Fundamentals of Electrical and Computer Engineering

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  • Fundamentals of Electrical and Computer Engineering

    Gary A. Ybarra

    Copyright 2014 by Gary A. Ybarra

    Version 2.3

  • Fundamentals of Electrical and Computer Engineering

    Table of Contents

    1. Introduction... 1 2. Digital Logic Circuits....5 3. Current and Voltage 17 4. Elements and Laws..... 27 5. Power.. 41 6. Node Voltage and Branch Current Methods... 54 7. Equivalent Circuits......67 8. Capacitance and Electromagnetics..... 84 9. RC Switched Circuits..... 99

    10. Complex Numbers. 110 11. Sinusoids, Phasors and Impedance... 114 12. Frequency Response and Filters 130 13. AC Circuit Response.. 140 14. AC Node and Branch Methods.. 144 15. Fourier Series. 149 16. Response to a Periodic Input.. 160 17. Inductance.. 165 18. RL Switched Circuits..... 171 19. RLC Circuits in the Frequency Domain.... 180 20. Dependent Sources. 193 21. Op-Amps 198 22. Semiconductors, Diodes, and MOSFETs.. 215 A1.Appendix 1..... 227

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    Chapter 1


    1.1 Engineering

    Engineering is the acquisition and processing of information to design products and processes

    that improve human life quality. Science and mathematics are used as tools to solve problems

    requiring the engineer to consider standards and constraints in the problem solution process.

    Good engineering design practice takes into consideration many factors such as cost,

    environmental impact, manufacturability, health and safety, ethics, as well as the social and

    political impacts of the product or process being created. Science is a systematic approach to the

    acquisition of knowledge based on testable explanations for phenomena in the universe enabling

    predictions of event outcomes. Science differs from engineering. Both are important to the

    process of learning about how the world works, and the exercise of one discipline often involves

    the other. Engineering goes beyond seeking to understand how the world works. Engineers

    design, build and test devices, systems and processes that involve the creation of something new.

    There is an inherent process of invention in generating new products and processes that make the

    lives of humans better and the state of the world better. Some of the inventions of engineers have

    led to problems in the environment and general state of the planet, but a responsible engineer is

    committed to considering the environmental impact of his/her products and is bound by ethical

    principles to produce devices and systems that promote a greener world and a safe environment

    in which our children are raised. Engineering is an exciting and satisfying career and provides an

    excellent foundation for any career endeavor.

    1.2 Electrical and Computer Engineering

    Electrical and Computer Engineering (ECE) is a profession that integrates several sub-

    disciplines including analog and digital circuits and devices, signal processing, communication

    systems, computer architecture and networking, micro and nanodevices, power systems

    including rotating machines and power distribution, quantum computing, photonics, sensing,

    waves and metamaterials, required to solve engineering problems to improve human life quality.

    The list of ECE sub-disciplines presented is not exhaustive, but reflects many of the strengths

    possessed by the faculty at many universities. It is very unusual to find an ECE program that

    excels in all areas of ECE, but depending on the expertise of the faculty, the various sub-

    disciplines of ECE are represented to some degree.

    1.3 Fundamentals of ECE

    Fundamentals of Electrical and Computer Engineering is intended to provide a rigorous

    introduction to the field of ECE, enabling informed selection of areas of concentration for

    students planning to continue further study within the field of ECE. It is also an excellent

    resource for students intending to take the Fundamentals of Engineering exam as part of the

    process for obtaining Professional Engineering licensure in a given state.

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    1.4 Engineering Notation

    It is common in the practice of ECE to encounter both large and small quantities. A set of

    engineering prefixes have been defined to efficiently deal with large and small quantities. The

    use of these engineering prefixes is called engineering notation. Engineering notation is similar

    to scientific notation, but the powers of ten are multiples of three. All engineering students

    should be familiar with the notation of engineering prefixes from 10-15

    (femto) to 1015


    The following table should be common knowledge to all engineering students.






    Engineering prefix

    Example usage


    femto f fs


    pico p pF


    nano n nm




    milli m mW

    103 kilo k km

    106 mega M M

    109 giga G GB


    tera T TB


    peta P PHz

    Figure 1.1 Table of engineering prefixes and their definitions.

    The notation used in this textbook for voltage and current expresses all time domain quantities

    with a lower case v for voltage and i for current. Upper case V and I are reserved for sinusoidal

    (AC) voltage maxima and current maxima respectively. A time domain voltage or current may

    be explicitly written as a function of time as in v(t) or simply v with the understanding that the

    voltage may be a constant (DC) or time varying.

    1.5 Plagiarism

    Every instructor has a different set of expectations regarding what is considered acceptable

    collaboration. It is the obligation of the instructor to make collaboration expectations known to

    the students. And it is the students responsibility to follow these expectations. The collaboration

    policy for ECE 331 is documented in detail. Any questions or comments regarding the

    collaboration policy are welcome and the reader is encouraged to discuss any issues in question

    with the instructor.

    Weekly homework assignments, tests, and a final comprehensive examination will sometimes

    require students to express their understanding of certain topics in writing. For example, students

    may be required to learn about batteries and the electrochemical reactions that take place within

    different batteries. At least two sources are required to be examined and cited properly. It is very

    important that students paraphrase what they learn by reading the sources and setting the sources

    aside as they write. If text is taken directly from a source, the text must be in quotations. It is

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    plagiarism to have a source of information open and simultaneously transcribe and

    paraphrase sequences of sentences taken from that source. The source may be re-examined

    to ensure correctness of content, but the user of that information is required to cite the source.

    On tests and the final examination, students must be prepared to answer essay questions without

    having access to any sources. Throughout the textbook, definitions are provided. Students are

    required to know these definitions and be able to provide the definitions in their own words

    accurately and completely.

    1.7 Solution of Transient Analysis (Switched Circuits)

    This book provides the reader with a complete analysis of RC and RL switched circuits including

    the extraction of the differential equations that arise from analyzing RC and RL circuits during

    the transient portion of the solution. Following the extraction of a differential equation, the

    solution is obtained using the method of undetermined coefficients. It is possible to analyze RL

    and RC switched circuits by solving for initial and final (steady state) values and the equivalent

    resistance seen by the energy storage element in the steady state, and then plugging those values

    into memorized equations. Due to the limited time available for teaching transient analysis in

    ECE 331, the memorized solution form is the approach taken in the course. No differential

    equations are extracted from switched circuits, only steady state values, and those values are then

    plugged into memorized formulas. The full approach of extracting differential equations and

    solving those differential equations are presented in this textbook for completeness.

    1.8 Recognition

    The electric circuit concepts presented in this book were in large part learned from Dr. Donald R.

    Rhodes (1923- ), University Professor Emeritus, North Carolina State University. Don Rhodes

    in turn learned a large portion of his conceptual understanding of electric circuits from Charles

    Steinmetz (1856-1923). In particular, the author is indebted to Don Rhodes for his understanding

    of the branch current method (BCM) of solving circuits, which uses physical currents instead of

    fictitious loop currents used in mesh analysis. To the authors knowledge, there is no textbook on

    electric circuits that utilizes the branch current method. Hence, the continued life of the BCM

    may be hinged upon the understanding of this technique by the readers of this textbook.

    The authors understanding of semiconductor physics was developed through discussions with

    Dr. Hisham Massoud, and attending many of his lectures on semiconductor devices and circuits

    utilizing those semiconductor devices


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