Bode magnitude plot · Adjust R and C · Switch filter type · See input vs output signals
Interactive RC filter simulation. Switch between low-pass, high-pass and band-pass modes. Adjust resistance and capacitance to see the Bode plot, cutoff frequency and signal attenuation update live.
An RC filter's cutoff frequency f_c = 1/(2πRC) defines where the output drops by 3 dB (~70.7% of input). Below f_c, a low-pass filter passes signals unchanged; above, it attenuates at −20 dB/decade. High-pass does the reverse.
Select filter type (LP/HP/BP). Drag resistance and capacitance sliders. The Bode magnitude plot shows the frequency response. The −3 dB marker moves with the cutoff. Input and output signals compare live.
Every audio equaliser, radio tuner and power supply uses RC filters. The simplest low-pass filter — a resistor and capacitor — is the same circuit that smooths the ripple in a DC power supply rectifier.
This simulation visualises how a passive RC (resistor-capacitor) circuit shapes a signal across frequency. It draws the Bode magnitude curve of the transfer function H(jω) on a logarithmic frequency axis from 1 Hz to 100 kHz. For a single-pole filter the cutoff is f_c = 1/(2πRC), where the response falls to 1/√2 (−3 dB) of its passband value, after which the slope settles at −20 dB per decade.
The filter-type tabs switch between low-pass, high-pass and band-pass responses; the resistance and capacitance sliders set the time constant τ = RC and therefore move the cutoff marker live. A second resistor R₂ appears in band-pass mode to cascade a high-pass stage. The test-signal slider sweeps a sine wave so you can compare input and output amplitude and phase. Such filters underpin audio equalisers, radio tuning and power-supply smoothing.
What is an RC filter?
An RC filter is a simple circuit built from one resistor and one capacitor that passes some frequencies while attenuating others. Depending on where the output is taken, it behaves as a low-pass, high-pass or, when stages are combined, a band-pass filter. It is the most basic frequency-selective network in electronics.
What is the cutoff frequency and how is it calculated?
The cutoff frequency f_c marks where the output power has halved, equivalent to a −3 dB drop in magnitude (a factor of 1/√2 ≈ 0.707). For a single RC stage it is f_c = 1/(2πRC). With the default 1 kΩ and 1 μF the cutoff sits near 159 Hz, shown by the orange dashed marker on the plot.
What is a Bode plot showing here?
The Bode plot shows the magnitude |H(jω)| of the filter against frequency on a logarithmic horizontal axis spanning 1 Hz to 100 kHz. Horizontal grid lines mark 0, −3, −6, −12, −20 and −40 dB so you can read attenuation directly. The blue curve traces the response and the orange dot tracks your chosen test frequency.
Both sliders set the time constant τ = RC, which fixes the cutoff via f_c = 1/(2πRC). Increasing either R (0.1–10 kΩ) or C (0.1–10 μF) raises τ and lowers the cutoff, shifting the response leftwards; reducing them raises the cutoff. The Filter Info panel updates f_c, ω_c, |H| and attenuation as you drag.
A low-pass filter passes frequencies below the cutoff and attenuates those above it, with magnitude |H| = 1/√(1+(ωτ)²). A high-pass filter does the reverse, using |H| = ωτ/√(1+(ωτ)²), passing high frequencies and blocking low ones. Both share the same cutoff formula and the same −20 dB/decade roll-off slope.
The band-pass response in this simulation is formed by cascading a low-pass stage and a high-pass stage: H = H_LP × H_HP. The first resistor R sets the upper corner f_c1 = 1/(2πR₁C) and the second resistor R₂ sets the lower corner f_c2 = 1/(2πR₂C). The passband lies between the two cutoffs.
Capacitors introduce a frequency-dependent phase shift. For the low-pass case the phase is −arctan(ω/ω_c), reaching −45° at the cutoff and approaching −90° at high frequency; the high-pass case is shifted by +90° relative to that. The signal panel shows this lag together with the reduced output amplitude.
It describes the slope of the response well beyond the cutoff: each tenfold change in frequency (a decade) changes the magnitude by 20 dB, a factor of ten. A single RC stage gives this first-order roll-off. Cascading stages steepens the slope, for example two stages give roughly −40 dB per decade.
It uses the ideal first-order transfer functions for passive RC filters, which are accurate for low frequencies and ideal components. It neglects real-world effects such as source and load impedance, capacitor leakage, parasitic inductance and component tolerance, so a physical breadboard circuit will differ slightly, especially at the band edges.
RC filters appear throughout electronics: smoothing ripple in DC power supplies, removing noise from sensor signals, setting tone controls in audio equalisers, providing anti-aliasing before analogue-to-digital conversion, and shaping bandwidth in radio receivers. Their simplicity and low cost make them a default first-stage filter in countless designs.