01 March, 2007

Transient Response and Time constant

It if defined as the response of a system caused by a sudden change of DC voltage, current, or load.These sudden changes are mostly found as the result of the operation of switching devices. Engineers use voltage regulators and surge suppressors to prevent transients in electricity from affecting delicate equipment.

Time constant (τ) :
In physics and engineering, the time constant usually denoted by the Greek letter τ, (tau), characterizes the frequency response of a first-order, linear time-invariant (LTI) system. Examples include electrical RC circuits and RL circuits. It 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 constant is the time required for a physical quantity to rise from zero to 1-1/e (that is, 63.2%) of its final steady value when it varies with time t as 1 - e-kt. The time required for a physical quantity to fall to 1/e (that is, 36.8%) of its initial value when it varies with time t as e-kt. Generally, the time required for an instrument to indicate a given percentage of the final reading resulting from an input signal. Also known as lag coefficient.

Time constants in electrical circuits :
In an RL circuit, the time constant τ (in seconds) is

where R is the resistance (in ohms) and L is the inductance (in henries).

Similarly, in an RC circuit, the time constant τ is:

where R is the resistance (in ohms) and C is the capacitance (in farads).

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