Basic Theory of Circuits, SJTU 1 Basic Theory of Circuits SEIEE Shanghai Jiao Tong University

Basic Theory of Circuits, SJTU 2 Introduction Course Title: Basic Theory of Circuits Periods/ Credits: 72/4 Prerequisites: Advanced math; General physics Lecturer: Associate Professor Li Ping address: Lecture time and classroom: 东下院 205 Wed34;Fri12 Tutorial arrangement: Website: jichu/index.htm jichu/index.htm Assessment:

Basic Theory of Circuits, SJTU 3 Course objective: The aim and task for this course is to help the students to grasp the circuits concepts correctly, grasp the basic rules and analyzing methods, which provides a solid basis for further study

Basic Theory of Circuits, SJTU 4 Topics covered: Basic concepts Basic concepts Lumped-parameter circuits Lumped-parameter circuits Variables Variables Circuit elements Circuit elements Circuit model Circuit model Basic rules Basic rules

Basic Theory of Circuits, SJTU 5 Topics covered: Analysis of linear resistive network Analysis of linear resistive network Mesh analysis Mesh analysis Nodal analysis Nodal analysis Loop analysis Loop analysis Cut sets analysis Cut sets analysis Analysis theorems Analysis theorems

Basic Theory of Circuits, SJTU 6 Topics covered: Analysis of linear dynamic circuit Analysis of linear dynamic circuit first-order RC, RL circuit first-order RC, RL circuit Step response and impulse response Step response and impulse response second-order RLC circuit second-order RLC circuit Analysis method in frequency domain Analysis method in frequency domain

Basic Theory of Circuits, SJTU 7 Topics covered: Analysis of sinusoidal stable state Analysis of sinusoidal stable state sinusoidal variable and phastor sinusoidal variable and phastor sinusoidal stable state response sinusoidal stable state response Circuit analysis in phasor model Circuit analysis in phasor model AC power analysis AC power analysis Magnetically coupled circuits Magnetically coupled circuits Concept of balanced three-phase circuits Concept of balanced three-phase circuits

Basic Theory of Circuits, SJTU 8 Topics covered: Analysis of two-port network Analysis of two-port network network parameter network parameter Interconnection of networks Interconnection of networks Reciprocal network Reciprocal network analysis of the terminated two-port circuit analysis of the terminated two-port circuit

Basic Theory of Circuits, SJTU 9 Place of Electrical Circuits in Modern Technology The design of the circuits has 2 main objectives: 1) To gather, store, process, transport, and present information. 2) To distribute and convert energy between various forms. The study of circuits provides a foundation for areas of electrical engineering such as: Communication system Computer system Control system Electronics Electromagnetic Power systems Signal processing

Basic Theory of Circuits, SJTU 10 Motivation for doing this course About the course Circuit Theory Circuit Analysis Circuit Synthesis Circuits (given) Excitation (given) Response (unknown) Circuit Analysis This is what we emphasize on, Since it provides the foundation for understanding the interaction of signal solution. Circuits (unknown) Excitation (given) Response (given) Circuit synthesis (design) In contrast to analysis, a design problem may have no solution or several solutions, As a student of SEIEE, you should : 1) Understand the main principles of how electrical equipment operates. So you can operate or maintain electrical systems. 2) Have a broad enough knowledge base to lead further study.

Basic Theory of Circuits, SJTU 11 Resistance circuits analysis Dynamic circuits analysis Sinusoidal steady state The course includes: Reference Books 1) Fundamentals of Electric Circuits Charles K Alexander TsingHua Uni Press (photocopy version) 2) The Analysis and Design of Linear Circuits Roland E.Thomas, Albert J.Rosa—2 nd ed 3) Electrical Engineering Principles and Applications Allan R.Hambley ---2 nd ed 4) 电路分析基础 李瀚荪 第三版 5) 电路 邱关源 第四版 6) Electric Circuits Joseph Edminister, Mahmood Nahvi rd ed

Basic Theory of Circuits, SJTU 12 Chapter 1 Fundamental Knowledge

Basic Theory of Circuits, SJTU 13 What is covered in Chapter 1: Circuit and Circuit model Circuit and Circuit model Circuit Variables Circuit Variables Circuit Elements Circuit Elements

Basic Theory of Circuits, SJTU 14 Circuit and Circuit Model Actual electrical component: a battery or a light bulb Actual electrical component: a battery or a light bulb Ideal circuit component: a mathematical model of an actual electric component. Actual electrical component Ideal circuit component Emphasize the main character Neglect the left characters Circuit Model

Basic Theory of Circuits, SJTU 15 Circuit model: A commonly used mathematical model for electric system.

