EE 202

Title: ELECTRICAL CIRCUITS II

Credits: 4

Catalog Description: Analysis of electrical circuits in the frequency domain.  Solution of linear time-invariant circuits using Laplace transform.  Formulation and solution of state equations.  Two-port representations. Filter design.        

Prerequisite: EE 201.

Coordinator: Kadri Özçaldıran, Professor of Electrical Engineering

Goals: To teach sophomores basic tools of  analysis for linear time-invariant circuits with special emphasis on frequency domain/transform techniques. 

Learning Objectives:

At the end of this course, students will be able to:

1. Write down ordinary differential equations describing a linear time-invariant circuit and solve it.
2. Use Laplace Transformation to transfer a circuit from time domain to frequency domain,  compute its transfer function, and  find its response.
3. Find and sketch (the Bode phase and magnitude) plots of a frequency response.
4. Find the harmonics of a periodic excitation input signal and use them to find the harmonics of the output signal.
5. Take Fourier Transform of commonly encountered functions in electrical engineering.
6. Calculate different parameters (Z,Y, transmission, hybrid, inverse hybrid and inverse tranmission) of two port networks.
7. Design some simple passive filters.

Textbook: R.C. Dorf and J. A. Svoboda, Introduction to Electric Circuits,  5th. Edition,Wiley, 2001.

Reference Texts:

1. J.W. Nilsson, S.A. Riedel, Electric Circuits, 5^th edition, Addison-Wesley,1996.
2. L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Non-Linear Circuits, McGraw-Hill, International Edition, 1987.
3. Almost any textbook on electrical circuits.

Prerequisites by Topic:

1. Ordinary differential equations
2. Loop and node equations
3. Rudimentary matrix algebra
4. Complex numbers
5. Phasors

Topics:

1. Network functions and frequency response.  Asymptotic Bode plots.  Series and parallel resonance.  (2 weeks)
2. Laplace Transformation: Basic definitions and properties (1 weeks)
3. Circuit equations in frequency domain.  Using Laplace Transform to solve for circuit variables.  Convolution.  (2 weeks)
4. Fourier Series.  Application of Fourier series to circuits with periodic excitations.(1 week)
5. Fourier Transform: Basic definitions and properties.  Applications to linear circuits. (2 weeks)
6. Rudimentary circuit topology.  State equations: Formulating and solving them. (2 weeks)
7. Two-port networks and two-port parameters. (1.5 weeks)
8. Basic filter design. (1.5 weeks)

Course Structure: The class meets for two lectures a week, each consisting of two 50-minute sessions. There is a 50-minute problem session each week which is carried out by a TA.  4 or 5 quizzes are given to cover homework sets.  One or two MATLAB homeworks are assigned per semester.  There are two in-class mid-term exams and a final exam.

Computer Resources: Any PC can be used to solve the MATLAB homework or to use MATLAB to solve standard homework problems.

Laboratory Resources: None.

Grading:

1. Quizzes plus the MATLAB homework (15%)
2. Two mid-term exams (25% each).
3. A final exam (35%).

Outcome Coverage:

• Apply math, science and engineering knowledge.  Linear, time-invariant circuits, when analyzed in time domain, yield a number of ordinary differential equations with constant coefficients.  Therefore, students are obliged to apply their knowledge of differential equations and of whatever calculus is necessary for o.d.e’s.   On the other hand, same circuits, when transformed to s-domain, yield a number of linear algebraic equations which require the students to apply their knowledge of elementary linear algebra.  Also, as the frequency variable s is complex, operations are in complex arithmetic.  Students also use their knowledge of circuit analysis from EE 201 (e.g., loop and node equations, power and complex power to name a few) and their background in physics becomes especially important in understanding the behavior of components and of circuits.

• Identify, formulate, and solve engineering problems. Despite some of its weaknesses, Dorf and Svoboda text is very successful in introducing examples of real-life problems in the very beginning of each chapter solution of which require the subject matter of that particular chapter.  Then, these real-life problems are formulated as engineering problems and finally they are solved using the methods presented in that chapter.  As anybody who has taken a course on circuit theory will agree, identification of circuit problems, their abstract formulations and finally their solutions is an integral part of this course.

• An understanding of professional and ethical responsibility.  This outcome is not an implicit and integral part of the subject matter of the course like (a) and (e) are.  Nonetheless, persistent preaching on this topic during lectures seems to work fine for coverng this outcome.

• A recognition of the need for, and an ability to engage in life-long learning. Please see the explanation given for (f) above. 

• Use of modern engineering tools. The first 4 or 5 problem sessions are reserved for lectures on MATLAB and SPICE in a PC laboratory environment.  From then on, students are encouraged to use Matlab in solving (at least some of ) their homework problems.  Finally, a somewhat comprehensive MATLAB homework is assigned towards the end of the semester.  MATLAB homework counts for 3-4% of the overall grade.

Prepared By: Kadri Özçaldıran

Last revised: May 1, 2003