Resonant series and parallel LC circuits may thus be combined to form a band-pass filter as shown in Figure. In this circuit, the resonant series LC circuits are used to allow only the desired frequency range to pass while the resonant parallel LC circuit is used to attenuate frequencies outside the passband by shunting them towards the ground.
The following equations apply to the band-pass filter in Figure above:
1) L = Zo / (π(f2-f1)); Lf = (f2-f1) / (4π(f2f1))
2) C = (f2-f1) / (4π(f2f1Zo)); Cf = 1 / (π(f2-f1)Zo)
3) fo = sqrt(f1f2) = 1 / (2π(sqrt(LC))) = 1 / (2π(sqrt(LfCf)))
4) Zo = sqrt(L/Cf) = sqrt(Lf/C)
where Zo = line impedance; f1 = lower cut-off frequency; f2 = upper cut-off frequency; fo = resonant frequency.
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