Resonant series and parallel LC circuits may thus be combined to form a notch filter as shown in Figure . In this circuit, the resonant parallel LC circuits are used to block frequencies within the stopband, while the resonant series LC circuit is used to attenuate frequencies within the stopband by shunting them towards the ground.
The following equations apply to the notch filter in Figure 1 above:
1) L = Zo (f2-f1) / (πf1f2); Lf = Zo / (4π(f2-f1))
2) C = 1 / (4π(f2-f1)Zo); Cf = (f2-f1) / (π(f2f1Zo))
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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