Biquad Filter

THREE AMPLIFIER BIQUAD

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Filter Transmission, Types and Specification

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H(s) = K/(as² + bs + 1),

where a = R1R2C1C2

and b = R1C1 + R2C1

This can be simplified by making

R1 = R2 and C1 = C2, resulting

in:

H(s) = K/(R²C²s² + 2RCs + 1)

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Three Amplifier Biquad

Figure shows the basic architecture of the 3

amplifier state variable Biquad. It comprises a

summing node followed by two integrators. This

architecture is quite versatile in that it gives a high-

pass, band-pass and low-pass output, but it also

allows independent control of fc, and the Q.

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Three amplifier state-variable biquad

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Four Amplifier Biquad State Variable Filter

TOW THOMAS BIQUAD

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The big difference is that for a biquad, as fc changes, the bandwidth stays

constant, but the Q value changes. Thus, if you change fc in the frequency

domain, as fc increases, the Q value increases and as fc decreases, the Q value

also decreases. Other than this difference, the biquad behaves like the state

variable. It allows very high Q values, it can be configured in a 3 or 4 amplifier

configuration, and it too is less sensitive to external component variations. The

3 and 4 amplifier circuits draw more power, and usually require more design

time, especially when multiple stages are cascaded to obtain a steeper filter

roll-off response.

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TOW THOMAS BIQUAD contd…

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The Tow-Thomas biquad with feedforward. The transfer function is

realized by feeding the input signal through appropriate components to

the inputs of the three op amps. This circuit can realize all special

second-order functions.

TOW THOMAS BIQUAD contd…

Passive Ladder structure

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Inductor Substitution using Gyrator

The Antoniou inductance-simulation circuit

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Analysis of the circuit assuming ideal op amps. The order of the analysis steps is indicated by the circled numbers.

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The Antoniou inductance-simulation circuit. Analysis

of the circuit assuming ideal op amps. The order of

the analysis steps is indicated by the circled numbers.

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(b) HP; (c) BP, (d) notch at 0;

Realization of second-order filter functions using opamp-RC resonator of Low Pass

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Realization of second-order filter functions using Opamp-RC resonator of High Pass

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Realization of second-order filter functions using opamp-RC resonator of Band Pass

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Realization of second-order filter functions using opamp-RC resonator of NOTCH

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LPN, n 0

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HPN, 0 n

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ALL PASS