Electric Circuits, 9th Edition P54. 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. | 506 The Laplace Transform in Circuit Analysis Summary We can represent each of the circuit elements as an s-domain equivalent circuit by Laplace-transforming the voltage-current equation for each element Resistor V RI Inductor V sLI - LIq Capacitor V l sC I Vo s In these equations V v I 7 is the initial current through the inductor and Vq is the initial voltage across the capacitor. See pages 468-469. We can perform circuit analysis in the 5 domain by replacing each circuit element with its s-domain equivalent circuit. The resulting equivalent circuit is solved by writing algebraic equations using the circuit analysis techniques from resistive circuits. Table summarizes the equivalent circuits for resistors inductors and capacitors in the s domain. See page 470. Circuit analysis in the 5 domain is particularly advantageous for solving transient response problems in linear lumped parameter circuits when initial conditions are known. It is also useful for problems involving multiple simultaneous mesh-current or node-voltage equations because it reduces problems to algebraic rather than differential equations. See pages 476-478. The transfer function is the s-domain ratio of a circuit s output to its input. It is represented as where Y s is the Laplace transform of the output signal and A s is the Laplace transform of the input signal. See page 484. The partial fraction expansion of the product H s X s yields a term for each pole of H s and Y .y . The H s terms correspond to the transient component of the total response the X s terms correspond to the steady-state component. See page 486. If a circuit is driven by a unit impulse x f 8 f then the response of the circuit equals the inverse Laplace transform of the transfer function y t X h f . See pages 488-489. A time-invariant circuit is one for which if the input is delayed by a seconds the response function is also delayed by a seconds. See page 488. Tire output of a circuit y t can be computed by convolving .
