Preface

• Place of Electrical Circuits in Modern Technology

Introduction

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 Theory

Circuit Analysis

Circuit Synthesis

Circuits(given)

Excitation(given)

Response(unknown)

Circuit Analysis

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,

Resistance circuits analysis

Dynamic circuits analysis

Sinusoidal steady state

The course includes 3 parts:

•Reference Books

1)Fundamentals of Electric Circuits Charles K Alexander, Matthew N O Sadiku 清华大学出版社

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

Chapter 1

Fundamental Knowledge

Circuit and circuit model

• Actual electrical component: a battery or a light bulb

Actual electrical component

Ideal circuit component

Emphasize the main character

Neglect the left character

• Ideal circuit component: a mathematical model of an actual electric component.

R1

Vs

Rs

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

Lumped elements Lumped circuit

i2

-V+

i1

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

Circuit Variables

dt

dqi

         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

Reference direction

i i >0 means the real direction is same to the reference direction

i <0 means the real direction is opposite to the reference direction

Circuit VariablesVoltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts(V).

dq

dwv

Reference direction or voltage polarity

-V+

V>0 means the real polarity is same to the reference polarity

V<0 means the real polarity is opposite to the reference polarity

passive sign convention

-V+

i Passive sign convention is satisfied when current enters through the positive polarity of the voltage.

Unless otherwise stated, we will follow the passive sign convention throughout this course.

Circuit Variables Power is the time rate of expending or absorbing energy.

Measured in watts(W)

dt

dwp

vidt

dqv

dt

dwp

vdqdw

P=VI in a DC circuit

using passive sign convention

Power absorbed = - Power supplied

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.

0p Power absorbed = - Power supplied

Energy is the capacity to do work, measured in joules(J)

t

t

t

tvidtpdtw

0 0

The energy absorbed or supplied by an element from time t0 to time t is

Circuit Elements

Passive elements: resistors, capacitors, and inductors

Active elements: source, operational amplifiers

Voltage and Current Sources

The most important active elements are voltage or current sources that generally deliver power to the circuit connected to them. There are two kinds of sources: independent and dependent 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 voltage source

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, namely:

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)

V1 V1

VCVS

V1 V1g

VCCS

I1

I1

CCCS

I1

V1I1

CCVS

What is the difference between independent and dependent sources?

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

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

iV=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 :

G

iGvvip

R

vRivip

22

22

RG

1

About nonlinear resistor