RC time constant

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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 time constant <math>\tau<math>, an alternative parameter of the RC circuit, is related the cutoff frequency fc, by

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

or, equivalently,

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

Short conditional equations:

(fc in Hz) = 159155 / (τ in Ás)
(τ in Ás) = 159155 / (fc 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:

Organization Time constant <math> \tau <math>
in Ás
Cuttoff frequency fc
in Hz
RIAA 7958 20
RIAA, NAB 3183 50
- 1592 100
RIAA 318 500
- 200 796
- 140 1137
MC 120 1326
- 100 1592
MC 90 1768
RIAA 75 2122
FM 70 2274
NAB, PCM 50 3183
DIN 35 4547
- 25 6366
AES 17.5 9095
PCM 15 10610

See also

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