 # Basic Electric Circuit Theory (a one-semester text)

## ENEE 205 - Electric Circuits # Preface

You have in your hands an undergraduate text on basic electric circuit theory. As such, it contains no new material for distinction or long remembrance; but it does reflect the current state of instruction of basic circuit theory in Electrical Engineering (EE) departments in the United States. And this is a state of transition. This transition is brought about by the necessity to introduce new topics into the undergraduate electrical engineering curriculum in order to accommodate the important recent developments in electrical engineering. This can be accomplished only by restructuring classical courses such as the basic circuit theory. As a result, there is increasing pressure to find new ways to teach basic circuit theory in a concise manner without compromising the quality and the scope of the exposition of this theory. This text represents an attempt to explore such new approaches.

The most salient feature of this book is that it is designed as a ``one semester'' text on basic circuit theory and it was used as such in our teaching of the topic at the University of Maryland. Since this is a ``one semester'' text, some traditional topics which are usually presented in other books on electric circuit theory are not covered in this text. These topics include Fourier series, Laplace and Fourier transforms and their applications to circuit analysis. There exists a tacit consensus that these topics should belong to a course on linear systems and signals. And this is actually the case at many EE departments where only a one semester course on basic circuit theory is offered.

Another salient feature of this text is its structure. Here, we substantially deviated from the existing tradition where resistive circuits are first introduced and numerous analysis techniques are first presented only for these circuits. In this text, resistors, capacitors and inductors along with independent sources are introduced from the very beginning and ac steady state analysis of electric circuits with the above basic elements is then developed.

It is known that the ac steady state equations and the basic equations for resistive electric circuits have identical mathematical structures. As a result, the analysis techniques for ac steady state and resistive circuits closely parallel one another and are almost identical. The only difference is that in the case of ac steady state one deals with phasors and impedances, while in the case of resistive circuits one deals with instantaneous currents (voltages) and resistances. For this reason, the analysis of resistive circuits can be treated as a particular case of ac steady state analysis. This is the approach which is adopted in this text.

There are several important reasons for this approach.

Firstly, we believe that EE undergraduate students are well prepared for this style of exposition of the material. They usually have (or should have) a sufficient familiarity with the basic circuit elements from a physics course on electricity and magnetism.

Secondly, this approach allows one to introduce the phasor technique and the notion of impedance at the very beginning of the course and to use them frequently and systematically throughout the course. As our teaching experience suggests, this results in better comprehension and absorption of the phasor technique and the impedance concept by the students. This is crucially important because the notions of phasor and impedance are central and ubiquitous in modern electrical engineering. When the traditional approach to the exposition of electric circuit theory is practiced in the framework of a one semester course, phasors and impedances are usually introduced toward the end of the course. As a result, students do not have sufficient experience with and exposure to these very important concepts.

Thirdly, the above approach allows one to present numerous analysis techniques (e.g., equivalent transformations of electric circuits, superposition principle, Thevenin's and Norton's theorems, nodal and mesh analysis) in phasor form. In the case of the traditional approach, these techniques are first presented for resistive circuits and subsequently modified for ac steady state analysis. As a result, this style of exposition requires more time which is very precious in the framework of a one semester course.

Finally, the introduction of phasors at the very beginning of the course, allows one to use them in the analysis of transients excited by ac sources. This makes the presentation of transients more comprehensive and meaningful. Furthermore, the machinery of phasors paves the road to the introduction of transfer functions which are then utilized in the analysis of transients, and the discussion of Bode plots and filters.

Another salient feature of the structure of this text is the consolidation of the material concerned with dependent sources and operational amplifiers. In many textbooks, this material is scattered over several chapters which somewhat undermines its integrity and importance. In this text, this material is consolidated in one chapter where dependent sources are introduced as linear models for semiconductor devices on the basis of small signal analysis. Then, electric circuits with dependent sources and operational amplifiers are systematically studied.

Finally, we have not completely avoided the temptation to introduce new topics in our textbook. These topics include the use of symmetry in the analysis of electric circuits, the Thevenin theorem for resistive electric circuits with single nonlinear resistors, diode bridge rectifier circuits with RL and RC loads, the transfer function approach to the analysis of transients in electric circuits, active RC filters and the synthesis of transfer functions by using RC operational amplifier circuits. These topics are either not discussed or barely covered in the existing textbooks. We have realized that the choice of new topics is always debatable. However, we have felt that the above topics are of sufficient educational importance which prompted our decision to introduce them in this text.

Usually, the basic circuit theory course is the first electrical engineering course taken by undergraduates. For this reason, we believe that it is incumbent upon this course to give students a ``taste'' of electrical engineering, to kindle their curiosity and enthusiasm toward electrical engineering and to prepare them psychologically for future courses. Probably, the appropriate way to achieve this is to emphasize the connections of electric circuit theory with various areas of electrical engineering. This is exactly what we have tried to accomplish in this text. For instance, we have stressed the connections of basic circuit theory with the area of linear systems and signals when we covered such topics as unit impulse and step responses of linear circuits, the convolution integral technique, the concept of transfer functions and utilization of their poles and zeroes in transient analysis, Bode plots and synthesis of transfer functions by RC circuits with operational amplifiers. We have emphasized the connections of basic circuit theory with electronics when we covered dependent sources as linear models for transistors. Finally, we have also stressed that circuit theory has close ties with electromagnetic theory. In basic circuit theory, it is assumed that the values of resistances, inductances and capacitances are given. The calculation of these quantities is the task of electromagnetic field theory. Furthermore, Kirchhoff's Laws, which are treated as basic axioms in the circuit theory, can be derived (can be proven) from Maxwell's equations of electromagnetic field theory. More importantly, by using electromagnetic field theory, the approximate nature of Kirchhoff's Laws can be clearly elucidated and the limits of applicability of these Laws (and circuit theory) can be established.

There is on-going discussion concerning the place and role of SPICE (or PSpice) simulators in a basic circuit theory course. We believe that these circuit simulators should play a complementary role in this course. It is important to emphasize the usefulness of these CAD tools and that their effectiveness increases in the hands of ``educated consumers''. It is equally important to stress that these tools are not a substitute for the sound knowledge of electric circuit theory and to provide this knowledge is the ultimate goal of the basic circuit theory course. In other words, we would like to warn against undue invasion of the basic circuit theory course by SPICE and PSpice simulators, an invasion which may compromise the very goals of this course. For this reason, PSpice examples are confined to the final sections of some of the later chapters and a list of PSpice references is relegated to Appendix C.

By undertaking this project, we wanted to produce a student-friendly textbook. We have come to the conclusion that student's interests will be best served by writing a short book which will closely parallel the presentation of material in class. We have not avoided the discussion of complicated concepts; on the contrary, we have tried to introduce them in a straightforward way and strived to achieve clarity and precision in exposition. We believe that the material which is carefully and rigorously presented is better absorbed. From our teaching experience, we have found that there are some topics which are more difficult for students to digest than others. We have observed that the mathematical form of circuit theory is not the major obstacle. Students usually encounter more difficulties in reading connectivity of electric circuits than in understanding the mathematics of circuit equations. For instance, we have found that it is difficult for students to recognize even simple series and parallel connections if they are masked (obscured) by the drawing of electric circuit. For this reason, we have made a special effort to carefully explain these ``psychologically'' difficult topics. It is for the students to judge to what extent we have succeeded. 