RLC filters. How to determine band pass filter?

I have done question on frequency response of RLC it is easy to find whether a given circuit is high pass filter or low pass filter. But I am wondering how to determine for band pass or band reject filters. Please help me and I would be obliged if someone explain it by considering an example of a passive filter (containing all R,L,C).

• What precisely are you having difficulty with - understanding the circuit topology or the formula? – Andy aka Sep 20 '14 at 17:43
• see in case of low pass filters and high pass filters we just have to see that increasing the frequency or decreasing it whether making it small or bigger . I mean if given circuit is high pass filter then we will compute its transfer characteristic and then put w(angular frequency) tending to infinity and it will give us the transfer function is also tending to infinity , but in case of band pass filter how we will know it is band pass , i mean band pass is about just a band so how come we know about the band and its lower and upper cut off frequencies ? – Pankaj Kumar Sep 20 '14 at 17:59

A "parallel" band pass filter constructed from R,L and C has a centre frequency determined largely by the formula below: -

Fc = $\dfrac{1}{2\pi\sqrt{LC}}$

Given the following circuit: -

The impedance reaches a maximum at resonance and current I will only flow thru the resistor at resonance. Clearly, if R is big less current flows and if the frequency is moved away from Fc then the impedance drops rapidly. This type of circuit is used to let one frequency through (Fc) and rapidly attenuate frequencies that are not at resonance.

More typically the parallel RLC circuit looks like this (because it takes into account the biggest losses that tend to occur in the inductor): -

Now the frequency of resonance is slightly shifted from the previous formula to take into account R: -

Fc = $\dfrac{1}{2\pi}\sqrt{\dfrac{1}{LC} - \dfrac{R^2}{L^2}}$

The resistance in series with the coil (L) also reduces the Q of the circuit which makes the filter less peaky.

There is a lot more to these types of circuits and I'd take a look here - wiki page for RLC circuits (includes series RLC).