TAILIEUCHUNG - Electric Circuits, 9th Edition P52

Electric Circuits, 9th Edition P52. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 486 The Laplace Transform in Circuit Analysis assessment problem Objective 3 Understand the definition and significance of the transfer function be able to derive a transfer function a Derive the numerical expression for the transfer function V 7 for the circuit shown. b Give the numerical value of each pole and zero of H s . NOTE Also try Chapter Problem . Answer a H s 10 s 2 2s 10 b -pi -1 j3 -p2 -1 - 3 z -2. The Location of Poles and Zeros of s For linear lumped-parameter circuits H s is always a rational function of .y. Complex poles and zeros always appear in conjugate pairs. The poles of H s must lie in the left half of the .v plane if the response to a bounded source one whose values lie within some finite bounds is to be bounded. The zeros of H s may lie in either the right half or the left half of the 5 plane. With these general characteristics in mind we next discuss the role that H s plays in determining the response function. We begin with the partial fraction expansion technique for finding y t . The Transfer Function in Partial Fraction Expansions From Eq. we can write the circuit output as the product of the transfer function and the driving function Y s H s X s . We have already noted that H s is a rational function of s. Reference to Table shows that X 5 also is a rational function of 5 for the excitation functions of most interest in circuit analysis. Expanding the right-hand side of Eq. into a sum of partial fractions produces a term for each pole of H s and A s . Remember from Chapter 12 that poles are the roots of the denominator polynomial zeros are the roots of the numerator polynomial. The terms generated by the poles of H a give rise to the transient component of the total response whereas the terms generated by the poles of X .s- give rise to the steadystate component of the response. By steady-state response we mean the response that exists after the transient components have become negligible. .

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