Teach Yourself Algebra for Electronic Circuits

Overview

Practical math to help you plan, design, and problem-solve electric circuits

The ideal tool for upgrading career-enhancing math skills, Teach Yourself Algebra for Electronic Circuits helps you learn the methods that support today's technological growth and innovation. Author Ken Jenkins has put together a genuinely user-friendly tutorial. Every chapter is a self-contained unit, making it easier to find the answers you want and learn at your own pace – without flipping through ...

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Overview

Practical math to help you plan, design, and problem-solve electric circuits

The ideal tool for upgrading career-enhancing math skills, Teach Yourself Algebra for Electronic Circuits helps you learn the methods that support today's technological growth and innovation. Author Ken Jenkins has put together a genuinely user-friendly tutorial. Every chapter is a self-contained unit, making it easier to find the answers you want and learn at your own pace – without flipping through pages, looking for connections or background. Learn or upgrade your skills with:


* Self-teaching text, complete with worked-out questions/solutions and final exams
*Math that goes beyond elementary algebra, without the burden of heavy-duty calculus you don't need
* Circuit-focused applications, illustrations, and examples
* Special help with the algebra of logic and matrices
*Hundreds of practical problems with detailed solutions throughout the book
* Over 300 illustrations to help you learn quickly and easily

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Product Details

  • ISBN-13: 9780071381826
  • Publisher: McGraw-Hill Companies, The
  • Publication date: 8/1/2001
  • Series: Tab Electronics Ser.
  • Edition number: 1
  • Pages: 576
  • Product dimensions: 7.86 (w) x 11.04 (h) x 0.94 (d)

