ELECTRIC CIRCUITS EIGHTH EDITION

Slides:



Advertisements
Similar presentations
THE LAPLACE TRANSFORM IN CIRCUIT ANALYSIS
Advertisements

Applications of Laplace Transforms Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.
Electronic Circuits, Tenth Edition James W. Nilsson | Susan A. Riedel Copyright ©2015 by Pearson Higher Education. All rights reserved. CHAPTER 9 Sinusoidal.
Lect15EEE 2021 Systems Concepts Dr. Holbert March 19, 2008.
The Laplace Transform in Circuit Analysis
Lect13EEE 2021 Laplace Transform Solutions of Transient Circuits Dr. Holbert March 5, 2008.
ECE 3183 – EE Systems Chapter 2 – Part A Parallel, Series and General Resistive Circuits.
Lecture 181 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001.
Feb 23, 2007 EEE393 Basic Electrical Engineering K.A.Peker Signals and Systems Introduction EEE393 Basic Electrical Engineering.
Chapter 4 The Fourier Transform EE 207 Dr. Adil Balghonaim.
Introduction to Frequency Selective Circuits
Lecture 27 Review Phasor voltage-current relations for circuit elements Impedance and admittance Steady-state sinusoidal analysis Examples Related educational.
Chapter 10 Sinusoidal Steady-State Analysis
ES250: Electrical Science
A sinusoidal current source (independent or dependent) produces a current That varies sinusoidally with time.
Network Functions Definition, examples , and general property
ECE 8443 – Pattern Recognition EE 3512 – Signals: Continuous and Discrete Objectives: First-Order Second-Order N th -Order Computation of the Output Signal.
Copyright ©2011, ©2008, ©2005 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Electric Circuits, Ninth Edition James.
APPLICATION OF THE LAPLACE TRANSFORM
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc. Lecture 12 First Order Transient.
Sinusoidal Steady-state Analysis Complex number reviews Phasors and ordinary differential equations Complete response and sinusoidal steady-state response.
THE LAPLACE TRANSFORM IN CIRCUIT ANALYSIS. A Resistor in the s Domain R + v i v=Ri (Ohm’s Law). V(s)=RI(s R + V I.
Chapter 16 Applications of the Laplace Transform
ES250: Electrical Science
The Laplace Transform in Circuit Analysis
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc. Lecture 16 Phasor Circuits, AC.
Review Part 3 of Course. Passive Circuit Elements i i i + -
ECE 8443 – Pattern Recognition ECE 3163 – Signals and Systems Objectives: First-Order Second-Order N th -Order Computation of the Output Signal Transfer.
Chapter 3 mathematical Modeling of Dynamic Systems
CHAPTER 4 Laplace Transform.
CHAPTER 4 Laplace Transform.
CIRCUIT ANALYSIS USING LAPLACE TRANSFORM
1 ECE 3336 Introduction to Circuits & Electronics Note Set #10 Phasors Analysis Fall 2012, TUE&TH 4:00-5:30 pm Dr. Wanda Wosik.
Depok, October, 2009 Laplace Transform Electric Circuit Circuit Applications of Laplace Transform Electric Power & Energy Studies (EPES) Department of.
Fundamentals of Electric Circuits Chapter 16 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Leo Lam © Signals and Systems EE235. Leo Lam © Laplace Examples A bunch of them.
APPLICATION OF THE LAPLACE TRANSFORM
10. Laplace TransforM Technique
1 Alexander-Sadiku Fundamentals of Electric Circuits Chapter 16 Applications of the Laplace Transform Copyright © The McGraw-Hill Companies, Inc. Permission.
ECE Networks & Systems Jose E. Schutt-Aine
EE 207 Dr. Adil Balghonaim Chapter 4 The Fourier Transform.
Lecture 18 Review: Forced response of first order circuits
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc. Lecture 3 Circuit Laws, Voltage.
Complex Impedances Sinusoidal Steady State Analysis ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall.
Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.
1 Lecture #18 EGR 272 – Circuit Theory II Transfer Functions (Network Functions) A transfer function, H(s), can be used to describe a system or circuit.
A sinusoidal current source (independent or dependent) produces a current That varies sinusoidally with time.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
CSE 245: Computer Aided Circuit Simulation and Verification Instructor: Prof. Chung-Kuan Cheng Winter 2003 Lecture 2: Closed Form Solutions (Linear System)
CONTROL SYSTEM UNIT - 6 UNIT - 6 Datta Meghe Institute of engineering Technology and Research Sawangi (meghe),Wardha 1 DEPARTMENT OF ELECTRONICS & TELECOMMUNICATION.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL.
ELECTRIC CIRCUITS EIGHTH EDITION
Sinusoidal Excitation of Circuits
ELECTRIC CIRCUITS EIGHTH EDITION
DEPT.:-ELECTRONICS AND COMMUNICATION SUB: - CIRCUIT & NETWORK
Chapter 16 Applications of the Laplace Transform
Network Analysis and Synthesis
Electrical Circuits_Lecture4
5. Modeling of Electrical Systems
ECE 3301 General Electrical Engineering
Application of the Laplace Transform
Fundamentals of Electric Circuits Chapter 16
Fundamentals of Electric Circuits Chapter 15
Signals and Systems EE235 Lecture 31 Leo Lam ©
UNIT-1 Introduction to Electrical Circuits
CHAPTER 4 Laplace Transform. EMT Signal Analysis.
Presentation transcript:

ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL ELECTRIC CIRCUITS EIGHTH EDITION

THE LAPLACE TRANSFORM IN CIRCUIT ANALYSIS CHAPTER 13 THE LAPLACE TRANSFORM IN CIRCUIT ANALYSIS © 2008 Pearson Education

CONTENTS 13.1 Circuit Elements in the s Domain 13.2 Circuit Analysis in the s Domain 13.3 Applications 13.4 The Transfer Function 13.5 The Transfer Function in Partial Fraction Expansions © 2008 Pearson Education

CONTENTS 13.6 The Transfer Function and the Convolution Integral 13.7 The Transfer Function and the Steady- State Sinusoidal Response 13.8 The Impulse Function in Circuit Analysis © 2008 Pearson Education

13.1 Circuit Elements in the s Domain We can represent each of the circuit elements as an s-domain equivalent circuit by Laplace-transforming the voltage-current equation for each elements: Resistor: V = RI Inductor: V = s LI – LI0 Capacitor: V = (1/s C)I + V0 /s © 2008 Pearson Education

13.1 Circuit Elements in the s Domain In these equations, I0 = initial current through the inductor, V0 = initial voltage across the capacitor. V = L {v}, I = L {i) © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The resistance element. Time domain Frequency domain © 2008 Pearson Education

13.1 Circuit Elements in the s Domain An inductor of L henrys carrying an initial current of I0 amperes © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The series equivalent circuit for an inductor of L henrys carrying an initial current of I0 amperes © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The parallel equivalent circuit for an inductor of L henrys carrying an initial current of I0 amperes © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The s-domain circuit for an inductor when the initial current is zero © 2008 Pearson Education

13.1 Circuit Elements in the s Domain A capacitor of C farads initially charged to V0 volts © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The parallel equivalent circuit for a capacitor initially charged to V0 volts © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The series equivalent circuit for a capacitor initially charged to V0 volts © 2008 Pearson Education

13.1 Circuit Elements in the s Domain The s-domain circuit for a capacitor when the initial voltage is zero © 2008 Pearson Education

13.1 Circuit Elements in the s Domain We can perform circuit analysis in the s- 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. © 2008 Pearson Education

13.1 Circuit Elements in the s Domain Summary of the s-domain equivalent circuits © 2008 Pearson Education

13.2 Circuit Analysis in the s Domain Circuit analysis can be performed in the s domain by replacing each circuit element with its s-domain equivalent circuit. Ohm’s Law in the s-domain © 2008 Pearson Education

13.3 Applications Circuit analysis in the s domain is particularly advantageous for solving transient response problems in linear lumped parameter circuits when initial conditions are known. © 2008 Pearson Education

