AC Transient Analysis.

Introduction:

A transient analysis deals with the behaviour of an electric circuit as a function of time . A circuit passes though a transition period before arriving steady-state condition when the circuit is switched with an ac supply, in which the currents and voltages are not periodic functions of time. If a circuit contains an energy storage element(s), a transient can also occur in a dc circuit after a sudden change due to switching.SPICE allows simulating transient behaviors, by assigning initial conditions to circuit elements, generating sources, and the opening and closing of switches. Students are advised to apply the techniques for transient analysis of simple circuit laws and to verify the SPICE results by hand calculations.

Theory: If an RL circuit is energized with and ac voltage then the expression of dynamic

Equilibrium is:

.

where, i is current through RL branch, Em sin(ώ+λ) is the applied voltage with λ phase. The solution for current in RL circuit is:

........................1 

where, impedance

 

   

and phase difference between voltage and current,

In (1) first and second terms are steady-state and transient respectively.

Similarly, for RC circuit the expression of dynamic Equilibrium is:

where, q is the charge and i= dq/dt

The solution for current in RC circuit is:

................................2

where, impedance-

  

and phase difference between voltage and current,

In (2) first and second terms are steady-state and transient respectively.

For RLC branch circuit the expression of dynamic Equilibrium is:

 

If

 then expression of current can be written as follow:

If

then expression of current can be written as follow:

where,