Table of Contents
What Is a Low-Pass Filter?
A low-pass filter (LPF) is an electronic circuit that passes signals with frequencies below its cutoff frequency while attenuating signals with higher frequencies. The simplest implementations use a resistor-capacitor (RC) or resistor-inductor (RL) combination. Low-pass filters are ubiquitous in electronics: audio systems use them for bass signals, digital systems use them as anti-aliasing filters before ADCs, and power supplies use them to smooth rectified voltage.
At the cutoff frequency, the output signal amplitude is reduced to 1/sqrt(2) (about 70.7%) of the input, corresponding to -3 dB. Above the cutoff, a first-order RC or RL filter attenuates the signal at -20 dB per decade (or -6 dB per octave).
Filter Formulas
Frequency Response
| Frequency | Attenuation | Phase Shift |
|---|---|---|
| 0.1 fc | -0.04 dB | -5.7° |
| 0.5 fc | -0.97 dB | -26.6° |
| fc | -3.01 dB | -45° |
| 2 fc | -6.99 dB | -63.4° |
| 10 fc | -20.04 dB | -84.3° |
Frequently Asked Questions
RC vs RL: which should I use?
RC filters are preferred at low to moderate frequencies because capacitors are cheap, small, and have no parasitic resistance. RL filters are used at very high frequencies or when inductors are already present in the circuit. Inductors are generally larger, more expensive, and have significant parasitic resistance at lower frequencies.
What does -3 dB mean?
The -3 dB point is where the output power is half the input power, or equivalently, the voltage is 1/sqrt(2) = 0.707 of the input. This is the standard definition of the cutoff frequency. In audio, 3 dB is approximately the smallest change in volume most people can detect.
How do I make a steeper filter?
Cascade multiple first-order stages for steeper roll-off: two stages give -40 dB/decade, three give -60 dB/decade. Alternatively, use active filter topologies (Butterworth, Chebyshev, Bessel) that provide sharper cutoffs with controlled passband and stopband behavior using operational amplifiers.