I'm trying to design a second order low-pass filter using the following transfer function:
\$\ H(s)=\frac{f_c^2}{s^2 + 2 f_c s +f_c^2} \$
with cutoff frequency fc = 3400 Hz
Whenever I plot this, the cutoff frequency is at -6 dB instead of -3 dB. I'm not really sure what I'm doing wrong. Here's my Matlab code:
fc = 3400;
s = 1i*logspace(0,6,1000);
H_d = fc^2 ./ (s.^2 + 2*fc*s + fc^2);
semilogx(abs(s), 20 * log10(abs(H_d)))