The RC time constant, also called tau, the
time constant In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a s ...
(in
seconds) of an
RC circuit
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC c ...
, is equal to the product of the circuit
resistance (in
ohms) and the circuit
capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized ar ...
(in
farads), i.e.
:
econds
It is the time required to charge the
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
, 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 initial charge voltage. (These values are derived from the mathematical constant ''
e'':
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 across resistor and capacitor together)
:Discharging toward zero from initial voltage (initially across capacitor, constant zero voltage across resistor and capacitor together)
Cutoff frequency
The time constant
is related to the
cutoff frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather tha ...
''f''
c, 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
:
:''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%)
In more complicated circuits consisting of more than one resistor and/or capacitor, the
open-circuit time constant method The open-circuit time constant (OCT) method is an approximate analysis technique used in electronic circuit design to determine the corner frequency of complex circuits. It is a special case of zero-value time constant (ZVT) method technique when ...
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
group delay
In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifie ...
or
phase delay
In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifier, ...
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
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
effects in other realms.
Resistive-capacitive delay, or RC delay, hinders the further increasing of speed in
microelectronic
Microelectronics is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture (or microfabrication) of very small electronic designs and components. Usually, but not always, this means micrometre-sc ...
integrated circuits. When the feature size becomes smaller and smaller to increase the
clock speed
In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the pro ...
, the RC delay plays an increasingly important role. This delay can be reduced by replacing the
aluminum
Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It ha ...
conducting wire by
copper
Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
, thus reducing the resistance; it can also be reduced by changing the interlayer
dielectric
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
(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
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemica ...
in such a wire, as explained by
Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...
in the mid nineteenth century. Until
Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vec ...
discovered that
Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
...
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. That old analysis was superseded in the telegraph domain, but remains relevant for long on-chip interconnects.
[{{cite book , title = An Analog Electronics Companion , author = Scott Hamilton , publisher = Cambridge University Press , year = 2007 , isbn = 978-0-521-68780-5 , url = https://books.google.com/books?id=2BntAEtXsBMC&dq=preece+distributed+heaviside+diffusion+thomson&pg=PA580 ]
See also
*
Cutoff frequency
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather tha ...
and
frequency response
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of s ...
*
Emphasis,
preemphasis
Typically, prior to some process, such as transmission over cable, or recording to phonograph record or tape, the input frequency range most susceptible to noise is boosted. This is referred to as "pre-emphasis"before the process the signal will u ...
,
deemphasis
Typically, prior to some process, such as transmission over cable, or recording to phonograph record or tape, the input frequency range most susceptible to noise is boosted. This is referred to as "pre-emphasis"before the process the signal will u ...
*
Exponential decay
*
Filter (signal processing) and
transfer function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used ...
*
High-pass filter
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency ...
,
low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filt ...
,
band-pass filter
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.
Description
In electronics and signal processing, a filter is usually a two-port ...
*
RL circuit
A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or current source. A first-order RL circuit is composed of one resistor and one inductor, eithe ...
, and
RLC circuit
An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent componen ...
*
Rise time In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. These values may be expressed as ratiosSee for example , and . or, equivale ...
References
External links
RC Time Constant Calculator*
ttp://www.tpub.com/neets/book2/3d.htm RC time constant
Analog circuits