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Sixth Edition, last update July 25, 2007 2 Lessons In Electric Circuits, Volume II – AC By Tony R. Kuphaldt Sixth Edition, last update July 25, 2007 i c 2000-2008, Tony R. Kuphaldt This book is published under the terms and conditions of the Design Science License. These terms and conditions allow for free copying, distribution, and/or modification of this document by the general public. The full Design Science License text is included in the last chapter. As an open and collaboratively developed text, this book is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Design Science License for more details. Available in its entirety as part of the Open Book Project collection at: www.ibiblio.org/obp/electricCircuits PRINTING HISTORY • First Edition: Printed in June of 2000. Plain-ASCII illustrations for universal computer readability. • Second Edition: Printed in September of 2000. Illustrations reworked in standard graphic (eps and jpeg) format. Source files translated to Texinfo format for easy online and printed publication. • Third Edition: Equations and tables reworked as graphic images rather than plain-ASCII text. • Fourth Edition: Printed in November 2001. Source files translated to SubML format. SubML is a simple markup language designed to easily convert to other markups like LATEX, HTML, or DocBook using nothing but search-and-replace substitutions. • Fifth Edition: Printed in November 2002. New sections added, and error corrections made, since the fourth edition. • Sixth Edition: Printed in June 2006. Added CH 13, sections added, and error corrections made, figure numbering and captions added, since the fifth edition. ii Contents 1 BASIC AC THEORY 1 1.1 What is alternating current (AC)? ........................... 1 1.2 AC waveforms ....................................... 6 1.3 Measurements of AC magnitude ............................ 12 1.4 Simple AC circuit calculations ............................. 19 1.5 AC phase .......................................... 20 1.6 Principles of radio .................................... 23 1.7 Contributors ........................................ 25 2 COMPLEX NUMBERS 27 2.1 Introduction ........................................ 27 2.2 Vectors and AC waveforms ............................... 30 2.3 Simple vector addition .................................. 32 2.4 Complex vector addition ................................. 35 2.5 Polar and rectangular notation ............................. 37 2.6 Complex number arithmetic .............................. 42 2.7 More on AC ”polarity” .................................. 44 2.8 Some examples with AC circuits ............................ 49 2.9 Contributors ........................................ 55 3 REACTANCE AND IMPEDANCE – INDUCTIVE 57 3.1 AC resistor circuits .................................... 57 3.2 AC inductor circuits ................................... 59 3.3 Series resistor-inductor circuits ............................. 64 3.4 Parallel resistor-inductor circuits ............................ 71 3.5 Inductor quirks ...................................... 74 3.6 More on the “skin effect” ................................. 77 3.7 Contributors ........................................ 79 4 REACTANCE AND IMPEDANCE – CAPACITIVE 81 4.1 AC resistor circuits .................................... 81 4.2 AC capacitor circuits ................................... 83 4.3 Series resistor-capacitor circuits ............................ 87 4.4 Parallel resistor-capacitor circuits ........................... 92 iii iv CONTENTS 4.5 Capacitor quirks ..................................... 95 4.6 Contributors ........................................ 97 5 REACTANCE AND IMPEDANCE – R, L, AND C 99 5.1 Review of R, X, and Z ................................... 99 5.2 Series R, L, and C .................................... 101 5.3 Parallel R, L, and C ................................... 106 5.4 Series-parallel R, L, and C ............................... 110 5.5 Susceptance and Admittance .............................. 119 5.6 Summary ......................................... 120 5.7 Contributors ........................................ 120 6 RESONANCE 121 6.1 An electric pendulum ................................... 121 6.2 Simple parallel (tank circuit) resonance ........................ 126 6.3 Simple series resonance ................................. 131 6.4 Applications of resonance ................................ 135 6.5 Resonance in series-parallel circuits .......................... 136 6.6 Q and bandwidth of a resonant circuit ........................ 145 6.7 Contributors ........................................ 151 7 MIXED-FREQUENCY AC SIGNALS 153 7.1 Introduction ........................................ 