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. τ = 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. These values are derived from the mathematical constant e, specifically 1 − e − 1 and e − 1 respectively.
The time constant τ is related to the cutoff frequency fc, an alternative parameter of the RC circuit, by
.
or, equivalently,
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%)
- rise time (10% to 90%)
Standard time constants and cutoff frequencies
for pre-emphasis/de-emphasis RC filters:
| Organization |
Time constant τ in µs |
Cutoff frequency fc in Hz |
|---|---|---|
| RIAA | 7958 | 20 |
| RIAA, NAB | 3183 | 50 |
| — | 1592 | 100 |
| RIAA | 318 | 500.5 |
| — | 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 |
| RIAA | 3.18 | 50000 |
[edit] 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
