📡 RC Frequency Filters

Bode magnitude plot · Adjust R and C · Switch filter type · See input vs output signals

Filter Type

RC Parameters

Test Signal

Filter Info

f_c (cutoff)
ω_c (rad/s)
|H| at f
Attenuation

Formula

Low-pass:
τ = RC
|H| = 1/√(1+(ωτ)²)
f_c = 1/(2πRC)

📻 RC Frequency Filters — Bode Plot

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.

🔬 What It Demonstrates

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.

🎮 How to Use

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.

💡 Did You Know?

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.

About RC Frequency Filters

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.

Frequently Asked Questions

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.

What do the resistance and capacitance sliders do?

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.

How does a low-pass filter differ from a high-pass filter?

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.

How is the band-pass mode built?

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.

Why does the output signal lag the input?

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.

What does −20 dB per decade mean?

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.

Is this simulation physically accurate?

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.

Where are RC filters used in practice?

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.