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# Biquad filter

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

### Additional recommended knowledge

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: Glpf = − R2 / R1,
• Band-pass gain: Gbpf = − R3 / R1,
• 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 = 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.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Biquad_filter". A list of authors is available in Wikipedia.
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