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3/14/25, 2:50 AM about:blank EEE117: Electrical Circuits and Networks - Resonance Analysis and Q Factor EEE117: Electrical Circuits and Networks 10 Transient Analysis 10.1 Introduction ‘The analysis performed using the "jo" or phasor diagram approach is known as a frequency domain analysis. The driving source is assumed to be an ideal sinusoid and the independent variable is frequency; the analysis evaluates gain and phase as a function of frequency and time is not available as an explicit variable. (You will iscoverin ater years tha ther are methods that allow the time response to be deiveed from knowledge of the frequency domain behaviour -time and frequency are in fact intimately [inked - but we will not deal with those issues here.) ‘To work out circuit performance as a function of time one must perform a transient analysis. For transient problems, concepts such as impedance and admittance have no meaning so inductors and capacitors must be described by their differential (or integral) V-1 relationships. Resistors, of course, obey Ohm’s law irrespective of whether the variable of interest is time or frequency. Transient analysis usually investigates the response of a circuit to a driving source input in the form of an ideal step. An ideal step input is an instantaneous change in input voltage from one value that has existed from f =~ to t = 0 to another that exists fron t= 0 to f= +o Although it might appear that this is a fairly unrealistic sort of signal itis very useful tool for helping to work out the response due to pulses, a much more commonly encountered and useful signal form. 10.2 Working out initial conditions (One of the things one must define in order to complete the solution of.a step response problem is the set of initial conditions of voltages across and sometimes current through the various elements in the circuit. There are three sets of conditions that are relatively easy to work out + the conditions at = 0" (immediately before the instant of the step) + the conditions at ¢= 0° (immediately after the instant of the step) + the conditions at = o> (a very long time after the step) ‘Assume that the step input voltage changes from V; for all t <0 to V2 for all t > 0. The conditions at ¢ = 0- are easy to work out because the step voltage has been at V; for all time fore = 0 so is effectively a dc input. At de, the voltage across any (ideal) inductors must be zero and the current through any (ideal) capacitors must be zero. By a similar argument, the conditions at t=» can be found by working out the dc conditions resulting from an input of V;. The conditions at ¢= 0° are not hard to evaluate but one must bear in mind that both the Ls and Cs will have some stored energy. At the instant of the step, each L will want to keep constant the current through it and each C will want to keep constant the voltage across it. Thus the voltage across the Cs will not change during the transient (ie, Ve @ t= 0" = Ve@ 0” will be true) and the current through the Zs will not change during the transient (ie, 1, @ @t=0). Soatt=0" (and only at = 0°) the Zs can be represented as current sources and the Cs as voltage sources, both keeping the currents and voltages that they had at r= 0". As evolves from 1 = 0° towards 1 =o», the stored energy in the Ls and Cs changes slowly from its t= 0 value to its t= value, An example ‘on how to apply these ideas is given below. 1 HII7_3/RCT/O1-2013 1/20 