Table of Contents

Chapter 1 Electric Charge and Electric Field. Potential Difference 1
1.1 Electrification and Electric Charge 1
1.2 Coulomb's Law and the Unit of Charge 8
1.3 Electric Field Strength 10
1.4 Potential difference; the Volt 12
Chapter 2 Electric Current. Ohm's Law. Basic Circuit Configurations 15
2.1 Electric Current 15
2.2 Electromotive Force 18
2.3 Electrical Resistance. Ohm's Law. Power 21
2.4 Some Notes on Temperature Effects 25
2.5 The Series Circuit 27
2.6 The Parallel Circuit 32
2.7 Series-Parallel Circuits 35
Chapter 3 Determinants and Simultaneous Equations 38
3.1 Introduction to Determinants 38
3.2 The Second-Order Determinant 39
3.3 Minors and Cofactors. Value of any nth-Order Determinant 41
3.4 Some Important Properties of Determinants 46
3.5 Determinant Solution of Linear Simultaneous Equations 52
3.6 Systems of Homogeneous Linear Equations 55
Chapter 4 Basic Network Laws and Theorems 58
4.1 Introduction 58
4.2 Kirchhoff's Current Law 58
4.3 Kirchhoff's Voltage Law 60
4.4 The Method of Loop Currents 62
4.5 Conductance. Millman's Theorem 66
4.6 Thevenin's Theorem 68
4.7 Norton's Theorem 70
4.8 The Method of Node Voltages 73
Chapter 5 Sinusoidal Waves. rms Value. As Vector Quantities 76
5.1 Introduction 76
5.2 The Sinusoidal Functions and the Tangent Function 77
5.3 Graphics. Extension beyond 90 Degrees, Positive and Negative 80
5.4 Choice of Waveform. Frequency. The Radian 88
5.5 Power; rms Value of a Sine Wave of Voltage or Current 93
5.6 Sinusoidal Voltages and Currents as Vectors 96
5.7 Power Calculations 105
5.8 Application of Loop Currents 108
Chapter 6 Algebra of Complex Numbers 114
6.1 Imaginary Numbers 114
6.2 Complex Numbers. Addition and Multiplication 119
6.3 Conjugates and Division of Complex Numbers 120
6.4 Graphical Representation of Complex Numbers 122
6.5 Exponential Form of a Complex Number 125
6.6 Operations in the Exponential and Polar Forms. De Moivre's Theorem 128
6.7 Powers and Roots of Complex Numbers 131
6.8 Complex Numbers as Vectors 134
Chapter 7 Inductance and Capacitance 136
7.1 Introduction 136
7.2 Introduction to Magnetism 137
7.3 Electromagnetism 138
7.4 Self-Inductance 140
7.5 The Unit of Inductance 142
7.6 Capacitors and Capacitance 144
7.7 Capacitors in Series and in Parallel 148
Chapter 8 Reactance and Impedance. Algebra of ac Networks 151
8.1 Inductive Reactance. Impedance 151
8.2 RL Networks 155
8.3 Capacitive Reactance. RC Networks 160
8.4 The General RLC Network. Admittance 165
8.5 Real and Apparent Power. Power Factor 169
8.6 Series Resonance 174
8.7 Parallel Resonance 180
Chapter 9 Impedance Transformation. Electric Filters 187
9.1 Impedance Transformation. The "L" Section 187
9.2 The "T" and "Pi" Equivalent Networks 190
9.3 Conversion of Pi to T and T to Pi 196
9.4 Impedance Transformation by T and Pi Networks 198
9.5 Frequency Response. The Basic RC and RL Filter Circuits 201
9.6 The Symmetrical T Network. Characteristic Impedance 213
9.7 Low-Pass Constant-k Filter 219
9.8 High-Pass Constant-k Filter 223
Chapter 10 Magnetic Coupling. Transformers. Three-Phase Systems 227
10.1 Introduction to Magnetic Coupling; the Transformer 227
10.2 Dot-Marked Terminals. Induced Voltage Drops 230
10.3 Sinusoidal Analysis of Magnetically Coupled Circuits 234
10.4 The "T" Equivalent of a Transformer 239
10.5 The Band-Pass Double-Tuned Transformer 241
10.6 The Ideal Iron-Core Transformer 250
10.7 The Three-Phase Power System. Introduction 255
10.8 Y-Connected Generator; Phase and Line Voltages 256
10.9 Current and Power in Balanced Three-Phase Loads 261
10.10 The Unbalanced Case; Symmetrical Components 265
10.11 Some Examples of Unbalanced Three-Phase Calculations 272
Chapter 11 Matrix Algebra. Two-Port Networks 277
11.1 Introduction to Matrix Algebra 277
11.2 Product of Two Matrices 281
11.3 The Inverse of a Square Matrix 286
11.4 Some Properties of the Unit Matrix 291
11.5 Algebraic Operations. Transpose of a Matrix 292
11.6 Matrix Equations for the Two-Port Network 294
11.7 Continuing Discussion of the Two-Port Network 299
11.8 Matrix Conversion Chart for the Two-Port Network 303
11.9 Matrix Operations for Interconnected Two-Ports 306
11.10 Notes Regarding the Interconnection Formulas 312
11.11 Some Basic Applications of the Formulas 316
Chapter 12 Binary Arithmetic. Switching Algebra 324
12.1 Analog and Digital Signals. Binary Arithmetic 324
12.2 Boolean or "Switching" Algebra. Truth Tables 338
12.3 Digital Logic Symbols and Networks 347
Chapter 13 The Digital Processor. Digital Filters 357
13.1 Bandwidth Requirements for Digital Transmission. Sampling Theorem. PAM and PCM 357
13.2 Analog Signal in Sampled Form. Unit Impulse Notation 364
13.3 The z-Transform 366
13.4 The Inverse z-Transform 373
13.5 The Discrete-Time Processor 377
13.6 The Form of, and Basic Equations for, a DT Processor 379
13.7 Stability and Instability. Poles and Zeros 383
13.8 Structure of DT Processors 389
13.9 Digital Filters; The Basic Algebra 393
Appendix 401
Note 1. Some Basic Algebra 401
Note 2. Fundamental Units 404
Note 3. Prefix Nomenclature 405
Note 4. Vectors 405
Note 5. Increment (Delta) Notation 409
Note 6. Similar Triangles. Proof of Eq. (98) 410
Note 7. Identity for sin(x + y) 411
Note 8. Often-Used Greek Letters 412
Note 9. Sinusoidal Waves of the Same Frequency 412
Note 10. Sinusoidal Waves as Vectors 413
Note 11. Rational and Irrational Numbers 414
Note 12. The Concept of Power Series 415
Note 13. Series RL Circuit. L/R Time Constant 416
Note 14. Series RC Circuit. RC Time Constant 417
Note 15. [omega]L is in Ohms 418
Note 16. jZ = Z Rotated through 90 Degrees 419
Note 17. 1/[omega]C is in Ohms 419
Note 18. Harmonic Frequencies. Fourier Series 419
Note 19. Logarithms. Decibels 421
Note 20. Phase (Time-Delay) Distortion 423
Note 21. Logarithmic Graph Paper 425
Note 22. Log XY = Log X + Log Y 426
Note 23. Discussion of Eq. (344) 426
Note 24. Amplitude Modulation. Sidebands 427
Note 25. Trigonometric Identity for (sin x sin y) 429
Note 26. L Proportional to N[superscript 2] 429
Note 27. Arrow and Double-Subscript Notation 430
Note 28. Square Root of 3 in Three-Phase Work 431
Note 29. Proof of Eq. (467) (True Power) 432
Note 30. The Transistor as Amplifier 432
Note 31. Shifting Theorem 434
Note 32. Unit Impulse 435
Note 33. Algebraic Long Division 437
Solutions to Problems 440
Index 551
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