Design and Frequency Response of Active Butterworth Low-Pass Filters

Abstract

Electronic systems frequently need to separate wanted signals from unwanted ones by frequency, passing the frequencies of interest while suppressing the rest, and the active filter, built from operational amplifiers together with resistors and capacitors, performs this function in a compact form without bulky inductors; the Butterworth design is favoured for the smoothness of its passband. This study examines the design and frequency response of active Butterworth low-pass filters and the effect of the filter order on the response. Low-pass filters of differing order were considered, and the magnitude of the response was determined as a function of frequency, the passband, the transition, and the stopband being examined, and the effect of increasing the order on the sharpness of the transition assessed. Every filter passed the low frequencies with little attenuation and suppressed the high frequencies, the response being flat in the passband, as the Butterworth design intends, and falling away beyond the cutoff frequency; the cutoff, where the response has fallen to a defined fraction of its passband value, marked the boundary between what was passed and what was suppressed. Increasing the order of the filter made the transition from passband to stopband sharper, the response falling more steeply beyond the cutoff, so that a higher-order filter separated nearby wanted and unwanted frequencies more cleanly, at the cost of more components and greater complexity. The study shows that active Butterworth low-pass filters provide a flat passband and a controllable, progressively sharper roll-off as the order increases, and it discusses the trade-off between selectivity and complexity that governs the choice of order. KEYWORDS: Active filter, Butterworth filter, Low-pass filter, Frequencyresponse, Filter order, Operational amplifier, Cutoff frequency, Roll-off Analog filter design