April 2026Guided SimulationBeginner

Build an RC Low-Pass Filter — Step by Step

An RC filter is two components — a resistor and a capacitor — that together pass some frequencies and block others. Low-pass filters are everywhere: in audio systems, sensor signal conditioning, power supply noise rejection, and ADC input filtering. This guide builds one from scratch.

Circuit Diagram

graph LR VIN["AC Input Signal"] --> R["Resistor (R)"] R --> VOUT["Vout (to load)"] VOUT --> C["Capacitor (C)"] C --> GND["GND"] style VIN fill:#1a3a4a,stroke:#00e5ff,color:#00e5ff style VOUT fill:#1a3a2a,stroke:#00ff88,color:#00ff88

Cutoff frequency: f_c = 1 / (2π × R × C)

Below f_c: signal passes through with little attenuation. Above f_c: signal is progressively attenuated at −20dB per decade (factor of 10 in frequency = factor of 10 in output voltage reduction).

Step-by-Step Guide

STEP 1

Choose Your Cutoff Frequency

Decide what frequency you want to cut off. Common targets: 160 Hz (audio low-pass, removes hiss), 1.6 kHz (removes high-frequency noise from a sensor), 16 kHz (anti-aliasing before a 32kHz ADC).

💡 An RC filter is like a bouncer at a club with an age limit: Frequencies below the cutoff walk straight in. Frequencies above it get turned away — and the further above the cutoff they are, the harder they're rejected. The resistor and capacitor together decide where the "age limit" sits.

For 160 Hz: Choose R = 10kΩ, then calculate C: C = 1 / (2π × R × f_c) = 1 / (2π × 10,000 × 160) = 99.5nF → use 100nF standard value.

Why 10kΩ? Start with a resistor in the 1kΩ–100kΩ range for audio and signal work. Too low (under 100Ω) and the resistor loads the source; too high (over 1MΩ) and leakage currents and stray capacitance affect performance.

STEP 2

Simulate at Different Frequencies

Open the RC low-pass filter simulation. Set R=10kΩ and C=100nF. Add a scope probe at the output node.

Change the input voltage source frequency: at 16 Hz (10× below cutoff), output ≈ input. At 160 Hz (cutoff), output ≈ 70.7% of input (−3dB). At 1600 Hz (10× above cutoff), output ≈ 10% of input (−20dB).

▶ Simulate RC Low-Pass Filter ▶ Simulate RC High-Pass Filter

STEP 3

Understand Phase Shift

The RC filter also introduces a phase shift between input and output. At the cutoff frequency, the output lags the input by exactly 45°. Well above cutoff, the lag approaches 90°.

In the simulator, use the scope to add both input and output probes. At the cutoff frequency, you will see the output waveform shifted to the right relative to the input. This matters in feedback circuits and audio phase relationships.

⚠️ Phase shift can cause oscillation. Multiple RC filter stages in a feedback loop can accumulate enough phase shift (180°) to cause unwanted oscillation. This is why op-amp compensation networks are carefully designed.

STEP 4

Test Loading Effects

Add a 10kΩ load resistor from the filter output to ground. The actual cutoff frequency shifts because the effective bottom resistance is now R2 || R_load = 10kΩ || 10kΩ = 5kΩ, which changes f_c.

New f_c with load ≈ 1 / (2π × 10,000 × (5000/(10,000+5000) × 10,000) × 100nF) — it shifts upward. To avoid this, buffer the output with a voltage follower op-amp.

STEP 5

Build a High-Pass Version

Swap the positions of R and C: put C in series with the signal path, R from the output to ground. The circuit now blocks DC and low frequencies, passing only frequencies above f_c. Same formula, same component values — just different positions.

High-pass filters are used for AC coupling (removing DC offset between amplifier stages) and removing 50/60 Hz mains hum from audio signals.

▶ Simulate High-Pass Version

Real-world use: Every microphone input on a mixing desk, audio interface, or smartphone has a high-pass filter (typically 80–120 Hz cutoff) to remove low-frequency rumble and HVAC noise before the signal enters the recording chain.

Frequently Asked Questions

What is the cutoff frequency formula for an RC filter?

f_c = 1 / (2π × R × C). R in ohms, C in farads. Example: R=10kΩ (10000 ohms), C=100nF (0.0000001F): f_c = 1/(2π × 10000 × 0.0000001) = 159 Hz.

What is the difference between a low-pass and high-pass RC filter?

Low-pass: resistor in series with signal, capacitor to ground. Passes low frequencies. High-pass: capacitor in series with signal, resistor to ground. Passes high frequencies and blocks DC. Same components, different positions.

Does an RC filter change the phase of the signal?

Yes. At the cutoff frequency, the output lags the input by 45 degrees. At frequencies well above cutoff (low-pass), the lag approaches 90 degrees. This phase shift matters in feedback systems and multi-stage amplifier design.