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In physics and engineering, the time constant, usually denoted by the Greek letter τ (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 system that can be modeled by a single first order differential equation in time. Examples include the simplest single-stage electrical RC circuits and RL circuits.〕 The time constant is the main characteristic unit of a first-order LTI (linear time-invariant) system. In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at low frequencies. The time constant is also used to characterize the frequency response of various signal processing systems – magnetic tapes, radio transmitters and receivers, record cutting and replay equipment, and digital filters – which can be modeled or approximated by first-order LTI systems. Other examples include time constant used in control systems for integral and derivative action controllers, which are often pneumatic, rather than electrical. Time constants are a feature of the lumped system analysis (lumped capacity analysis method) for thermal systems, used when objects cool or warm uniformly under the influence of convective cooling or warming. Physically, the constant represents the time it takes the system's step response to reach of its final (asymptotic) value ''for systems that increase in value'' (say from a step increase), or it can represent the time for systems to decrease in value to (say from a step decrease). In radioactive decay the time constant is called the decay constant (λ), and it represents both the mean lifetime of a decaying system (such as an atom) before it decays, or the time it takes for all but 36.8% of the atoms to decay. For this reason, the time constant is longer than the half-life, which is the time for only 50% of the atoms to decay. ==Differential equation== (詳細はexponential decay constant and ''V'' is a function of time ''t'' : The right-hand side is the ''forcing function'' ''f(t)'' describing an external driving function of time, which can be regarded as the system ''input'', to which ''V(t)'' is the ''response'', or system output. Classical examples for ''f(t)'' are: The Heaviside step function, often denoted by ''u(t)'': : the impulse function, often denoted by ''δ(t)'', and also the sinusoidal input function: : or : where ''A'' is the ''amplitude'' of the forcing function, ''f'' is the frequency in Hertz, and ω = 2π ''f'' is the frequency in radians per second. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Time constant」の詳細全文を読む スポンサード リンク
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