RC time constant
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In an RC circuit, 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. (Those values are derived from the mathematical constant e, specifically 1-e^-1 and e^-1 respectively.)
The time constant <math>\tau</math> is related the cutoff frequency fc, an alternative parameter of the RC circuit, 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 | Cutoff 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
- Time constant and exponential decay
- RC circuit and RL circuit
- Filter (signal processing) and transfer function
- Cutoff frequency and frequency response
- Emphasis, preemphasis, deemphasis
- High-pass filter, low-pass filter, band-pass filter