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New Generalized Impedance Converter (GIC)-Based Two-Opamp Active RC Biquads

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Abstract

In this paper, two three-opamp-based active RC biquad structures based on generalized impedance converters (GIC) due to Mikhael–Bhattacharyya and Padukone–Mulawka–Ghausi are re-visited and their equivalence is pointed out. Next, a new two-opamp GIC-based biquad topology derived from them is investigated. The various configurations which can be derived from the proposed biquad topology to realize (a) tuneable pole-frequency (ωp) and constant bandwidth (ωp/Qp) or (b) constant pole frequency with tuneable pole-Q (Qp) are investigated. The effect of opamp finite bandwidth product B as well passive and active sensitivities are presented together with simulation results.

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Data Availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study, and detailed circuit simulation results are given in the manuscript.

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There is no code associated with this work.

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    P. V. Ananda Mohan

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Appendix A

Appendix A

The equations describing MB and PMG biquad taking into account finite Gain bandwidth products of the opamps with frequency-dependent gain modeled as \(A_{i} \left( s \right) = - \frac{{B_{i} }}{s}\) are as follows:

MB biquad:

$$ \left| {\begin{array}{*{20}c} { - \left( {\frac{s}{{B_{3} }} + \frac{{Y_{8} }}{p}} \right)} & { - \frac{{Y_{10} }}{p} + \frac{s}{{B_{2} }}} & {\beta_{2} - \frac{{Y_{11} }}{p}} \\ { - \frac{{Y_{8} }}{p}} & {\gamma_{2} - \frac{{Y_{10} }}{p}} & { - \left( {\frac{s}{{B_{1} }} + \frac{{Y_{11} }}{p}} \right)} \\ {\alpha_{2} - \frac{{Y_{8} }}{p}} & { - \left( {\frac{s}{{B_{2} }} + \frac{{Y_{10} }}{p}} \right)} & { - \frac{{Y_{11} }}{p}} \\ \end{array} } \right|\left| {\begin{array}{*{20}c} {\begin{array}{*{20}c} {V_{x} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} {V_{y} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} {V_{z} } \\ {} \\ \end{array} } \\ \end{array} } \right| = \left| {\begin{array}{*{20}c} {\begin{array}{*{20}c} { - V_{i} \beta_{1} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} { - V_{i} \gamma_{1} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} { - V_{i} \alpha_{1} } \\ {} \\ \end{array} } \\ \end{array} } \right| $$
(A.1)

PMG biquad:

$$ \left| {\begin{array}{*{20}c} { - \frac{{Y_{8} }}{p}} & { - \frac{{Y_{10} }}{p} - \frac{s}{{B_{2} }}} & {\beta_{2} - \frac{{Y_{11} }}{p}} \\ { - \frac{{Y_{8} }}{p}} & {\gamma_{2} - \frac{{Y_{10} }}{p}} & { - \frac{{Y_{11} }}{p} - \frac{s}{{B_{3} }}} \\ {\alpha_{2} - \frac{{Y_{8} }}{p} - \frac{s}{{B_{1} }}} & { - \frac{{Y_{10} }}{p}} & { - \frac{{Y_{11} }}{p}} \\ \end{array} } \right|\left| {\begin{array}{*{20}c} {\begin{array}{*{20}c} {V_{x} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} {V_{y} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} {V_{z} } \\ {} \\ \end{array} } \\ \end{array} } \right| = \left| {\begin{array}{*{20}c} {\begin{array}{*{20}c} { - V_{i} \beta_{1} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} { - V_{i} \gamma_{1} } \\ {} \\ \end{array} } \\ {\begin{array}{*{20}c} { - V_{i} \alpha_{1} } \\ {} \\ \end{array} } \\ \end{array} } \right| $$
(A.2)

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Ananda Mohan, P.V. New Generalized Impedance Converter (GIC)-Based Two-Opamp Active RC Biquads. Circuits Syst Signal Process 43, 1366–1390 (2024). https://doi.org/10.1007/s00034-023-02548-3

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