Sensitivity and frequency limitations of biquadratic active filters

Abstract

A comparative study of single-amplifier filters, fifteen different two-amplifier circuits, and the state-variable three-amplifier configuration is given. The figures-of-merit used are the passive sensitivities, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_0</tex> gain-sensitivity products, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> gain-sensitivity products, and the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_0</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> deviations due to the amplifiers' limited bandwidth. In addition, practical matters such as input impedance and component spread are considered. Among the circuits considered a particular twoamplifier resonator emerges as the "best" biquadratic section. Some of the interesting results include a unified expression, applicable to a large class of low-sensitivity circuits, for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_0</tex> deviation due to the amplifier's limited frequency response. In this expression, which applies for all active filters which have low <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_0</tex> active sensitivities, the only configurationdependent quantities are the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> gain-sensitivity products.