*figure V : passive band pass
filter*

,

,

for** S = jw**, and because ** S ^{2} = -w^{2} **
=>

=>

**
K** is the DC gain which is set equal to
unity for simplicity.

The roots of the denominator should be real and different for
each other in order for the band pass filter to maintain its characteristics.
In order to do so, the** Q** factor should be
greater than 0.5.

.....(A)

transfer function

The amplitude would be :

or relating to decibels of loss :

....(B) ....(C)

amplitude response phase response

*figure W : bode plots of second order BPF*