Circuit Analysis I with MATLAB Applications

Table of Contents......Page 1
Signals Described in Math Form......Page 13
The Unit Step Function......Page 14
The Unit Ramp Function......Page 22
Sampling Property of the Delta Function......Page 24
Sifting Property of the Delta Function......Page 25
Higher Order Delta Functions......Page 27
Summary......Page 31
Exercises......Page 32
Solutions to Exercises......Page 33
Definition of the Laplace Transformation......Page 37
Properties of the Laplace Transform......Page 38
The Laplace Transform of Common Functions of Time......Page 48
The Laplace Transform of Common Waveforms......Page 59
Summary......Page 65
Exercises......Page 70
Solutions to Exercises......Page 73
Partial Fraction Expansion......Page 79
Case where is Improper Rational Function ( )......Page 91
Alternate Method of Partial Fraction Expansion......Page 93
Summary......Page 96
Exercises......Page 98
Solutions to Exercises......Page 100
Circuit Transformation from Time to Complex Frequency......Page 103
Complex Impedance......Page 110
Complex Admittance......Page 112
Transfer Functions......Page 115
Summary......Page 118
Exercises......Page 120
Solutions to Exercises......Page 123
Expressing Differential Equations in State Equation Form......Page 135
Solution of Single State Equations......Page 141
The State Transition Matrix......Page 143
Computation of the State Transition Matrix......Page 145
Eigenvectors......Page 152
Circuit Analysis with State Variables......Page 156
Relationship between State Equations and Laplace Transform......Page 162
Summary......Page 169
Exercises......Page 173
Solutions to Exercises......Page 175
The Impulse Response in Time Domain......Page 183
Even and Odd Functions of Time......Page 187
Convolution......Page 189
Graphical Evaluation of the Convolution Integral......Page 190
Circuit Analysis with the Convolution Integral......Page 200
Summary......Page 202
Exercises......Page 204
Solutions to Exercises......Page 206
Wave Analysis......Page 211
Evaluation of the Coefficients......Page 212
Symmetry......Page 217
Waveforms in Trigonometric Form of Fourier Series......Page 221
Gibbs Phenomenon......Page 234
Alternate Forms of the Trigonometric Fourier Series......Page 235
Circuit Analysis with Trigonometric Fourier Series......Page 239
The Exponential Form of the Fourier Series......Page 241
Line Spectra......Page 245
Computation of RMS Values from Fourier Series......Page 250
Computation of Average Power from Fourier Series......Page 252
Numerical Evaluation of Fourier Coefficients......Page 254
Summary......Page 258
Exercises......Page 261
Solutions to Exercises......Page 263
Definition and Special Forms......Page 269
Special Forms of the Fourier Transform......Page 270
Properties and Theorems of the Fourier Transform......Page 277
Fourier Transform Pairs of Common Functions......Page 285
Finding the Fourier Transform from Laplace Transform......Page 293
Fourier Transforms of Common Waveforms......Page 295
Using MATLAB to Compute the Fourier Transform......Page 301
The System Function and Applications to Circuit Analysis......Page 302
Summary......Page 309
Exercises......Page 315
Solutions to Exercises......Page 317
Definition and Special Forms......Page 329
Properties and Theorems of the Z Tranform......Page 331
The Z Transform of Common Discrete Time Functions......Page 339
Computation of the Z transform with Contour Integration......Page 348
Transformation Between and Domains......Page 350
The Inverse Z Transform......Page 352
The Transfer Function of Discrete Time Systems......Page 366
State Equations for Discrete Time Systems......Page 371
Summary......Page 375
Exercises......Page 380
Solutions to Exercises......Page 382
The Discrete Fourier Transform (DFT)......Page 393
Even and Odd Properties of the DFT......Page 400
Properties and Theorems of the DFT......Page 402
The Sampling Theorem......Page 405
Number of Operations Required to Compute the DFT......Page 408
The Fast Fourier Transform (FFT)......Page 409
Summary......Page 420
Exercises......Page 423
Solutions to Exercises......Page 425
Filter Types and Classifications......Page 431
Basic Analog Filters......Page 432
Low-Pass Analog Filters......Page 437
Design of Butterworth Analog Low-Pass Filters......Page 441
Design of Type I Chebyshev Analog Low-Pass Filters......Page 452
Other Low-Pass Filter Approximations......Page 464
High-Pass, Band-Pass, and Band-Elimination Filters......Page 469
Digital Filters......Page 479
Summary......Page 499
Exercises......Page 503
Solutions to Exercises......Page 509
Command Window......Page 521
Roots of Polynomials......Page 523
Polynomial Construction from Known Roots......Page 524
Evaluation of a Polynomial at Specified Values......Page 526
Rational Polynomials......Page 528
Using MATLAB to Make Plots......Page 530
Multiplication, Division and Exponentiation......Page 538
Script and Function Files......Page 545
Display Formats......Page 550
Definition of a Complex Number......Page 553
Addition and Subtraction of Complex Numbers......Page 554
Multiplication of Complex Numbers......Page 555
Exponential and Polar Forms of Complex Numbers......Page 556
Matrix Definition......Page 563
Matrix Operations......Page 564
Special Forms of Matrices......Page 567
Determinants......Page 571
Minors and Cofactors......Page 574
Cramer\'s Rule......Page 578
Gaussian Elimination Method......Page 581
The Adjoint of a Matrix......Page 582
The Inverse of a Matrix......Page 583
Solution of Simultaneous Equations with Matrices......Page 585
Exercises......Page 592