Download Circuit Variables

Basic Theory of Circuits
SEIEE
Shanghai Jiao Tong University
2009.9
Basic Theory of Circuits, SJTU
1
Introduction
Course 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/dianlujichu/index.htm
http://eelab.sjtu.edu.cn/dl/
Assessment:
Basic Theory of Circuits, SJTU
2
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
3
Topics covered:

Basic concepts





Lumped-parameter circuits
Variables
Circuit elements
Circuit model
Basic rules
Basic Theory of Circuits, SJTU
4
Topics covered:

Analysis of linear resistive network





Mesh analysis
Nodal analysis
Loop analysis
Cut sets analysis
Analysis theorems
Basic Theory of Circuits, SJTU
5
Topics covered:

Analysis of linear dynamic circuit

first-order RC, RL circuit

Step response and impulse response

second-order RLC circuit

Analysis method in frequency domain
Basic Theory of Circuits, SJTU
6
Topics covered:

Analysis of sinusoidal stable state






sinusoidal variable and phastor
sinusoidal stable state response
Circuit analysis in phasor model
AC power analysis
Magnetically coupled circuits
Concept of balanced three-phase circuits
Basic Theory of Circuits, SJTU
7
Topics covered:

Analysis of two-port network




network parameter
Interconnection of networks
Reciprocal network
analysis of the terminated two-port circuit
Basic Theory of Circuits, SJTU
8
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
• Electromagnetic
• Computer system
• Power systems
• Control system
• Signal processing
• Electronics
Basic Theory of Circuits, SJTU
9
Motivation for doing this course
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.
About the course
Circuit Analysis
Circuit Theory
Circuit Synthesis
Excitation
(given)
Circuits
(given)
Response
(unknown)
This is what we emphasize on,
Since it provides the foundation
for understanding the interaction
of signal solution.
Circuit Analysis
Excitation
(given)
Circuits
(unknown)
Response
(given)
In contrast to analysis,
a design problem may have no
solution or several solutions,
Circuit synthesis (design)
Basic Theory of Circuits, SJTU
10
Resistance circuits analysis
The course includes:
Dynamic circuits analysis
Sinusoidal steady state
Reference Books
1) Fundamentals of Electric Circuits Charles K Alexander TsingHua
Uni Press (photocopy version)
2) The Analysis and Design of Linear Circuits
Albert J.Rosa—2nd ed
Roland E.Thomas,
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, SJTU
11
Chapter 1
Fundamental Knowledge
Basic Theory of Circuits, SJTU
12
What is covered in
Chapter 1:
 Circuit
and Circuit model
 Circuit Variables
 Circuit Elements
Basic Theory of Circuits, SJTU
13
Circuit and Circuit Model

Actual electrical component: a battery or a light
bulb
• Ideal circuit component: a
mathematical model of an actual
electric component.
Circuit
Model
Actual electrical
component
Emphasize the main character
Ideal circuit
component
Neglect the left characters
Basic Theory of Circuits, SJTU
14
Circuit model: A commonly used mathematical model for
electric system.
Basic Theory of Circuits, SJTU
15
Lumped element
i1
+
Lumped circuit
i2
V
-
i1=i2 ; V is certain
Actual scale of the circuit is much
smaller than the wavelength
relating to the running frequency
of the circuit.
• Linear----Nonlinear
• Time invariant----Time variant
Circuit Type:
• Passive----Active
• Lumped----Distributive
Basic Theory of Circuits, SJTU
16
Circuit Variables
n
Electric current is the time rate of
change of charge, measured in amperes (A).
i=
Sort
dq
dt
Where q is charge in coulombs(C)
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.
Basic Theory of Circuits, SJTU
17
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
Basic Theory of Circuits, SJTU
18
Circuit Variables
Voltage (or potential difference) is the energy required
to move a unit charge through an element, measured in
volts(V).
dw
Where w is energy in joules(J)
v=
dq
And q is charge in coulombs(C)
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
Basic Theory of Circuits, SJTU
19
passive sign convention
i
+
V
-
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.
Basic Theory of Circuits, SJTU
20
Circuit Variables
Power is the time rate of expending or absorbing energy.
Measured in watts(W)
\ p = vi
dw
p=
dt
using passive sign
convention
P=VI in a DC circuit
The algebraic sum of power in a circuit, at any instant
of time, must be zero.
Power absorbed = - Power supplied
Basic Theory of Circuits, SJTU
21
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
Basic Theory of Circuits, SJTU
22
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
w =  pdt =  vidt
t
t
t0
t0
Basic Theory of Circuits, SJTU
23
Circuit Elements
Passive elements: resistors, capacitors, and
inductors
Active elements:
amplifiers
source, operational
Basic Theory of Circuits, SJTU
24
Voltage and Current Sources
independent sources
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 current source
The voltage is determined by itself but the current through it
is determined by the outside circuit
Basic Theory of Circuits, SJTU
25
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
26
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
27
I1
V1
V1
I1
VCVS
CCVS
I1
V1
g V1
VCCS
I1
CCCS
 What is the difference between independent
and dependent sources?
Basic Theory of Circuits, SJTU
28
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
29
The i-v characteristic
u
u
u
t2
t1
i
Linear Time Invariant
u
i
i
Linear Time variant
u
Open Circuit
u
t2
t1
i
Nonlinear Time Invariant
i
i
Nonlinear Time Variant
Short Circuit
Basic Theory of Circuits, SJTU
30
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;
Basic Theory of Circuits, SJTU
31
Conductance G is the reciprocal of the resistance,
measured in siemens (s)
1
=
G
R
Power : P=vi (passive sign convention)
always absorbs power from the circuit
Other methods of
expressing :
2
v
p = vi = i 2 R =
R
2
i
p = vi = v 2G =
G
About nonlinear resistor ( diode, triode)
Basic Theory of Circuits, SJTU
32
Thank you
Basic Theory of Circuits, SJTU
33
University of Sydney
Basic Theory of Circuits, SJTU
34