Basic Theory of Circuits, SJTU 16 i 1 =i 2 ; V is certain Actual scale of the circuit is much smaller than the wavelength relating to the running frequency of the circuit. Circuit Type: Linear----Nonlinear Time invariant----Time variant Passive----Active Lumped----Distributive Lumped element Lumped circuit i2 -V+ i1

Basic Theory of Circuits, SJTU 17 Circuit Variables Electric current is the time rate of change of charge, measured in amperes (A). A direct current (DC) is a current that remains constant with time. (I) An alternating current (AC) is a current that varies sinusoidally with time. Sort Where q is charge in coulombs(C) dt dq i 

Basic Theory of Circuits, SJTU 18 Reference direction i >0 means the real direction is same to the reference direction i <0 means the real direction is opposite to the reference direction i

Basic Theory of Circuits, SJTU 19 Circuit Variables Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts(V). Reference direction or voltage polarity V>0 means the real polarity is same to the reference polarity V<0 means the real polarity is opposite to the reference polarity Where w is energy in joules(J) And q is charge in coulombs(C) dq dw v  -V+

Basic Theory of Circuits, SJTU 20 passive sign convention Passive sign convention is satisfied when current enters through the positive polarity of the voltage. Unless stated, we will follow the passive sign convention throughout this course. -V+ i

Basic Theory of Circuits, SJTU 21 Circuit Variables Power is the time rate of expending or absorbing energy. Measured in watts(W) P=VI in a DC circuit using passive sign convention Power absorbed = - Power supplied The algebraic sum of power in a circuit, at any instant of time, must be zero. dt dw p  vip 

Basic Theory of Circuits, SJTU 22 Reference polarities for power using passive sign convention P > 0 absorbing power P < 0 releasing or supplying power Examples Law of conservation of energy must be obeyed in any electric circuit. Power absorbed = - Power supplied   0p

Basic Theory of Circuits, SJTU 23 Energy is the capacity to do work, measured in joules(J) The energy absorbed or supplied by an element from time t0 to time t is   t t t t vidtpdtw 00

Basic Theory of Circuits, SJTU 24 Circuit Elements Passive elements: resistors, capacitors, and inductors Active elements: source, operational amplifiers

Basic Theory of Circuits, SJTU 25 Voltage and Current Sources An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit variables. Symbols for independent voltage source Symbols for independent current source The voltage is determined by itself but the current through it is determined by the outside circuit independent sources dependent sources

Basic Theory of Circuits, SJTU 26 Note:  2 or more voltage sources with different value are not permissible to be connected in parallel  2 or more current sources with different value are not permissible to be connected in series  Voltage sources connected in series is equivalent to one voltage source  Current sources connected in parallel is equivalent to one current source  A voltage source connected to any branch in parallel is equivalent to itself  A current source connected to any branch in series is equivalent to itself

Basic Theory of Circuits, SJTU 27 An ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current. Symbols for a) dependent voltage sources b) dependent current sources There are a total of four variations 1. A voltage –controlled voltage source (VCVS) 2. A current –controlled voltage source (CCVS) 3. A voltage –controlled current source (VCCS) 4. A current –controlled current source (CCCS)

Basic Theory of Circuits, SJTU 28  What is the difference between independent and dependent sources? VCVS  V1  I1 CCVS I1 g VCCS V1  CCCS I1

Basic Theory of Circuits, SJTU 29 Resistors The circuit element used to model the current –resisting behavior of a material is the resistor. Resistance is the capacity of materials to impede the flow of current. The resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms (Ω) Symbol: R1 1k

Basic Theory of Circuits, SJTU 30 i u i u t1 t2 u i i u i u t1 t2 u i Linear Time Invariant Linear Time variant Nonlinear Time Invariant Nonlinear Time Variant Open Circuit Short Circuit The i-v characteristic

Basic Theory of Circuits, SJTU 31 Linear Resistor: The resistance of the idea resistor is constant and its value does not vary over time. The relation between voltage and current. (VAR) v i V=Ri (passive sign convention) Ohm’s Law Since the value of R can range from zero to infinity, it is important that we consider the two extreme possible value of R: R= is called a short circuit; V=0; R=∞------is called an open circuit, I=0;

Basic Theory of Circuits, SJTU 32 Conductance G is the reciprocal of the resistance, measured in siemens (s) Power : P=vi (passive sign convention) always absorbs power from the circuit Other methods of expressing : About nonlinear resistor ( diode, triode) R G 1  G i Gvvip R v Ri p  

Basic Theory of Circuits, SJTU 33 Thank you

Basic Theory of Circuits, SJTU 34 University of Sydney