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Biquad filter

For the digital implementation of a biquad filter, check digital biquad filter.

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A biquad filter is a type of active filter consisting of a two-integrator feedback loop with an inverter. In its basic configuration, it can be used as either a low-pass or band-pass filter, depending on where the output signal is taken from.

For a second-order filter, the low-pass transfer function is given by

$H(s)=\frac{G_{lpf}\omega^{2}_{0}}{s^{2}+\frac{\omega_{0}}{Q}s+\omega^{2}_{0}}$

and the band-pass transfer function, by

$H(s)=\frac{G_{bpf}\frac{\omega_{0}}{Q}s}{s^{2}+\frac{\omega_{0}}{Q}s+\omega^{2}_{0}}$ .

For the topology shown in Figure 1, the filter properties are given by:

Low-pass gain: $G l p f = - R 2 / R 1$ ,
Band-pass gain: $G b p f = - R 3 / R 1$ ,
Natural frequency: $\omega_{0}=1/\sqrt{R_{2}R_{4}C_{1}C_{2}}$ , and
Quality factor: $Q=\sqrt{\frac{R_{3}^{2}C_{1}}{R_{2}R_{4}C_{2}}}$ .

The bandwidth is approximated by $B = ω 0 / Q$ , and Q is sometimes expressed as a damping constant $ζ = 2 / Q$ .

If a noninverting low-pass filter is required, the output can be taken at the output of the second operational amplifier. If a noninverting band-pass filter is required, the order of the second integrator and the inverter can be switched, and the output taken at the output of the inverter's operational amplifier.

Category: Filters