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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. = 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 fc, an alternative parameter of the RC circuit, is related to the time constant by
- ,
or, equivalently,
- .
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
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
|
| - | 90 | 1768
|
| RIAA | 75 | 2122
|
| FM | 70 | 2274
|
| NAB | 50 | 3183
|
| DIN | 35 | 4547
|
| - | 25 | 6366
|
| AES | 17.5 | 9095
|
| PCM | 15 | 10610
|
1 See also
- Filter (signal processing)In electronics and signal processing, a filter is a device or process that modifies a signal. Usually a filter has a non-uniform transfer function; i. its gain or attenuation depends on the signal's frequency. An analog filter is implemented using analog and transfer functionA transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. It is mainly used in linear system theory, signal processing, communications theory, and control theory. Signal processing
- Cutoff frequency and frequency response
- EmphasisThe word emphasis in addition to its main dictionary meaning, may have the following techincal meanings. Emphasis, a notion from FM signal transmission Emphasis, in typography: visual enhancement a part of a text to make it noticeable., preemphasisIn telecommunication, preemphasis is a system process designed to increase, within a band of frequencies, the magnitude of some (usually higher) frequencies with respect to the magnitude of other (usually lower) frequencies in order to improve the overall, deemphasis
- High-pass filter, low-pass filter, band-pass filter
