Canonical controllability equations for independent pole/zero frequency, bandwidth, and q factor are formulated for biquadratic transfer functions. Corresponding root loci for the digital tuning case are also shown. Elementary building blocks of programmable analog-computer-type active filters (integrators and summers) using multiplying digital-to-analog converters are introduced. The canonical controllability of two important state-variable biquads (KHN and Thomas-Tow) is discussed. Parasitic effects such as differential linearity, offset, and high-frequency limitations of programmable biquads are evaluated. The measurements of practical biquads show good agreement with low-frequency design and demonstrate the feasibility of discussed filters.
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