Circuit Analysis A Systems Approach

by Mersereau, Russell; Jackson, Joel

• ISBN13: 9780130932242
• ISBN10: 0130932248
• Edition: 1st
• Format: Paperback
• Copyright: 2005-07-29
• Publisher: Pearson

Summary

This unique circuit analysis text was written from the perspective that circuits are implementations of continuous-time systems and stresses such system-related concepts as their frequency responses, system functions, and time-domain behavior. Intended for a one-semester course, Circuit Analysis: A Systems Approach builds upon the approach of the best-selling texts DSP First and SP First by McClellan et al. and assumes familiarity and makes extensive use of the transform domain for solving problems.Each chapter contains worked examples and is followed by problems, which are grouped into four categories: Drill Problems, Basic Problems, Advanced Problems, and Design Problems.Supplementary materials are available on a website. Materials include visualization and analysis tools designed to complement the text and increase student engagement and understanding. Solved problems and step-by-step solutions are available for instructors.

Table of Contents

Foreword	xiii
Preface	xv
Circuit Elements and Models	1	(51)
Introduction	1	(1)
Network Elements	2	(9)
Sign Conventions for Defining Element Variables	4	(1)
Resistors	5	(3)
Inductors	8	(1)
Capacitors	9	(1)
Short Circuits	10	(1)
Open Circuits	11	(1)
Switches	11	(1)
Independent Sources	11	(1)
Kirchhoff's Laws	12	(17)
Kirchhoff's Current Law (KCL)	13	(4)
Kirchhoff's Voltage Law (KVL)	17	(4)
Solving for the Element Variables in a Circuit	21	(1)
A Confusing Issue: Selecting Reference Directions	22	(3)
Elements Connected in Series and Parallel	25	(3)
Circuits with Inductors and/or Capacitors	28	(1)
Dependent Sources	29	(4)
The Role of Models	33	(1)
Chapter Summary	34	(2)
Important Points Introduced	34	(1)
New Abilities Acquired	35	(1)
Links	35	(1)
Problems	36	(16)
Drill Problems	36	(3)
Basic Problems	39	(6)
Advanced Problems	45	(5)
Design Problems	50	(2)
Writing Circuit Equations	52	(54)
The Exhaustive Method for Writing a Sufficient Set of Circuit Equations	53	(5)
Proof of Sufficiency of the Method*	53	(2)
Examples of the Method	55	(3)
Supernodes and Supermeshes	58	(6)
Supernodes	58	(1)
Supermeshes	59	(3)
Dependent Sources	62	(2)
Solving Circuit Equations	64	(8)
Matrices	64	(1)
Matrix Operations	64	(2)
Representing Linear Equations in MATLAB*	66	(1)
Matrix Descriptions of Resistive Circuits	67	(2)
Superposition of Independent Sources	69	(3)
The Node Method	72	(6)
The Mesh Method	78	(5)
Conservation of Power	83	(4)
A Confusing Issue: Proper Treatment of Sources	83	(4)
Chapter Summary	87	(1)
Important Points Introduced	87	(1)
New Abilities Acquired	87	(1)
Problems	88	(18)
Drill Problems	88	(4)
Basic Problems	92	(10)
Advanced Problems	102	(2)
Design Problems	104	(2)
Subnetworks	106	(44)
Resistor-Only Subnetworks	107	(9)
Resistors in Series	107	(2)
Resistors in Parallel	109	(1)
A Confusing Issue: Identifying Series and Parallel Elements	110	(6)
The v---i Characteristics of Two-Terminal Networks	116	(4)
Thevenin Equivalent Networks	120	(8)
Thevenin's Theorem for Resistive Networks	120	(5)
Norton's Theorem for Resistive Networks	125	(2)
Other Equivalence Relations	127	(1)
