Low- & High-Pass Filters

One resistor and one capacitor make a filter: a low-pass lets slow signals through and blocks fast ones, a high-pass the other way round. Find the cut-off frequency, the parts for a cut-off you want, and how much of a signal gets through.

ElectronicsFiltersSignals

Inputs

Input examples

A first-order RC filter without a load on its output. Click Solve next to R, C or the cut-off frequency. The signal frequency is the frequency you want to know the effect at.

Resistance R

Capacitance C

Cut-off frequency f_c — −3 dB point

Signal frequency f

How an RC Filter Works

A capacitor blocks steady (DC) voltages but lets fast-changing signals through more and more easily as the frequency rises. Put it after a resistor to ground and fast signals leak away: a low-pass filter, used to remove noise or hum. Swap the two and slow signals are blocked: a high-pass, used to pass audio while blocking a DC offset.

At the cut-off frequency the output is 1/√2 = 71% of the input, which is −3 dB. Far beyond it, every ten times higher frequency gives ten times less output (−20 dB per decade). The output also shifts in time: the phase moves by 45° at f_c, up to 90°.

at f_c−3 dB, 71%

beyond−20 dB per decade

phase at f_c45°

1.6 kΩ + 100 nFf_c ≈ 1 kHz

Bode Plot: Gain

f_c

gain of the filter

cut-off frequency, −3 dB

your signal

Bode Plot: Phase

phase

Result

Enter the values above

Low-Pass Gain at a Glance

first order, exact

Frequency	Output	Gain	Phase
f_c / 10	99.5%	−0.04 dB	−5.7°
f_c	70.7%	−3.01 dB	−45°
2 f_c	44.7%	−6.99 dB	−63.4°
10 f_c	9.95%	−20.0 dB	−84.3°

Worked Techniques

Choosing the Capacitor

Pick a sensible resistor (1–100 kΩ), then calculate C and round to a standard value.

Example: 1 kHz with 10 kΩ: 15.9 nF, use 15 nF or 18 nF.

Gain in Decibels

−20 dB means a tenth of the voltage, −40 dB a hundredth.

Example: 10 kHz through a 1 kHz low-pass: −20.1 dB.

High-Pass Gain

The mirror image: full output well above f_c, little below.

Example: audio coupling, 10 µF and 10 kΩ: f_c = 1.6 Hz, 20 Hz passes at 99.7%.

Sources & Verification

References

A. R. Hambley, Electrical Engineering: Principles and Applications, 7th ed., Pearson, 2018 — Ch. 6 (Frequency Response, Bode Plots, and Resonance), Sec. 6.2 (First-Order Lowpass Filters) and Sec. 6.5 (First-Order Highpass Filters).