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 µs)
- (τ in µs) = 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 µs | 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
- 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 fc and back (http://www.sengpielaudio.com/calculator-timeconstant.htm)de:Zeitkonstante