Time constant

Time constant is a parameter that characterizes the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is denoted by the Greek letter τ (tau). In physical systems, it must be positive.

Definition

The time constant of a system is the time it takes for the system's step response to reach approximately 63.2% of its final (asymptotic) value, under the assumption that the system's impulse response is exponential. This is equivalent to the time it takes for the system's impulse response to decay to approximately 36.8% of its initial value.

Applications

The time constant is used in many areas of science and engineering, including physics, electrical engineering, control theory, and neuroscience. It is used to characterize the frequency response of first-order systems such as RC circuits, RL circuits, and exponential decay processes.

See also

• Exponential decay
• RC circuit
• RL circuit
• Control theory
• Neuroscience

References

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