Index Signal & AmplificationRC Filter

RC Filter

Corner frequency, magnitude and phase of the simplest filter there is.

Corner, −3 dB22.6Hz

Time constant7.04ms

Level at 20 Hz−3.57dB

Level at 20 kHz−0.00dB

Circuit

Magnitude

Phase

Input

Filter

Resistance

R

= 32 Ω

Capacitance

C

µF

= 220 µF

Real situations

How it works

One resistor, one capacitor

A capacitor's impedance falls as frequency rises. Put it in series and it blocks lows (high-pass); put it across the signal and it shorts highs (low-pass). Either way the corner, where the output is 3 dB down and the phase has turned 45°, is

f_c = \frac{1}{2\pi R C}

Response

\left|H_{LP}\right| = \frac{1}{\sqrt{1 + (f/f_c)^2}}

\left|H_{HP}\right| = \frac{1}{\sqrt{1 + (f_c/f)^2}}

\varphi_{LP} = -\arctan\frac{f}{f_c}

\varphi_{HP} = \arctan\frac{f_c}{f}

Far from the corner the slope settles at 6 dB per octave, 20 dB per decade.

Where these hide in a hi-fi system

An output coupling capacitor and the headphone impedance form a high-pass. Too small a capacitor thins the bass of low-impedance headphones.
Source output impedance and cable capacitance form a low-pass. It only matters with high source impedances such as passive volume controls.
A moving-magnet cartridge expects a specific load capacitance; the cable is part of it.

For a flat audio band, aim for a high-pass corner below 2 Hz or a low-pass corner above 200 kHz, a decade clear at each end.