Applications such as audio equalizers require bandpass filters with a constant maximum gain that's independent of the filter's quality factor, Q. However, all of the well-known filter architectures – Sallen-Key, multiple-feedback, state-variable, and Tow-Thomas – suffer from altered maximum gain when Q varies. Equation 1 expresses the second-order bandpass transfer function of a bandpass filter: (1) where K represents the filter's gain constant. When the input frequency equals ω0, the filter's gain, AMAX, is proportional to the product, KQ. Thus, modifying the quality factor alters the gain and vice versa. Figure 1. This bandpass active filter features adjustable Q and maximum gain in the passband and consists of a twin-T cell with Q adjustment and a differential output stage. You can also extract a frequency-notch output from the voltage-follower stage. This Design Idea describes a filter structure in which K is inversely proportional to Q. Altering Q also modifies K, producing a magnitude-plot set in which the curves maintain the same maximum gain at the central frequency ω0 – that is, KQ remains constant. Figure 1 shows the filter, which comprises a twin T cell with an adjustable quality factor and a differential stage. The differential stage comprises op amp IC3 and resistors R5A through R< ...
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