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Interactive Bode plot: visualize magnitude and phase response in real time.
RC Low-Pass Filter
When to use this: Use this to design a simple low-pass or high-pass filter — for audio crossovers, sensor signal conditioning, removing switching noise from a power rail, or AC-coupling amplifier stages. For steeper rolloff, cascade two stages or use an active Sallen-Key filter.
An RC low-pass filter lets DC and low-frequency signals through while attenuating anything above its cutoff frequency. The higher the frequency, the more the capacitor looks like a short circuit to ground, pulling the output down. At the cutoff frequency f₀ = 1/(2πRC), the output is already −3dB — about 70.7% of the input amplitude. Above that, you lose 20dB for every factor-of-10 increase in frequency.
The cutoff depends only on the product R×C. Double either value and f₀ halves. This gives you flexibility: a 10kHz filter might use R = 10kΩ and C = 1.6nF, or R = 1kΩ and C = 16nF — same frequency, different impedance. Choose higher resistor values when you need to minimize current draw; choose lower values when driving capacitive loads.
You'll use low-pass filters most often to smooth noisy sensor signals before an ADC, to strip switching noise from a PWM signal, or as anti-aliasing filters before audio digitization. The time constant τ = RC tells you how fast the filter responds to step inputs: after one time constant, the output reaches 63.2% of the final value.
One limitation: a single RC stage rolls off at only −20dB/decade. If you need a sharper cutoff, cascading two RC stages gives −40dB/decade, but they interact and load each other, degrading the response. For a precise steeper filter, use an active Sallen-Key topology with an op-amp — it maintains the designed frequency response regardless of loading.
Transfer Function
H(jω) = 1 / (1 + jωRC)Cutoff Frequency
f₀ = 1 / (2π · R · C)Anti-aliasing filter for audio ADC. Passes all audible frequencies, removes ultrasonic noise above 20 kHz.
f₀ = 1/(2π×10kΩ×820pF) = 19.4 kHz
Filter mains-frequency ripple from a rectified supply. Smooth DC with a gentle low-pass.
f₀ = 1/(2π×1kΩ×1.5µF) = 106 Hz
Block DC offset between amplifier stages while passing all audio frequencies above 10 Hz.
f₀ = 1/(2π×100kΩ×150nF) = 10.6 Hz
| Cutoff Frequency | R | C | Application |
|---|---|---|---|
| 10 Hz | 100 kΩ | 150 nF | AC coupling, subsonic filter |
| 100 Hz | 10 kΩ | 150 nF | Mains ripple removal |
| 1 kHz | 10 kΩ | 15 nF | Tone control, general filtering |
| 10 kHz | 10 kΩ | 1.5 nF | Audio treble rolloff |
| 20 kHz | 10 kΩ | 820 pF | Anti-aliasing before ADC |
| 100 kHz | 1 kΩ | 1.5 nF | RF interference suppression |
RC filter rolloff rate
A single RC filter rolls off at −20 dB/decade (equivalently, −6 dB/octave). At 2× the cutoff frequency the signal is already −7 dB (about 45% amplitude). At 10× the cutoff the signal is −20 dB (10% amplitude). To get steeper rolloff, cascade two RC stages (−40 dB/decade) or use an active Sallen-Key filter.
Classic telephone-bandwidth low-pass filter. The PSTN voice band cuts off at 3.4 kHz — replicate it with a single RC stage using a standard capacitor value.
C = 47 nF → R = 1/(2π × 3400 × 47×10⁻⁹) = 996 Ω ≈ 1 kΩ (E12 standard value)
Add a simple RC on an analog sensor line before the ADC pin to suppress high-frequency noise without affecting the slowly-changing sensor signal.
R = 10 kΩ → C = 1/(2π × 160 × 10000) = 99 nF ≈ 100 nF (E6 standard value)
Tip: standard component values
Use E12 series resistors (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 — repeated per decade) and E6 series capacitors (10, 22, 47, 100 nF, then µF) for the closest standard value matches. Designing around these values avoids special-order parts and reduces cost.
The Bode plot above shows two things: magnitude (how much the filter attenuates the signal in dB) and phase (how much it shifts the signal's timing). For a low-pass filter:
The slope of −20dB/decade is the "fingerprint" of a first-order filter. If you see −40dB/decade, there are two poles (either two RC stages or an active second-order filter).
At the right frequency ranges, RC filters behave as mathematical operations on the signal:
| Configuration | Condition | Output | Use case |
|---|---|---|---|
| Low-pass RC | f ≫ f₀ (well above cutoff) | ∫ Vin dt (integral of input) | Converting square wave to triangle wave, averaging signals |
| High-pass RC | f ≪ f₀ (well below cutoff) | dVin/dt (derivative of input) | Edge detection, removing slow drift, coupling transients |
In practice, a 555 timer's integrating capacitor, the soft-start circuit on a power supply, and the AC coupling capacitor in an op-amp stage are all RC circuits doing integration or differentiation in specific frequency ranges.
| Filter type | Order / rolloff | Pros | Cons |
|---|---|---|---|
| Single RC | 1st order / −20dB/dec | Two components, trivial to build | Gentle rolloff, lossy (R dissipates power) |
| Two-stage RC | 2nd order (approx) / −40dB/dec | Still passive, no supply needed | Stages interact, actual rolloff softer than ideal 2nd order |
| Sallen-Key (active) | 2nd order / −40dB/dec | True 2nd order, Butterworth/Chebyshev selectable | Needs op-amp and supply |
| LC filter | 2nd order / −40dB/dec | No power needed, handles high current | Inductors are bulky and have parasitic resistance |
For most signal-level filtering below 1MHz, a Sallen-Key active filter gives much better performance than cascaded RC stages. For switching power supplies and RF circuits, LC filters are preferred because they don't waste power in resistors.
Did you know? The RC filter is one of the oldest electronic circuits, used in early radio receivers to tune stations. In modern audio equipment, the same principle shapes tone controls and speaker crossover networks.