Selecting an Analysis Method	128	(5)
Graphical Analysis*	133	(2)
Chapter Summary	135	(1)
Important Points Introduced	135	(1)
New Abilities Acquired	136	(1)
Problems	136	(14)
Drill Problems	136	(2)
Basic Problems	138	(6)
Advanced Problems	144	(5)
Design Problems	149	(1)
Operational Amplifiers	150	(26)
The Ideal Opamp	150	(4)
The Node Method for Opamp Circuits	154	(2)
A Confusing Issue: Writing KCL Equations at the Input Nodes	155	(1)
Additional Examples of Operational-Amplifier Circuits	156	(8)
Noninverting Amplifier	156	(1)
Difference Amplifier	157	(1)
Summing Amplifier	158	(1)
A Confusing Issue: Opamp Output Current	159	(1)
Buffer Amplifiers and Loading	160	(1)
Voltage-Controlled Current Source	161	(1)
A ``Negative Resistor''	162	(1)
Integrator	163	(1)
Differentiator	164	(1)
Chapter Summary	164	(1)
Important Points Introduced	164	(1)
New Abilities Acquired	165	(1)
Problems	165	(11)
Drill Problem	165	(1)
Basic Problems	165	(5)
Advanced Problems	170	(5)
Design Problems	175	(1)
Laplace Transforms	176	(28)
Some Basic Signals	178	(5)
Sinusoids	178	(2)
Exponentially Weighted Sinusoids	180	(2)
Switched-Exponential Signals	182	(1)
Definition of the Laplace Transform	183	(2)
Some Properties of the Laplace Transform	185	(3)
Inverse Laplace Transforms	188	(11)
Case 1: More Poles than Zeros	189	(3)
Case 2: Fewer Poles than Zeros (m ≥ n)	192	(5)
A Confusing Issue: Using Limits to Compute Residues	197	(1)
Case 3: Repeated Roots	198	(1)
Chapter Summary	199	(1)
Important Points Introduced	199	(1)
New Abilities Acquired	199	(1)
Problems	199	(5)
Drill Problems	199	(1)
Basic Problems	200	(2)
Advanced Problems	202	(2)
Circuits in the Laplace Domain	204	(49)
Circuits with One Reactive Element	205	(8)
Differential-Equation Descriptions	205	(3)
Solving Differential Equations with Exponential Inputs	208	(3)
Solving Differential Equations by Using Laplace Transforms	211	(2)
Circuits in the Laplace Domain	213	(12)
KCL in the Laplace Domain	214	(1)
KVL in the Laplace Domain	215	(1)
Element Relations in the Laplace Domain	215	(8)
A Confusing Issue: Modelling Initial Capacitor Voltages and Inductor Currents	223	(2)
Inspection Methods for First-Order Circuits with Constant Inputs	225	(4)
Circuit Behavior at t = ∞	225	(1)
Circuit Behavior at t = 0	226	(1)
Calculating the Time Constant τ	227	(2)
Impedances and Admittances	229	(5)
Impedances Connected in Series and Parallel	230	(2)
Thevenin and Norton Equivalent Circuits*	232	(2)
Systematic Analysis Methods	234	(6)
A Set of Sufficient Equations for Analyzing a Circuit*	234	(3)
Node and Mesh Methods in the Laplace Domain	237	(2)
Operational Amplifiers in the Laplace Domain	239	(1)
Chapter Summary	240	(1)
Important Points Introduced	240	(1)
New Abilities Acquired	241	(1)
Problems	241	(12)
Drill Problems	241	(3)
Basic Problems	244	(5)
Advanced Problems	249	(3)
Design Problems	252	(1)
System Functions	253	(44)
Circuits as Systems	254	(12)
The Input-Output Point of View	254	(1)
The Complete Solution of a Circuit	255	(4)
Circuits at Initial Rest	259	(1)
Impulse Responses, Poles, and Zeros	260	(4)
The Unit-Step Response	264	(2)
Linearity and Time Invariance	266	(6)
Circuits at Initial Rest as Linear Systems	266	(1)
Circuits at Initial Rest as Time-Invariant Systems	267	(1)
Exploiting Linearity and Time Invariance	268	(4)
