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RC time constant : ウィキペディア英語版
RC time constant
The RC time constant, also called tau, is the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.
: \tau = RC
It is the time required to charge the capacitor, through the resistor, by ≈ 63.2 percent of the difference between the initial value and final value or discharge the capacitor to ≈36.8 percent. This value is derived from the mathematical constant ''e'', specifically 1-e^, more specifically as voltage to charge the capacitor versus time
:Charging V(t) = V_0(1-e^) 〔http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capdis.html〕
:Discharging V(t) = V_0(e^)
==Cutoff frequency==
The time constant \tau is related to the cutoff frequency ''f''c, an alternative parameter of the RC circuit, by
:\tau = RC = \frac
or, equivalently,
:f_c = \frac = \frac
where resistance in ohms and capacitance in farads yields the time constant in seconds or the frequency in Hz.
Short conditional equations:
:''f''c in Hz = 159155 / τ in µs
:τ in µs = 159155 / ''f''c in Hz
Other useful equations are:
:rise time (20% to 80%) t_r \approx 1.4 \tau \approx \frac
:rise time (10% to 90%) t_r \approx 2.2 \tau \approx \frac
Standard time constants and cutoff frequencies
for pre-emphasis/de-emphasis RC filters:
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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