Bandwidth of low pass filter


Say I have some low pass filter of the form:

$$G(s) = \frac{a}{s+b}$$

How do I find the bandwidth? I know for example that with bandpass filters it's the difference between +-3dB of the cutoff frequency but I'm not sure how that would work for this example.

Best Answer

In your case $$G(s) = \frac{a}{s+b} = \left(\frac{a}{b}\right)\left( \frac {1}{1+\frac {s}{b}}\right)$$

The output will be -3dB compared to the passband when \$s = jb\$ (equivalent to \$\frac{b}{2\pi}\$ Hz) so the bandwidth is \$b\$ radians/second and the passband gain is (a/b).