13.3 Applications 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. © 2008 Pearson Education

13.3 Applications The Natural Response of an RC Circuit The capacitor discharge circuit An s-domain equivalent circuit An s-domain equivalent circuit © 2008 Pearson Education

13.3 Applications The Step Response of a Parallel Circuit The step response of a parallel RLC circuit An s-domain equivalent circuit © 2008 Pearson Education

13.3 Applications The Step Response of a Multiple Mesh Circuit The multiple-mesh RL circuit An s-domain equivalent circuit © 2008 Pearson Education

13.3 Applications The Use of Thévenin’s Equivalent A circuit to be analyzed using Thévenin’s equivalent in the s domain An s-domain model of the circuit A simplified version of the circuit, using a Thévenin’s equivalent © 2008 Pearson Education

13.3 Applications The Use of Superposition A circuit showing the use of superposition in s-domain analysis The s-domain equivalent for the above circuit © 2008 Pearson Education

13.3 Applications The Use of Superposition The circuit with Vg acting alone The circuit with Ig acting alone © 2008 Pearson Education

13.3 Applications The Use of Superposition The circuit with energized inductor acting alone The circuit with energized capacitor acting alone © 2008 Pearson Education

13.4 The Transfer Function The transfer function is the s-domain ratio of a circuit’s output to its input. It is represented as Y(s) is the Laplace transform of the output signal, X(s) is the Laplace transform of the input signal. © 2008 Pearson Education

13.5 The Transfer Function in Partial Fraction Expansions The partial fraction expansion of the product H(s)X(s) yields a term for each pole of H(s) and X(s). The H(s) terms correspond to the transient component of the total response; the X(s) terms correspond to the steady-state component. © 2008 Pearson Education

13.5 The Transfer Function in Partial Fraction Expansions If a circuit is driven by a unit impulse, x(t) = δ(t), then the response of the circuit equals the inverse Laplace transform of the transfer function, y(t) = L -1{H(s)} = h(t) © 2008 Pearson Education

13.5 The Transfer Function in Partial Fraction Expansions 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. © 2008 Pearson Education

13.6 The Transfer Function and the Convolution Integral The output of a circuit, y(t), can be computed by convolving the input, x(t), with the impulse response of the circuit, h(t): © 2008 Pearson Education

13.6 The Transfer Function and the Convolution Integral The excitation signal of x(t) A general excitation signal Approximating x(t) with series of pulses Approximating x(t) with a series of impulses © 2008 Pearson Education

13.6 The Transfer Function and the Convolution Integral The approximation of y(t) The impulse response Summing the impulse responses © 2008 Pearson Education

13.6 The Transfer Function and the Convolution Integral © 2008 Pearson Education

13.6 The Transfer Function and the Convolution Integral © 2008 Pearson Education

13.7 The Transfer Function and the Steady-State Sinusoidal Response We can use the transfer function of a circuit to compute its steady-state response to a sinusoidal source. To make the substitution s = jω in H(s) and represent the resulting complex number as a magnitude and phase angle. © 2008 Pearson Education

13.7 The Transfer Function and the Steady-State Sinusoidal Response If x(t) = A cos(ωt + ø), H(jω) = |H(jω)|e jθ(ω) then Steady-state sinusoidal response computed using a transfer function © 2008 Pearson Education

13.8 The Impulse Function in Circuit Analysis Laplace transform analysis correctly predicts impulsive currents and voltages arising from switching and impulsive sources. The s-domain equivalent circuits are based on initial conditions at t = 0-, that is, prior to the switching. © 2008 Pearson Education

13.8 The Impulse Function in Circuit Analysis A circuit showing the creation of an impulsive current The s-domain equivalent circuit © 2008 Pearson Education

13.8 The Impulse Function in Circuit Analysis The plot of i(t) versus t for two different values of R © 2008 Pearson Education

13.8 The Impulse Function in Circuit Analysis A circuit showing the creation of an impulsive voltage The s-domain equivalent circuit © 2008 Pearson Education

THE END © 2008 Pearson Education