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

and the band-pass transfer function, by

.

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

• Low-pass gain: G_lpf = − R₂ / R₁,
• Band-pass gain: G_bpf = − R₃ / R₁,
• Natural frequency: , and
• Quality factor: .

The bandwidth is approximated by B = ω₀ / 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.