**Course Name: Advanced Circuits and Systems**

Course Number: 70220013

Program: Graduate program

Type: Elective

Credits: 3

Term Offered: Fall

Prerequisites: Advanced Mathematics，Calculus and Algebra，Linear Algebra, Numerical Analysis, Complex Analysis，Real Analysis，Differential Equations，Partial Differential Equations，University Physics，Fundamentals of Circuit Theory, Electromagnetic Fields

**Instructor(s): WANG Zanji, WANG Fuping**

**Textbook(s): **

**XIAO Dachuan, Linear and nonlinear circuits, Science Press, 1992**

**WANG Zanji & WANG Fuping, Advanced Circuits and Systems, Teaching materials**

**Reference(s): **

**QIU Guanyuan, Modern Circuit Theory, Higher Education Press, 2001**

**GAO Jinfeng, Nonlinear Circuits and Chaos, Science Press, 2005**

**Leon O. Chua, Charles A. Desoer, Ernest S. Kuh. Linear and nonlinear circuits. McGraw-Hill Companies, 1987**

**Rüdiger U. Seydel, Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos, Elsevier Science Ltd, 1988**

**J.M.T. Thompson & H.B Stewart. Nonlinear Dynamics and Chaos (Second Edition), Wiley, 2002**

**Course Description: **

**On the basis of the earlier knowledge of the fundamentals of the circuit theory, the course mainly focuses on the extended concepts and analysis methods of multiport, time-variant circuits, dynamic characteristics especially the behaviors of the bifurcation and chaos of nonlinear circuits and systems.**

**Course Objectives and Outcomes: **

** Numbers in brackets are linked to department educational outcomes.**

**Students may attain the following outcomes by the course:**

**1.To better master the basic concepts such as the category of the complex components and multiport networks and their corresponding behaviors, for example, the different behavior of the linear time-variant system and the nonlinear system. [1,3,5,6,9]**

**2.To better master the generalized techniques of modeling and analysis for the complex electrical system such as power system, power apparatus, power electronics equipments, control system, signal measurement and transmission and so on. [1,2,3,5,11]**

**3.To better master the general methods to analyze the dynamic stabilities of the equilibriums and limit-cycles. [1,5]**

**4.To better understand the behaviors of the bifurcations and chaotic phenomenon of the nonlinear systems and have the ability to analyze the behavior for electrical systems such as power systems, power electronics systems and so on. [1,2,3,4,5,7,11]**

**5.To get basic training for doing research and paper writing. [5, 6, 7, 10, 11]**

**Course Topics: **

**1.General concepts of the analysis and synthesis of the electrical networks, including the category of the components and circuits, the formulation of the multiport, the steady state analysis of the time-variant circuit and so on.**

**2.Linear dynamic circuits and systems, including the formulation in the state space, the transformation of the CE loop and the LJ cut set, the concept and computation of state transfer matrix of the time-invariant circuit, time-variant circuit and periodic time-variant circuit, the zero-input response and zero-state response, the solution of the discrete linear systems and so on.**

**3.The stability analysis of the linear dynamic systems, including the trajectory and the phase map, equilibrium and periodic orbit, the eigenvalues and stabilities and so on.**

**4.The steady state analysis of the nonlinear circuits, including characteristics of the nonlinear components, the differential parameters, the existence of the solutions and so on.**

**5.Nonlinear autonomous circuits and systems, including the formulation of the state equations, the equilibrium and its stability, Lyapunov function, indirect and direct methods for stability analysis, the stability of the limit-cycle, the stability of the discrete dynamic systems and so on.**

**6.The bifurcation of the nonlinear systems, including the basic concept of the bifurcation, theoretical and practical examples, central manifold theorem, low codimensional bifurcations and so on.**

**7.Chaotic phenomenon of the nonlinear circuits and systems, including chaotic phenomenon and chaotic signal, theoretical and practical examples, the dynamic mechanism of the chaos, the identification of the chaos, the geometric behavior of the chaotic motion, the characteristic parameters of the chaotic orbit, chaotic control and chaotic synchronization and so on.**

**Experiment(s): Numerical experiments, which is the entitled as projects as follows.**

**Project(s):**

l Active filter design, to match the practical use either in harmonics cancellation of the power system or in digital communication system, in measurement system and so on.

l Stability analysis, to analyze a linear time-variant system or a nonlinear system.

l Bifurcation and Chaos, to analyze a nonlinear continued system or a discrete system.

**l Free topic, to match the course requirements.**

**Each student has to finish 3 projects at least, and each project has to be completed with the procedures of topic review, theoretical analysis and modeling, simulation or experiment, data interpretation and conclusion. The project report should be written in a journal paper format.**

**Course Assessment: **

** The course assessment consists of three parts:**

**Homework 20%;**

**Three projects 45%, 15% each;**

**Final examination 35%.**