The cutoff frequency separates the passband from the stopband of a filter and is one of the most important parameters in analog electronics. With the Cutoff Frequency Calculator (RC/RL) you can determine the value for RC and RL networks in seconds. This tutorial covers the formulas, their physical meaning and a fully worked example.
What is the cutoff frequency?
The cutoff frequency f_c is the frequency at which the output amplitude of a first-order filter has dropped to -3 dB relative to the passband. This corresponds to about 70.7 % of the amplitude (exactly 1/sqrt(2)). At this frequency the delivered power is exactly half, which is why it is also called the half-power point.
- Passband: signals are transmitted almost unchanged.
- Cutoff frequency: amplitude has fallen to -3 dB (70.7 %).
- Stopband: for a first-order filter the attenuation increases by 20 dB per decade.
Formulas for RC and RL networks
For an RC network: f_c = 1 / (2π · R · C), with the time constant τ = R · C. For an RL network: f_c = R / (2π · L) with the time constant τ = L / R. The time constant describes how quickly the network responds to a step input; after one time constant the voltage across the capacitor has reached about 63 % of its final value.
Worked example: RC low-pass
Consider an RC network with R = 1 kΩ and C = 1 µF. The cutoff frequency is:
- f_c = 1 / (2π · 1000 Ω · 1·10⁻⁶ F)
- f_c ≈ 159 Hz
- Time constant τ = R · C = 1000 Ω · 1·10⁻⁶ F = 1 ms
Signals below 159 Hz pass almost unattenuated, while higher frequencies are progressively attenuated at 20 dB/decade.
Low-pass or high-pass?
Whether an RC network acts as a low-pass or high-pass depends solely on the tap point. Taking the voltage across the capacitor yields a low-pass - high frequencies are shorted to ground. Taking it across the resistor yields a high-pass - low frequencies and DC are blocked. The cutoff frequency is identical in both cases because it depends only on R and C.
