RC time constant

The RC time constant, usually denoted by the Greek letter τ (tau), is a parameter that characterizes the frequency response of a resistance-capacitance (RC) circuit. It is also used to characterize the frequency response of various signal processing systems – magnetic tapes, radio transmitters and receivers, record cutting and replay equipment, and digital filters – which can be modeled or approximated by RC circuits.

The value of the time constant (in seconds) is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e. <math>\tau<math> = R · C. It is the time required to charge the capacitor, through the resistor, to 63.2 (~ 63) percent of full charge; or to discharge it to 36.8 (~ 37) percent of its initial voltage.

The cutoff frequency f_c, an alternative parameter of the RC circuit, is related to the time constant by

<math>f_c = \frac{1}{2 \pi \cdot R C} = \frac{1}{2 \pi \cdot \tau}<math>,

or, equivalently,

<math>\tau = R \cdot C = \frac{1}{2 \pi \cdot f_c}<math>.

Short conditional equations:

(f_c in Hz) = 159155 / (τ in µs)

(τ in µs) = 159155 / (f_c in Hz)

Other useful equations are:

rise time (20% to 80%) <math>t_r \approx 1.4 \tau<math>

rise time (10% to 90%) <math>t_r \approx 2.2 \tau<math>

Standard time constants and cutoff frequencies
for pre-emphasis/de-emphasis RC filters:

See also

• Filter (signal processing) and transfer function
• Cutoff frequency and frequency response
• Emphasis, preemphasis, deemphasis
• High-pass filter, low-pass filter, band-pass filter

External links

• Conversion time constant <math> \tau <math> to cutoff frequency f_c and back