How it works
A first-order RC or RL filter is the simplest way to remove noise from a signal or to shape a frequency response. A low-pass filter passes frequencies below its cutoff and attenuates higher ones at 20 dB per decade; a high-pass filter does the opposite.
Enter any two of the three values (resistance, capacitance or inductance, cutoff frequency) and the calculator solves for the third. It then suggests the nearest standard E-series part values and shows how much the cutoff frequency moves when you use them.
The Bode plot shows the ideal magnitude response. At the cutoff frequency the gain is −3 dB, meaning the output amplitude is about 70.7% of the input. Real circuits deviate because of source and load impedance, component tolerance and parasitic elements.
Design procedure
- 1Decide what you want to keep and what you want to remove, for example a 50 Hz measurement signal and 20 kHz PWM ripple.
- 2Place the cutoff between them. A first-order filter only attenuates 20 dB per decade, so with a 2 kHz cutoff the 20 kHz ripple is reduced by about 10 times.
- 3Pick a practical resistor first (for example 1 kΩ to 100 kΩ for signal filters), then compute the capacitor and round it to a standard value.
- 4Check the loading: the source impedance adds to R, and the input impedance of the next stage appears in parallel with the output.
- 5If one stage is not enough, cascade buffered stages or use a second-order filter.
Formulas
- RC cutoff frequency
- f_c = 1 / (2π · R · C)
- RL cutoff frequency
- f_c = R / (2π · L)
- Low-pass magnitude
- |H(f)| = 1 / √(1 + (f / f_c)²)
- High-pass magnitude
- |H(f)| = (f / f_c) / √(1 + (f / f_c)²)
Worked example
To filter PWM ripple from a 10 kΩ sense divider with a 1.6 kHz cutoff, C = 1 / (2π · 10 kΩ · 1.6 kHz) ≈ 10 nF. The nearest standard value of 10 nF gives f_c ≈ 1.59 kHz.
Common mistakes
- Placing the cutoff too close to the signal, which attenuates and phase-shifts the signal you want to measure.
- Ignoring the phase lag of the filter in a control loop; it adds delay to the measured value.
- Using a high-value resistor that interacts with the input bias current or leakage of the next stage.
- Choosing capacitors with large tolerance or strong voltage dependence, such as high-K ceramics, where the cutoff frequency matters.
Frequently asked questions
What does the −3 dB point mean?
It is the frequency where the output power is half of the input power, or the amplitude is 1/√2 of the input. It is the conventional definition of a filter's cutoff frequency.
How do I get a steeper roll-off?
Cascade stages or use a second-order filter such as an RLC or Sallen-Key topology, which rolls off at 40 dB per decade.
Why does my measured cutoff differ from the calculation?
The source impedance adds to R, the load appears in parallel, and capacitors often have ±10% or worse tolerance. Account for these or buffer the filter with an op-amp.
Results are engineering estimates. Verify your design with datasheets, simulation and measurement.