RC time constant

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. $au$ = "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.

A convenient short-cut is that the same formula for time constant in seconds works if R is in megohms (MΩ) and C is in microfarads (μF); or for milliseconds (ms) with kilohms (kΩ) and microfarads, the most common units in typical radio and audio electronics.

Cutoff frequency

The time constant $au$ is related to the cutoff frequency "f"_c, an alternative parameter of the RC circuit, by:$au\; =\; RC\; =\; frac\{1\}\{2\; pi\; f\_c\}$. or, equivalently,:$f\_c\; =\; frac\{1\}\{2\; pi\; R\; C\}\; =\; frac\{1\}\{2\; pi\; au\}$

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%) $t\_r\; approx\; 1.4\; au$:rise time (10% to 90%) $t\_r\; approx\; 2.2\; au$

Standard time constants and cutoff frequencies
for pre-emphasis/de-emphasis RC filters:

Delay

The signal delay of a wire or other circuit, measured as group delay or phase delay or the effective propagation delay of a digital transition, may be dominated by resistive-capacitive effects, depending on the distance and other parameters, or may alternatively be dominated by inductive, wave, and speed of light effects in other realms.

Resistive-capacitive delay, or RC delay, hinders the further increasing of speed in microelectronic integrated circuits. When the feature size becomes smaller and smaller to increase the clock speed, the RC delay plays a more and more important role. This delay can be reduced by replacing the aluminum conducting wire by copper, thus reducing the resistance; it can also be reduced by changing the interlayer dielectric (typically silicon dioxide) to low-dielectric-constant materials, thus reducing the capacitance.

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 diffusion in such a wire. Until Heaviside discovered that Maxwell's equations imply wave propagation when sufficient inductance is in the circuit, this square diffusion relationship was thought to provide a fundamental limit to the improvement of long-distance telegraph cables. [cite book | title = From Obscurity to Enigma | author = Ido Yavetz | publisher = Birkhäuser | year = 1995 | isbn = 3764351802 | url = http://books.google.com/books?id=SQszfj7biVMC&pg=PA245&dq=preece+heaviside+telegraph+square&ei=MR7uSOafJYLwsQPzm4idBw&sig=ACfU3U0-1ZMeNjbKwbRbt-DjqKXpoTWcXw#PPA244,M1 ] That old analysis was superseded in the telegraph domain, but remains relevant for long on-chip interconnects.

ee 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

References

External links

* [http://www.cvs1.uklinux.net/cgi-bin/calculators/time_const.cgi RC Time Constant Calculator]
* [http://www.sengpielaudio.com/calculator-timeconstant.htm Conversion time constant $au$ to cutoff frequency f_c and back]
* [http://www.tpub.com/neets/book2/3d.htm RC time constant]