Calculate RC Cutoff Frequency

Calculate the cutoff frequency of a capacitor-resistor circuit

Calculate Cutoff Frequency

RC Cutoff Frequency

This function can calculate the cutoff frequency of a capacitor and resistor, or the capacitance or resistance for a given frequency. Two of the values must be known to calculate the third.

Results
Capacitor:
Cutoff Frequency:
Resistance:

Cutoff Frequency

RC Cutoff Frequency

The cutoff frequency is the frequency at which the output voltage has dropped to 70.7% (≈ 1/√2) of the input voltage. This corresponds to an attenuation of -3dB.

Basic Formula
\[f = \frac{1}{2\pi RC}\]

Cutoff frequency of an RC circuit at -3dB attenuation.

Formula Variations
\[R = \frac{1}{2\pi fC}\]
\[C = \frac{1}{2\pi fR}\]

Calculate R or C for a given cutoff frequency.

RC Cutoff Frequency - Theory and Formulas

What is the Cutoff Frequency?

The cutoff frequency is an important parameter in filter and timing circuits. It defines the point at which the output voltage has dropped to 70.7% of the input voltage, which corresponds to an attenuation of -3dB.

Calculation Formulas

Cutoff Frequency
\[f = \frac{1}{2\pi RC}\]

The frequency is calculated from resistance R and capacitance C.

Resistance
\[R = \frac{1}{2\pi fC}\]

The resistance can be calculated from frequency f and capacitance C.

Capacitance
\[C = \frac{1}{2\pi fR}\]

The capacitance is calculated from frequency f and resistance R.

Practical Applications

Low-Pass Filters:
• Audio filters
• Anti-aliasing filters
• Noise suppression
• Smoothing filters
High-Pass Filters:
• AC coupling
• DC blockers
• High-frequency filters
• Amplifier coupling
Timing Circuits:
• Oscillators
• Timer circuits
• Delay circuits
• Time constants

Filter Types and Cutoff Frequency

RC Low-Pass
  • Output at the capacitor
  • Attenuates high frequencies
  • Passes low frequencies
  • -20dB/decade roll-off
  • Cutoff frequency at -3dB
RC High-Pass
  • Output at the resistor
  • Attenuates low frequencies
  • Passes high frequencies
  • +20dB/decade rise
  • Cutoff frequency at -3dB

Important Characteristics

Cutoff Frequency Properties
  • -3dB Point: Output voltage = 70.7% of input voltage
  • Phase Shift: 45° at the cutoff frequency
  • Time Constant: τ = RC, cutoff frequency = 1/(2πτ)
  • Bandwidth: For filters, defined by the cutoff frequency
  • Roll-off Rate: 20dB/decade (≈ 6dB/octave)
  • Transfer Function: H(jω) = 1/(1 + jωRC) for low-pass

Related Calculations

Further RC Calculations

Calculation Examples

Example 1: Cutoff Frequency

Given: R = 1kΩ, C = 100nF

\[f = \frac{1}{2\pi \cdot 1000 \cdot 100 \times 10^{-9}} = 1592Hz\]

Result: The cutoff frequency is approximately 1.59kHz.

Example 2: Capacitor

Given: f = 1kHz, R = 1.6kΩ

\[C = \frac{1}{2\pi \cdot 1000 \cdot 1600} = 99.5nF\]

Result: The required capacitance is approximately 100nF.


Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •