Time constant: Difference between revisions
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== Time_constant == | |||
<gallery> | |||
File:Single-pole_sine_wave_response.JPG|Single-pole sine wave response | |||
File:Single-pole_frequency_response.JPG|Single-pole frequency response | |||
File:Single-pole_step_response.JPG|Single-pole step response | |||
File:Series_RC_capacitor_voltage.svg|Series RC capacitor voltage | |||
File:Series_RC_resistor_voltage.svg|Series RC resistor voltage | |||
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Latest revision as of 04:33, 18 February 2025
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[edit]
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[edit]
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[edit]
References[edit]
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