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Fundamentals of Electric Circuits

**Course Code**: B82001Y

**Course Name**: Fundamentals of Electric Circuits

**Credits**: 3.0

**Level**: Undergraduate

**Pre-requisite**: Calculus, Linear Algebra, College General Physics

**Lecture Time**: 30 sessions, 2 hours/session

**Course Description**

This course is the public foundation on which most courses in the electronic information engineering. The concepts and methods introduced in this course will be used in the next course. It is an important basis of technology. It is an introductory course to study the theory of circuit. Through the learning of this course, students can master the basic theories and basic analysis methods of circuits, and prepare necessary circuit knowledge for subsequent courses. At the same time, this course is somewhere in between science and engineering. In the course, it is not only to learn the knowledge of circuit theory, but also to learn how to think in some very important views such as engineering views, abstract views, and equivalent views. It plays an important role in cultivating students' rigorous scientific style and abstract thinking ability, analysis and calculation ability, summing up and induction ability.

**Course Objectives**

Through the learning of this course, students can learn several methods of analysis and calculation of circuits, and be able to skillfully apply these methods to complete the analysis of actual circuits.

- Understand the basic electrical engineering principles and abstractions on which the design of electronic systems is based. These include lumped circuit models, digital circuits, and operational amplifiers.
- Use these engineering abstractions to analyze and design simple electronic circuits.
- Formulate and solve differential equations describing the time behavior of circuits containing energy storage elements.
- Use intuition to describe the approximate time and frequency behavior of circuits containing energy storage elements.
- Understand the concepts of employing simple models to represent non-linear and active elements-such as the MOSFET-in circuits.
- Build circuits and take measurements of circuit variables using tools such as oscilloscopes, multimeters, and signal generators. Compare the measurements with the behavior predicted by mathematic models and explain the discrepancies.
- Understand the relationship between the mathematical representation of circuit behavior and corresponding real-life effects.
- Appreciate the practical significance of the systems developed in the course.

**Learning Outcomes**

- Employ simple lumped circuit models for resistors, sources, inductors, capacitors, and transistors in circuits.
- Analyze circuits made up of linear lumped elements. Specifically, analyze circuits containing resistors and independent sources using techniques such as the node method, superposition and the Thevenin method.
- Employ Boolean algebra to describe the function of logic circuits.
- Design circuits which represent digital logic expressions. Specifically, design a gate-level digital circuit to implement a given Boolean function.
- Determine the output produced by a circuit for a given set of inputs using the switch resistor model of a MOSFET.
- Perform a small-signal analysis of an amplifier using small signal models for the circuit elements.
- Calculate the time behavior of first order and second order circuits containing resistors, capacitors and inductors.
- Calculate the frequency response of circuits containing resistors, capacitors and inductors.
- Simulate and Construct simple gates, amplifiers, or filters in the laboratory.
- Determine in the laboratory the time-domain and frequency-domain behavior of an RLC circuit.
- Use operational amplifier models in circuits which employ negative feedback.
- Use complex impedances to determine the frequency response of circuits.
- Design, build and test an DC-DC circuit which includes both analog and digital components.

**Topics and Schedule**

The main content of this course is divided into seven chapters. The first chapter comes as an overview to introduce lumped-parameter circuit and parameters and reference direction. The second chapter introduces the basic laws that govern electric circuits such as the Kirchhoff’s Law. Also discusses some techniques commonly applied in the simple resistance circuit design and analysis. The third chapter is designed to discuss some powerful techniques for circuit analysis: node analysis and mesh analysis. In addition, such theorems include Thevenin’s and Norton’s theorems are discussed in this chapter. The fourth chapter introduces the Nonlinear Circuit Analysis and discusses the small-signal analysis of an amplifier using small signal models for the circuit elements. The fifth chapter is to discuss basic analysis of linear circuit in the time domain. The sixth chapter is to discuss sinusoidal steady-state analysis. The seventh chapter discusses the Nonsinusoidal periodic signal circuits Analysis. Also this course includes 8 Recitations (2 Hours each) and 2 Applications (2 Hours each) Introduction lessons and 4 simulations. Students should finish the simulations in extra-curricular time.

1. Introduction (1 hour)

1.1 Lumped abstraction relationship to physics.

1.2 Basic component、parameters and Reference direction.

2. Simple resistance circuit design and analysis (9 hours)

2.1 Resistor (1 hour)

2.2 Independ Source、Controlled Source or Dependent Source、Kirchhoff’s Law、（2 hours）

2.3 Two element constraints and Circuit Equation, the equivalent circuit ,One-Port network(include series resistors and parallel resistors, Wye-Delta transformations，Voltage source and current source are connected in series and parallel, source ).

Recitation 1.

2.4 The external characteristics of an operational amplifier and Operational amplifier models in circuits which employ negative feedback, inverting amplifier, summing amplifier, differential amplifier, voltage follower amplifier, signal processing circuit of operational amplifier, measuring amplifier, digital-analog converter, the voltage controlled current source MOSFET;.

