Transient Response Analysis

Unit - III

TRANSIENT RESPONSE ANALYSIS

INTRODUCTION

The V - i relationships across the inductors and capacitors involve integral and differential relationship. By applying KCL and KVL to circuits containing L and C we get equations called integro differential equations. Differential equations contain functions and their derivatives. Integral equations contain functions and their integrals.

Consider the differential equation,

This equation involves a relationship between two variables i.e., x (t) and t. t is independent variable whereas x (t) is dependent variable.

f (t) is called forcing function.

The order of a differential equation represents the highest derivative present in the equation. In the d²x(t) / dt² equation (1), second derivation is the highest derivative. Hence equation (1) is the second-order differential equation. The coefficients of the terms (ɑ₀, ɑ₁, ɑ₂) on the left hand side of the equation (1) are constants. So it is considered as time-invariant.

A linear differential equation is one in which the dependent variable and its derivatives appear in first power only. For example, equation (1) is a linear differential equation.

If f (t) is zero, then it is homogeneous differential equations, otherwise it is non-homogeneous.