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In order to have a thorough understanding of AC circuit operation and calculations, it is necessary to consider the phase relationships of currents and voltages. The basic tools for this understanding are trigonometry and vectors. If the vector approach is not used, AC circuit calculations can become long and tedious. How vectors are used to simplify AC calculations is thoroughly presented in Essentials of Vector 8, Phase Analysis. The author, who has an extensive electronics background and has taught mathematics at one of the larger electronic technical institutes, covers the subject in a clear and concise manner. The first two SECTIONs offer a comprehensive review of AC fundamentals, with emphasis on phase. These SECTIONs review sine waves, inductive and capacitive circuits, angles, units of measurements, trig functions, solutions of triangles, and the coordinate system. Vectors can be added, subtracted, multiplied, and divided. How to perform these mathematical operations is covered in Section 3. A discussion on imaginary numbers, conversion of forms, and vector algebra follows. The last two SECTIONs cover AC network calculations (series, parallel, and complex circuits) and vector applications. To clarify the various topics, the author includes numerous examples as well as practice problems. The answers to the practice problems are contained in an appendix, along with a table of Natural Trigonometric Functions, enabling the reader to use this guide as a selfteaching medium. It is also particularly suited for use as a supplementary textbook in any school or training program in electronics. PrefaceWhen working with AC circuits, the phases of the currents and voltages must be considered. This applies both to analyses of circuit operation and to calculations involving the various characteristics of AC circuits. This volume reviews the fundamentals of AC, with special emphasis on phase relationships. Included is an extensive coverage of trigonometry and vectors, the basic tools for AC calculations. AC network calculations are thoroughly presented and explained, followed by examples of how vectors can be used in analyzing phase relationships and circuit operations. The discussion of AC in this guide is necessarily different from others, concentrating on the specific aspects of phase angles and phase relationships. For some readers the information in the first two SECTIONs may be understood well enough to omit them in this study. However, other readers may want a more comprehensive review of the fundamentals of both electronics and mathematics. Such readers are referred to the twovolume set, Electronics Math Simplified. For the average reader, how ever, the information contained in this volume should provide sufficient background. This text has been prepared to provide a deeper understanding of AC circuits, clearly explaining how to use the vector approach to simplify circuit analyses that may otherwise involve long and tedious calculations. ContentsSECTION 1: ALTERNATING CURRENT and PHASE Sine Waves  Inductive Circuits  Capacitive Circuits SECTION 2: ANGULAR MEASUREMENTS Angles  Units of Measurements  Trig Functions  Solution of Triangles  The Coordinate System SECTION 3: VECTORS Vector Components  Vector Addition  Vector Subtraction  Multiplication and Division  Rotating Vectors SECTION 4: COMPLEX NUMBERS Imaginary Numbers  Conversion of Forms  Vector Algebra SECTION 5: AC NETWORK CALCULATIONS Series Circuits  Parallel Circuits  Complex Circuits SECTION 6: MISCELLANEOUS VECTOR APPLICATIONS Resonance  Transformers  ThreePhase Power  Tuned Plate, TunedGrid Oscillator  Phase Modulation  Discriminator – Synchros
Also see: Transistor Circuit Manual (1961) Practical Electronic Filters (1991) Using Electronics  through DIY and Experiments (1958) Electronic Experimenter's Manual (1959)

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