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

Basic Theory of Circuits, SJTUBasic Theory of Circuits, SJTU 11

Basic Theory of CircuitsBasic Theory of Circuits

SEIEE SEIEE

Shanghai Jiao Tong UniversityShanghai Jiao Tong University

2009.92009.9

Basic Theory of Circuits, SJTUBasic Theory of Circuits, SJTU22

IntroductionIntroductionCourse Title: Basic Theory of Circuits

Periods/ Credits: 72/4

Prerequisites: Advanced math; General physics

Lecturer: Associate Professor Li Ping

Email address: [email protected]

Lecture time and classroom: 东下院 205 Wed34;Fri12

Tutorial arrangement:

Website: http://ee.sjtu.edu.cn/po/Class-web/dianlu-jichu/index.htm

http://eelab.sjtu.edu.cn/dl/

Assessment:


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


Topics covered:Topics covered:

Basic conceptsBasic concepts Lumped-parameter circuitsLumped-parameter circuits VariablesVariables Circuit elements Circuit elements Circuit modelCircuit model Basic rulesBasic rules



Analysis of linear resistive networkAnalysis of linear resistive network Mesh analysisMesh analysis Nodal analysisNodal analysis Loop analysis Loop analysis Cut sets analysisCut sets analysis Analysis theoremsAnalysis theorems



Analysis of linear dynamic circuitAnalysis of linear dynamic circuit

first-order RC, RL circuitfirst-order RC, RL circuit

Step response and impulse responseStep response and impulse response

second-order RLC circuitsecond-order RLC circuit

Analysis method in frequency domainAnalysis method in frequency domain



Analysis of sinusoidal stable stateAnalysis of sinusoidal stable state sinusoidal variable and phastorsinusoidal variable and phastor sinusoidal stable state responsesinusoidal stable state response Circuit analysis in phasor modelCircuit analysis in phasor model AC power analysisAC power analysis Magnetically coupled circuitsMagnetically coupled circuits Concept of balanced three-phase circuitsConcept of balanced three-phase circuits



Analysis of two-port networkAnalysis of two-port network network parameternetwork parameter Interconnection of networksInterconnection of networks Reciprocal networkReciprocal network analysis of the terminated two-port circuitanalysis of the terminated two-port circuit


Place of Electrical Circuits Place of Electrical Circuits in Modern Technology 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


Motivation for doing this course

About the course

Circuit TheoryCircuit 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.


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—2nd ed

3) Electrical Engineering Principles and Applications Allan R.Hambley ---2nd 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 -----3rd ed

Basic Theory of Circuits, SJTUBasic Theory of Circuits, SJTU 1212

Chapter 1Chapter 1Fundamental KnowledgeFundamental Knowledge


What is covered in What is covered in Chapter 1:Chapter 1:

Circuit and Circuit modelCircuit and Circuit modelCircuit VariablesCircuit VariablesCircuit ElementsCircuit Elements


Circuit and Circuit ModelCircuit and Circuit Model

Actual electrical component:Actual electrical component: a battery or a light a battery or a light bulbbulb

• 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

R1

Vs

Rs

Circuit Model


Circuit model: A commonly used mathematical model for electric system.


i1=i2 ; 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


Circuit VariablesCircuit 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

dqi


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


Circuit VariablesCircuit VariablesVoltage (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

dwv

-V+


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


Circuit VariablesCircuit 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

dwp

vip


Reference polaritiesReference polarities for power for power using passive sign conventionusing 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


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

tvidtpdtw

0 0


Circuit ElementsCircuit Elements

Passive elements: resistors, capacitors, and inductors

Active elements: source, operational amplifiers


Voltage and Current Sources 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


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


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)


What is the difference between independent and dependent sources?

VCVS

V1 V1 I1

CCVS

I1

g

VCCS

V1 V1

CCCS

I1

I1


Resistors 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


i

u

i

u

t1t2

u

i

i

u

i

u

t1t2

u

i

Linear Time Invariant Linear Time variant

Nonlinear Time Invariant Nonlinear Time Variant

Open Circuit

Short Circuit

The i-v characteristic


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=0-------is called a short circuit; V=0;

R=∞------is called an open circuit, I=0;


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)

RG

1

G

iGvvip

R

vRivip

22

22


Thank you


University of Sydney

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