Transient analysis is done for a circuit undergoing a transition period. When the circuit is switched from one condition to another the circuit undergoes a transition. Transition is due to a change in the applied source or change in the circuit element. During the transition period, currents and voltages of the elements change from one value to another. This is called the transient period and its analysis is called transient analysis. After this period the circuit enters into a steady state. This article gives notes on transient analysis.
The value of current and voltage changing depends upon the type of circuit element and their inherent property so, knowledge of these elements is important.
Transient Analysis Notes: Inherent Property of Circuit Element
Resistor opposes the flow of current in an electric circuit. It dissipates power in the circuit in the form of heat so, it cannot store energy. Hence resistor behavior does not change during switching of the circuit from one condition to another.
Then for resistor, the mathematical term defining the relationship of voltage and current is given by Ohm’s law.
Where, V= Voltage across resistor
I= Current through the resistor
R= Resistance of the resistor in Ohms
The inductor is an energy storage device. It stores energy in an electromagnetic field and opposes the rate of flow of current in the circuit. When the current is increasing, the inductor tries to decrease the current and vice-versa. Hence transient occurs in the circuit having an inductor. As there is a change in stored energy of the inductor during circuit operation.
The figure below shows an inductor with voltage vL (t) and the current through it is iL(t).
Where L is the inductance of the inductor measured in henry.
Then expression for current through the inductor is,
Here, for the second expression of iL(t) we just breakdown the limits of integrals. Where iL(0+) is the initial condition of the inductor. It gives the value of energy stored in the inductor in terms of current at the instant of switching.
The capacitor is an energy storage device and it stores energy in an electrostatic field. So, transient occurs in a circuit having a capacitor as there is a change in stored energy of the capacitor during circuit operation.
The figure below shows a capacitor with voltage vC (t) and current through it is iC (t).
Where C is the capacitance of the capacitor measured in Farad.
Expression for the voltage across the capacitor is,
Where vC(0+) is the initial condition of the capacitor which gives the value of energy stored in the capacitor in terms of voltage at the instant of switching.
Relationship Parameter of Circuit Element for Transient Analysis
For transient analysis, the relationship parameter is very important because it shows the current-voltage relationship of the circuit elements (resistor, capacitor, and inductor). For transient analysis whose approach can be either classical method or by Laplace transformation these relationships must be known.
|Parameter of Circuit Element||Voltage and Current Relationships|
The current-voltage relationship for inductor and capacitor is in differential form. So the equation governing the circuit will be a differential equation and hence for solving differential equations we have to find the boundary conditions or the initial conditions.
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