Library / Electrical / ELE-39
Electrical
Cutoff frequency of a first-order RC filter
Frequency at which a first-order RC filter passes about 71 % (−3 dB) of the input amplitude.
- Ref
- ELE-39
- Rev
- v1
- Field
- Electrical
- Result
- fc [Hz]
A first-order RC filter has a cutoff (corner) frequency fc = 1/(2πRC), where the output amplitude has fallen to 1/√2 (0.707, or −3 dB) of its passband value. Below fc a low-pass filter passes the signal; above it, the output falls at 20 dB per decade. Here R is entered in kΩ and C in nF, and the result is in Hz.
Frequency at which a first-order RC filter passes about 71 % (−3 dB) of the input amplitude. It is the same for the low-pass and high-pass arrangements.
Calculator
- Time constant, RC100 µs
- Angular cutoff frequency, 1/(RC)10,000 rad/s
- Gain at ten times the cutoff frequency0.0995
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 1 kΩ resistor with a 100 nF capacitor has a corner at 1,592 Hz and a time constant of 100 µs.
- To move the corner by a decade, change R or C by a factor of ten; two cascaded stages with buffering give a roll-off of 40 dB per decade.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Hz) | Local step | Change in result |
|---|---|---|---|---|---|---|
| C Capacitance | 1 to 10,000 nF | 15.92 | 159,200 | 159,100 | +10% | −9.09 % |
| R Resistance | 0.1 to 100 kΩ | 15.92 | 15,920 | 15,900 | +10% | −9.09 % |
Sweep of Capacitance
| Capacitance (nF) | Cutoff frequency (Hz) |
|---|---|
| 1 | 159,200 |
| 3.162 | 50,330 |
| 10 | 15,920 |
| 31.62 | 5,033 |
| 100 | 1,592 |
| 316.2 | 503.3 |
| 1,000 | 159.2 |
| 3,162 | 50.33 |
| 10,000 | 15.92 |
Sweep one variable
Variables and how each one contributes
Cutoff frequency
What the equation gives you. Everything else feeds it.
Resistance
The resistance, in kΩ. Lowers the cutoff frequency in inverse proportion: a larger resistance charges the capacitor more slowly. Raising it by 0.5 kΩ (to 1.5 kΩ) moves the result by −33.3 %, from 1,592 to 1,061 Hz.
Capacitance
The capacitance, in nF. Lowers the cutoff frequency in inverse proportion: a larger capacitor takes longer to charge. Raising it by 10 nF (to 110 nF) moves the result by −9.09 %, from 1,592 to 1,447 Hz.
Worked example with the values above
- Time constant: RC = 1 kΩ × 100 nF = 100 µs = 1×10−4 s.
- Denominator: 2π × 1×10−4 = 6.283×10−4 s.
- fc = 1 / 6.283×10−4 = 1,592 Hz.
Assumptions and limits
- An ideal resistor and capacitor driven from a low-impedance source into a high-impedance load, so nothing else loads the filter.
- Sinusoidal signals in the steady state.
Common mistakes
- Using kΩ with µF or nF without converting to the consistent system.
- Confusing the cutoff frequency in Hz with the angular frequency in rad/s (factor 2π).
Statistics and uncertainty
Capacitors of 10 % or 20 % tolerance and resistors of 1 % give a corner uncertain by 10 % or more, which is dominated by the capacitor. Use C0G or film capacitors if the corner frequency matters, since ceramic types change with voltage and temperature.
Where it is used
- Anti-aliasing and noise filters in sensor and data-acquisition circuits.
- Setting the bandwidth of a coupling or smoothing circuit.
Maths you need
- Capacitor: stores energy in an electric field
- Decibel: 20 log₁₀ of an amplitude ratio