RC time constant
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The RC time constant, denoted τ (lowercase
- [seconds]
It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately 36.8% of its final charge voltage. These values are derived from the mathematical constant e, where and . The following formulae use it, assuming a constant voltage applied across the capacitor and resistor in series, to determine the voltage across the capacitor against time:
- Charging toward applied voltage (initially zero voltage across capacitor, constant V0 across resistor and capacitor together) [1]
- Discharging toward zero from initial voltage (initially V0 across capacitor, constant zero voltage across resistor and capacitor together)
Cutoff frequency
The time constant is related to the cutoff frequency fc, an alternative parameter of the RC circuit, by
or, equivalently,
where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in Hz.
Short conditional equations using the value for :
- 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%)
In more complicated circuits consisting of more than one resistor and/or capacitor, the open-circuit time constant method provides a way of approximating the cutoff frequency by computing a sum of several RC time constants.
Delay
The signal delay of a wire or other circuit, measured as
Resistive-capacitive delay, or RC delay, hinders the further increasing of speed in
The typical digital propagation delay of a resistive wire is about half of R times C; since both R and C are proportional to wire length, the delay scales as the square of wire length. Charge spreads by
See also
- Cutoff frequency and frequency response
- deemphasis
- Exponential decay
- Filter (signal processing) and transfer function
- High-pass filter, low-pass filter, band-pass filter
- RL circuit, and RLC circuit
- Rise time
References
- ^ "Capacitor Discharging".
- ^ Andrew Gray (1908). Lord Kelvin. Dent. p. 265.
- ISBN 3-7643-5180-2.
- ISBN 1-4020-7835-8.
- ISBN 978-0-521-68780-5.