Active and Passive Filter Design

A filter is a circuit that passes some frequencies while attenuating others, shaping the spectrum of a signal. Filters are described by their response: a low-pass filter allows frequencies below a cutoff to pass and weakens those above it, a high-pass filter does the opposite, and band-pass and band-stop filters select or reject a range. The cutoff frequency marks the boundary, conventionally the point at which the output power has fallen to half, equivalent to a drop of about three decibels.

Passive filters are built only from resistors, capacitors and inductors and need no power supply. A simple resistor-capacitor (RC) network forms a basic low-pass or high-pass filter, while inductor-capacitor (LC) combinations give sharper responses and are common at radio frequencies. Because the reactance of capacitors and inductors changes with frequency, these components naturally divide a signal according to its frequency content. Bode plots, which show gain in decibels against a logarithmic frequency axis, make the roll-off and cutoff easy to read.

Active filters add an amplifying element, usually an operational amplifier, to the resistors and capacitors. This brings several advantages: the filter can provide gain, its stages do not load one another, and sharp responses can be obtained without bulky inductors, which is valuable at audio frequencies. Standard response shapes such as Butterworth and Chebyshev trade off flatness in the passband against steepness of roll-off. The choice between passive and active design depends on the frequency range, the need for gain, and constraints on size and power.

Frequently asked questions

What is the cutoff frequency of a filter?

It is the frequency that marks the edge of the passband, usually defined as the point where the output power has dropped to half its maximum, a fall of about three decibels.

Why use an active filter instead of a passive one?

Active filters can provide gain, isolate their stages from each other, and achieve sharp responses at audio frequencies without large inductors, at the cost of needing a power supply.

What is the difference between a low-pass and a high-pass filter?

A low-pass filter lets through frequencies below its cutoff and attenuates higher ones, while a high-pass filter attenuates low frequencies and passes those above the cutoff.