2.5 Two-Port Network analysis.

3. Analysis method and circuit theorem of linear resistance circuit (6 Hours)

3.1 Nodal Analysis

3.2 Mesh Analysis

3.3 Thevenin’s Theorem and Norton’s Theorem and Superposition Theorem and Reciprocity Theorem and Tellegen’s Theorem.

Recitation 2

Application Introduce 1: Digital abstraction.

4. Nonlinear Circuit Analysis (6 Hours)

4.1 Introduction to Nonlinear circuit analysis.

4.2 Analysis method of Small-Signal Model.

Recitation 3

5. Analysis of Dynamic Circuit in Time-Domain (11 Hours)

5.1 Capacitor、Inductor and duality principle，Switch and Initial State.

5.2 Analysis of First-Order Circuit (Zero State Response and Zero-Input Response)

Recitation 4

Application Introduction: The Application of Dynamic Circuit.

5.3 Analysis of Second-Order Circuit.

5.4 Analysis methods by using State-Variable and State-Equation.

5.5 Step Response and Unit Impulse Response.

5.6 The concept of convolution integration and the zero state response of arbitrary input is obtained by using convolution integration.

6. Sinusoidal Steady-State Analysis. (13 Hours)

6.1 The concept of Sinusoids and Phasors.

6.2 Sinusoidal Steady-State Analysis.

6.3 Frequency Response and Filters.

6.4 Series Resonance and Parallel Resonance.

6.5 Magnetically Coupled Circuits.

Recitation 5

6.6 AC Power Analysis.

Recitation 6

6.7 Three-Phase Circuits.

Recitation 7

7. Nonsinusoidal periodic signal circuits Analysis.

7.1 The Fourier Series and Average Power and RMA Values.

Recitation 8

**Homework**

Homework will be issued after lectures and collected a week later. Corrected homework with solutions will be returned in tutorials the week after it is collected. Welcome and encouraged to discuss the homework among your colleagues. However, the final formulation and write up of homework answers must be your own.

Late homework will not be accepted for grading. However, total homework grades will be based on the best twelve out of fourteen individual homework grades. Thus, with one exception, two homework assignments may be missed without a grading penalty. All homework will be graded on a coarse scale of 0 to 5 points. 5 points if all or nearly all problems are correct, 4 point if mostly correct, 3 points if homework is approximately half correct, 2 point if mostly incorrect,1 point if late and 0 points if not submitted.

**Labs**

One lab will be assigned, will be conducted during the 16^{th} week. Individual lab hours will be assigned and posted on website.

Lab assignments will be graded on a scale of 0 to 10 (10~9: lab complete, works well, good job on pre- and post-lab; 8~7: lab complete, works, reasonable job on pre and post lab; 6~5: lab mostly complete, reasonable job on pre and post lab; 4~3: lab partially done, reasonable job on pre and post lab; 2~1: lab partially done, poor job on pre- and post-lab; 0: lab not done, poor job on pre- and post-lab).

**Grading **

Homework: 12%;

Simulation: 4%;

Attendance: 4%;

Midterm examination: 20%;

Lab: 10%

Final examination (Closed-book written examination) : 50％;

This course consists of 60 class hours, 58 for lecturing, and 2 for the Midterm examination. We will arrange 8 class hours for recitation.

**Final Exam**

A three-hour final exam will be given during the end-of-term exam week.

**Textbook**

Xin-Jie Yu, Gui-Ping Zhu, Wen-Juan Lu, Principles of Electric Circuits, Tsinghua University Press, 2007.

**References**

[1] Gui-Ping Zhu, Xiu-Cheng Liu,Fu-Yuan Xi, Learning Guide and Exercises for Principle of Electric Circuit (Second Edition), Tsinghua University Press;

[2] Robert L. Boylestad. Introductory Circuit Analysis, 12th Edition(ISBN: 978013714666);

Chinese Version：Introductory Circuit Analysis，author: Robert L. Boylestad，Translator: Xi-You Chen, Xin-Yan Zhang, Guan-Lin Li, China Machine Press, 2014.3;

[3] Charles K. Alexander, Matthew N. O. Sadiku, Fundamentals of Electric Circuits, Fifth Edition (ISBN: 978-0-07-338057-5), McGraw-Hill Companies;

Chinese Version：Fundamentals of Electric Circuits，author: Charles K. Alexander, Matthew N. O. Sadiku，Annotator: Xin-Jie Yu, China Machine Press, 2013;

[4] Wei-Wei Hu， Principle of Circuit Analysis, Tsinghua University Press;

[5] James W. Nilsson, Susan A. Riedel, Electric Circuits, Tenth Edition (ISBN: 9780133760033), Pearson Education.

Chinese Version：Electric Circuits, Tenth Edition，author: James W. Nilsson, Susan A. Riedel，Translator: Yu-Kun Zhou, Li-Qin Xian, Li Li, Shu-Chun Su, Publishing House of Electronics Industry, 2015.3.