- RC time constant
In an
RC circuit , the value of thetime constant (insecond s) is equal to the product of the circuit resistance (in ohms) and the circuitcapacitance (infarad s), i.e. = "R × C". It is the time required to charge thecapacitor , through theresistor , 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 and 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 is related to the
cutoff frequency "f"c, an alternative parameter of the RC circuit, by:. or, equivalently,: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%) :rise time (10% to 90%)
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 orphase delay or the effective propagation delay of adigital transition, may be dominated by resistive-capacitive effects, depending on the distance and other parameters, or may alternatively be dominated by inductive, wave, andspeed of light effects in other realms.Resistive-capacitive delay, or RC delay, hinders the further increasing of speed in microelectronic
integrated circuit s. 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 thealuminum conducting wire bycopper , thus reducing the resistance; it can also be reduced by changing the interlayerdielectric (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. UntilHeaviside discovered thatMaxwell'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 andexponential decay
*RC circuit andRL circuit
*Filter (signal processing) andtransfer function
*Cutoff frequency andfrequency 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 to cutoff frequency fc and back]
* [http://www.tpub.com/neets/book2/3d.htm RC time constant]
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