biquad filter
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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
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