ABSTRACT
At the end of this chapter you should be able to: • determine the transient response of currents andvoltages in R-L, R-C and L-R-C series circuits using differential equations
• define the Laplace transform of a function • use a table of Laplace transforms of functions commonly met in electrical engineering for transient analysis of simple networks
• use partial fractions to deduce inverse Laplace transforms
• deduce expressions for component and circuit impedances in the s-plane given initial conditions
• use Laplace transform analysis directly from circuit diagrams in the s-plane
• deduce Kirchhoff’s law equations in the s-plane for determining the response of R-L, R-C and L-R-C networks, given initial conditions
• explain the conditions for which an L-R-C circuit response is over, critical, under or zero-damped and calculate circuit responses
• predict the circuit response of an L-R-C network, given non-zero initial conditions
45.1 Introduction
A transient state will exist in a circuit containing one or more energy storage elements (i.e. capacitors and inductors) whenever the energy conditions in the circuit change, until the new steady state condition is reached. Transients are caused by changing the applied voltage or current, or by changing any of the circuit elements; such changes occur due to opening and closing switches. Transients were introduced in Chapter 17 where growth and decay curves were constructed and their equations stated for step inputs only. In this chapter, such equations are developed analytically by using both differential equations and Laplace transforms for different waveform supply voltages.