153 7.2 Square wave signals ................................... 158 7.3 Other waveshapes .................................... 168 7.4 More on spectrum analysis ............................... 174 7.5 Circuit effects ....................................... 185 7.6 Contributors ........................................ 188 8 FILTERS 189 8.1 What is a filter? ...................................... 189 8.2 Low-pass filters ...................................... 190 8.3 High-pass filters ..................................... 196 8.4 Band-pass filters ..................................... 199 8.5 Band-stop filters ..................................... 202 8.6 Resonant filters ...................................... 204 8.7 Summary ......................................... 215 8.8 Contributors ........................................ 215 9 TRANSFORMERS 217 9.1 Mutual inductance and basic operation ........................ 218 9.2 Step-up and step-down transformers ......................... 232 9.3 Electrical isolation .................................... 237 9.4 Phasing .......................................... 239 9.5 Winding configurations ................................. 243 9.6 Voltage regulation .................................... 248 CONTENTS v 9.7 Special transformers and applications ......................... 251 9.8 Practical considerations ................................. 268 9.9 Contributors ........................................ 281 Bibliography ........................................... 281 10 POLYPHASE AC CIRCUITS 283 10.1 Single-phase power systems ............................... 283 10.2 Three-phase power systems ............................... 289 10.3 Phase rotation ....................................... 296 10.4 Polyphase motor design ................................. 300 10.5 Three-phase Y and ∆ configurations .......................... 306 10.6 Three-phase transformer circuits ............................ 313 10.7 Harmonics in polyphase power systems ........................ 318 10.8 Harmonic phase sequences ............................... 343 10.9 Contributors ........................................ 345 11 POWER FACTOR 347 11.1 Power in resistive and reactive AC circuits ...................... 347 11.2 True, Reactive, and Apparent power .......................... 352 11.3 Calculating power factor ................................. 355 11.4 Practical power factor correction ............................ 360 11.5 Contributors ........................................ 365 12 AC METERING CIRCUITS 367 12.1 AC voltmeters and ammeters .............................. 367 12.2 Frequency and phase measurement .......................... 374 12.3 Power measurement ................................... 382 12.4 Power quality measurement .............................. 385 12.5 AC bridge circuits ..................................... 387 12.6 AC instrumentation transducers ............................ 396 12.7 Contributors ........................................ 406 Bibliography ........................................... 406 13 AC MOTORS 407 13.1 Introduction ........................................ 408 13.2 Synchronous Motors ................................... 412 13.3 Synchronous condenser ................................. 420 13.4 Reluctance motor ..................................... 421 13.5 Stepper motors ...................................... 426 13.6 Brushless DC motor ................................... 438 13.7 Tesla polyphase induction motors ........................... 442 13.8 Wound rotor induction motors ............................. 459 13.9 Single-phase induction motors ............................. 462 13.10 Other specialized motors ................................ 467 13.11 Selsyn (synchro) motors ................................ 469 13.12 AC commutator motors ................................. 477 vi CONTENTS Bibliography ........................................... 480 14 TRANSMISSION LINES 481 14.1 A 50-ohm cable? ...................................... 481 14.2 Circuits and the speed of light ............................. 482 14.3 Characteristic impedance ................................ 484 14.4 Finite-length transmission lines ............................ 491 14.5 “Long” and “short” transmission lines ......................... 497 14.6 Standing waves and resonance ............................. 500 14.7 Impedance transformation ............................... 520 14.8 Waveguides ........................................ 527 A-1 ABOUT THIS BOOK 535 A-2 CONTRIBUTOR LIST 539 A-3 DESIGN SCIENCE LICENSE 545 INDEX 548 Chapter 1 BASIC AC THEORY Contents 1.1 What is alternating current (AC)? ........................ 1 1.2 AC
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