# lab4 - NORTHWESTERN UNIVERSITY Department of Electrical and...

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Page 1 NORTHWESTERN UNIVERSITY Department of Electrical and Computer Engineering ECE-221 Fundamentals of Circuits L AB 4: S ECOND -O RDER T RANSIENT R ESPONSES Part A: Second order transient response A1. Series RLC Filter Theory Consider the following series RLC circuit. Figure 1 We will determine the complete step response v R ( t ) through analysis of this circuit. The fundamental integro-differential equation for this series circuit is = - + + t t t idt C Ri dt di L 0 0 ) ( v 1 1.1) Carry out partial differentiation of this equation with respect to t to get a second- order differential equation. Clearly there are three cases of interest. Depending on the choice of R , L , and C , the response may be underdamped, critically damped, or overdamped. 1.2) Write down the general form of the solution for i ( t ) for all three cases. 1.3) What are a , w 0 , and w d for this circuit? Let ζ be defined as the damping ratio, ζ = a / w 0 . Express this ratio in terms of R , L , and

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lab4 - NORTHWESTERN UNIVERSITY Department of Electrical and...

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