Corner Cutoff Frequency, Bandwidth and Resonance Frequency

Corner Cutoff Frequency

For an RC circuit:

f_c = 1 / (2πRC)

This is the cutoff (corner) frequency in Hz, not the angular frequency.

• ω_c = 1 / RC → angular cutoff frequency (rad/s)
• f_c = 1 / (2πRC) → cutoff frequency (Hz)

At this frequency, the output magnitude is 1/√2 ≈ 0.707 of its maximum, corresponding to −3 dB.

Remember

RL: f_c = R / (2πL)

RC: f_c = 1 / (2πRC)

Cutoff (Corner) Frequency in LPF and HPF

The calculation of the cutoff (corner) frequency is applicable to both low-pass filters (LPF) and high-pass filters (HPF).

For example, an LPF and an HPF can be constructed using the same component values by changing the circuit configuration or by taking the output from a different point in the circuit.

The underlying cutoff-frequency calculation remains the same. For an RC filter:

\[ f_c = \frac{1}{2\pi RC} \]

For an RL filter:

\[ f_c = \frac{R}{2\pi L} \]

The same cutoff frequency is identified differently depending on whether the circuit is a low-pass or high-pass filter:

• For a low-pass filter (LPF), the cutoff frequency is commonly denoted as the upper cutoff frequency \(f_H\).
• For a high-pass filter (HPF), the cutoff frequency is commonly denoted as the lower cutoff frequency \(f_L\).

Summary

RC Low-Pass Filter (LPF): \(f_H = \frac{1}{2\pi RC}\)

RC High-Pass Filter (HPF): \(f_L = \frac{1}{2\pi RC}\)

RL Low-Pass Filter (LPF): \(f_H = \frac{R}{2\pi L}\)

RL High-Pass Filter (HPF): \(f_L = \frac{R}{2\pi L}\)

Note: The cutoff frequency is the frequency at which the magnitude of the filter response falls to \(1/\sqrt{2}\) (approximately 0.707) of its maximum passband value, corresponding to approximately −3 dB.

Bandwidth of a filter is the range of frequencies over which the filter allows signals to pass with acceptable attenuation.

For most filters, bandwidth is measured between the lower cutoff frequency fL​ and upper cutoff frequency fH​, where the response falls to −3 dB from its maximum.

Bandwidth, BW = fH - fL

Resonance Frequency

f₀ = 1 / (2π√(LC))

At resonance, the inductive and capacitive reactances are equal and cancel each other.

Filter Design Main Page →