Responses to Switched-Exponential Inputs	272	(5)
The General Case	273	(1)
Impulse Responses of First- and Second-Order Systems	274	(3)
Two Additional Circuit Descriptions*	277	(7)
Differential-Equation Characterization at Initial Rest	277	(4)
Impulse-Response Characterization	281	(3)
Chapter Summary	284	(1)
Important Points Introduced	284	(1)
New Abilities Acquired	285	(1)
Problems	285	(12)
Drill Problems	285	(1)
Basic Problems	286	(5)
Advanced Problems	291	(3)
Design Problems	294	(3)
Sinusoidal Input Signals	297	(54)
The Sinusoidal Steady State	298	(6)
Sinusoidal Signals	298	(1)
Physical Circuits and Mathematical Models	298	(1)
Responses to Real Sinusoidal Inputs	299	(4)
Responses to Unswitched Signals	303	(1)
Analyzing Circuits by Using Phasors	304	(15)
A Simple Circuit with a Complex Exponential Input	304	(4)
The General Case	308	(8)
Networks with Multiple Sources	316	(3)
Frequency-Domain Circuit Simplifications	319	(11)
Series and Parallel Connections	319	(2)
Thevenin and Norton Equivalent Circuits	321	(2)
The Node and Mesh Methods in the Phasor Domain	323	(6)
Operational-Amplifier Circuits	329	(1)
Power in the Phasor Domain	330	(6)
Average Power	330	(1)
RMS Values	331	(1)
Power in Circuits with Sinusoidal Excitations	332	(4)
Maximum Power Transfer	336	(3)
Resistive Circuits	336	(1)
General Circuits	337	(2)
Chapter Summary	339	(1)
Important Points Introduced	339	(1)
New Abilities Acquired	340	(1)
Problems	340	(11)
Drill Problems	340	(2)
Basic Problems	342	(5)
Advanced Problems	347	(2)
Design Problems	349	(2)
Frequency Responses of Circuits	351	(47)
Spectrum Representations of Periodic Signals	352	(10)
Spectrum of a Sum of Sinusoids	352	(2)
Periodic Waveforms	354	(1)
Fourier-Series Representations	355	(3)
Response of a Circuit to a Periodic Input	358	(4)
Spectrum Representations for Aperiodic Signals	362	(4)
The Fourier Transform	362	(1)
Circuit Analysis by Using Fourier Transforms	363	(3)
The System Function and the Frequency Response	366	(9)
Graphical Interpretation of Frequency Response	366	(5)
Resonance	371	(4)
Bode Plots	375	(10)
First-Order Systems	376	(2)
Second-Order Systems	378	(1)
Multifactor Bode Plots	379	(3)
A Confusing Issue: Normalized Forms for System Functions	382	(3)
Chapter Summary	385	(1)
Important Points Introduced	385	(1)
New Abilities Acquired	386	(1)
Problems	386	(12)
Drill Problems	386	(1)
Basic Problems	387	(6)
Advanced Problems	393	(3)
Design Problems	396	(2)
Filter Circuits	398	(25)
Lowpass Filters	399	(9)
Ideal vs. Buildable Filters	400	(1)
Butterworth and Chebyshev Lowpass Filters	401	(5)
Realizations of Lowpass Second-Order Sections That Use Operational Amplifiers	406	(2)
Transforming Basic Filters	408	(7)
Frequency Scaling	409	(1)
Lowpass-to-Highpass Transformations	410	(2)
Lowpass-to-Bandpass Transformations	412	(2)
Impedance Scaling	414	(1)
Chapter Summary	415	(1)
Important Points Introduced	415	(1)
New Abilities Acquired	415	(1)
Problems	415	(8)
Drill Problems	415	(1)
Basic Problems	416	(3)
Advanced Problems	419	(2)
Design Problems	421	(2)
A Review of Complex Numbers	423	(10)
Definitions	423	(1)
Graphical Interpretation of Complex Numbers	424	(2)
Complex Exponentials	426	(3)
The Complex Conjugate	429	(1)
Drill Problems	429	(2)
Basic Problems	431	(2)
B Answers to Selected Basic Problems	433	(6)
Index	439