Download Chapter 1 Fundamental Knowledge

Preface
Introduction
•
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
•Motivation for doing this course
•About the course
Circuit Analysis
Circuit Theory
Circuit Synthesis
Excitation
(given)
Circuits
(given)
Response
(unknown)
What we emphasize on,
Since it provides the foundation for
understanding the interaction of signal
solution.
Circuit Analysis
Excitation
(given)
Circuits
(unknown)
Circuit synthesis (design)
Response
(given)
In contrast to analysis,
a design problem may have no
solution or several solutions,
Resistance circuits analysis
The course includes 3 parts:
Dynamic circuits analysis
Sinusoidal steady state
•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
• Ideal circuit component: a
mathematical model of an actual
electric component.
Rs
R1
Vs
Actual electrical
component
Emphasize the main character
Neglect the left character
Ideal circuit
component
Circuit model: A commonly used mathematical model for
electric system.
Lumped elements
i1
+
i2
V
-
Lumped circuit
Actual scale of the circuit is much
smaller than the wavelength
relating to the running frequency
of the circuit.
i1=i2
V is certain
Circuit Type:
• Linear----Nonlinear
• Time invariant----Time variant
• Passive----Active
• Lumped----Distributive
Circuit Variables
n
Electric current is the time rate of
change of charge, measured in amperes (A).
dq
i
dt
Sort
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.
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 Variables
Voltage (or potential difference) is the energy required to
move a unit charge through an element, measured in
volts(V).
dw
v
dq
Reference direction or voltage polarity
V>0 means the real polarity is same
to the reference polarity
+ V
-
V<0 means the real polarity is
opposite to the reference polarity
passive sign convention
i
+
V
-
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)
 dw  vdq
dw
dq
 p
v
 vi
dt
dt
dw
p
dt
using passive sign
convention
P=VI in a DC circuit
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.
p0
Power absorbed = - Power supplied
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
t0
t0
w   pdt   vidt
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)
I1
V1
V1
V1
I1
VCVS
CCVS
I1
V1
I1
g V1
VCCS
CCCS
 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
u
u
u
t2
t1
i
Linear Time Invariant
u
i
i
Linear Time variant
Open Circuit
u
u
t2
t1
i
Nonlinear Time Invariant
i
i
Nonlinear Time Variant
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
V=Ri (passive sign convention)
i
-------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)
1
G
R
Power : P=vi (passive sign convention)
Other methods of expressing :
About nonlinear resistor
always absorbs power from the circuit
v2
p  vi  i R 
R
i2
2
p  vi  v G 
G
2