Active Filter Design

A filter is a circuit that passes some frequencies while attenuating others, shaping the frequency content of a signal. Active filters use operational amplifiers together with resistors and capacitors, which lets them provide gain and sharp responses without bulky inductors. Filter calculators take a designer's requirements, such as the cutoff frequency and the type of response, and return the component values needed to build the circuit, turning what is otherwise a substantial design calculation into a quick lookup.

Filters are classified by which band of frequencies they pass. A low-pass filter allows frequencies below its cutoff to pass and attenuates higher ones; a high-pass filter does the opposite; a band-pass filter passes a range between two limits; and a band-stop or notch filter rejects a range. The cutoff frequency marks the boundary, and the order of the filter sets how steeply the response rolls off beyond it, with higher-order filters giving a sharper transition at the cost of more stages and components.

The shape of the response is chosen by selecting a standard approximation. A Butterworth filter has the flattest possible passband, giving a smooth response with no ripple. A Chebyshev filter accepts some ripple in the passband in exchange for a steeper roll-off near the cutoff, and an elliptic filter is steeper still by allowing ripple in both the passband and the stopband. A Bessel filter sacrifices steepness to preserve the shape of pulses by keeping a linear phase response. Each approximation corresponds to a particular set of component-value ratios, and filter calculators apply these so the designer can compare the trade-offs and obtain the resistor and capacitor values for the chosen response.

Frequently asked questions

What is the difference between low-pass and high-pass filters?

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

How do Butterworth, Chebyshev and Bessel responses differ?

Butterworth gives the flattest passband, Chebyshev trades passband ripple for a steeper roll-off, and Bessel preserves pulse shape with a linear phase at the cost of steepness.

Why use active rather than passive filters?

Active filters use op-amps with resistors and capacitors, providing gain and sharp responses without inductors, which are bulky and less ideal at audio frequencies.