(dB3w, dB3p, 'pg')
hold off
xlabel('Frequency')
ylabel('Phase')
grid
The ‘dB3w’ array are the frequencies of the -3 dB points, and ‘dB3p’ are the phase values at those frequencies.
I’m not certain what you mean by ‘the intercepts of the axes’. Those would seem to be the beginning and end elements of the vectors, so ‘wout(1)’ and ‘wout(end)’, and so for the others.
