Chan, Shu-Park “Section I – Circuits”
The Electrical Engineering Handbook
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
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I
Circuits
1 Passive Components M. Pecht, P. Lall, G. Ballou, C. Sankaran, N. Angelopoulos
Resistors ? Capacitors and Inductors ? Transformers ? Electrical Fuses
2 Voltage and Current Sources R.C. Dorf, Z. Wan, C.R. Paul, J.R. Cogdell
Step, Impulse, Ramp, Sinusoidal, Exponential, and DC Signals ? Ideal and Practical
Sources ? Controlled Sources
3 Linear Circuit Analysis M.D. Ciletti, J.D. Irwin, A.D. Kraus, N. Balabanian,
T.A. Bickart, S.P. Chan, N.S. Nise
Voltage and Current Laws ? Node and Mesh Analysis ? Network Theorems ? Power and
Energy ? Three-Phase Circuits ? Graph Theory ? Two Port Parameters and Transformations
4 Passive Signal Processing W.J. Kerwin
Low-Pass Filter Functions ? Low-Pass Filters ? Filter Design
5 Nonlinear Circuits J.L. Hudgins, T.F. Bogart, Jr., K. Mayaram, M.P. Kennedy,
G. Kolumbán
Diodes and Rectifiers ? Limiters ? Distortion ? Communicating with Chaos
6 Laplace Transform R.C. Dorf, Z. Wan, D.E. Johnson
Definitions and Properties ? Applications
7 State Variables: Concept and Formulation W.K. Chen
State Equations in Normal Form ? The Concept of State and State Variables and Normal
Tree ? Systematic Procedure in Writing State Equations ? State Equations for Networks Described
by Scalar Differential Equations ? Extension to Time-Varying and Nonlinear Networks
8 The z-Transform R.C. Dorf, Z. Wan
Properties of the z-Transform ? Unilateral z-Transform ? z-Transform Inversion ? Sampled Data
9T-P Equivalent Networks Z. Wan, R.C. Dorf
Three-Phase Connections ? Wye ? Delta Transformations
10 Transfer Functions of Filters R.C. Dorf, Z. Wan
Ideal Filters ? The Ideal Linear-Phase Low-Pass Filter ? Ideal Linear-Phase Bandpass
Filters ? Causal Filters ? Butterworth Filters ? Chebyshev Filters
11 Frequency Response P. Neudorfer
Linear Frequency Response Plotting ? Bode Diagrams ? A Comparison of Methods
12 Stability Analysis F. Szidarovszky, A.T. Bahill
Using the State of the System to Determine Stability ? Lyapunov Stability Theory ? Stability of
Time-Invariant Linear Systems ? BIBO Stability ? Physical Examples
13 Computer Software for Circuit Analysis and Design J.G. Rollins, P. Bendix
Analog Circuit Simulation ? Parameter Extraction for Analog Circuit Simulation
? 2000 by CRC Press LLC
Shu-Park Chan
International Technological University
HIS SECTION PROVIDES A BRIEF REVIEW of the definitions and fundamental concepts used in the
study of linear circuits and systems. We can describe a circuit or system, in a broad sense, as a collection
of objects called elements (components, parts, or subsystems) which form an entity governed by certain
laws or constraints. Thus, a physical system is an entity made up of physical objects as its elements or
components. A subsystem of a given system can also be considered as a system itself.
A mathematical model describes the behavior of a physical system or device in terms of a set of equations,
together with a schematic diagram of the device containing the symbols of its elements, their connections, and
numerical values. As an example, a physical electrical system can be represented graphically by a network which
includes resistors, inductors, and capacitors, etc. as its components. Such an illustration, together with a set of
linear differential equations, is referred to as a model system.
Electrical circuits may be classified into various categories. Four of the more familiar classifications are
(a) linear and nonlinear circuits, (b) time-invariant and time-varying circuits, (c) passive and active circuits,
and (d) lumped and distributed circuits. A linear circuit can be described by a set of linear (differential)
equations; otherwise it is a nonlinear circuit. A time-invariant circuit or system implies that none of the
components of the circuit have parameters that vary with time; otherwise it is a time-variant system. If the
total energy delivered to a given circuit is nonnegative at any instant of time, the circuit is said to be passive;
otherwise it is active. Finally, if the dimensions of the components of the circuit are small compared to the
wavelength of the highest of the signal frequencies applied to the circuit, it is called a lumped circuit; otherwise
it is referred to as a distributed circuit.
There are, of course, other ways of classifying circuits. For example, one might wish to classify circuits
according to the number of accessible terminals or terminal pairs (ports). Thus, terms such as n-terminal circuit
and n-port are commonly used in circuit theory. Another method of classification is based on circuit configu-
rations (topology),
1
which gives rise to such terms as ladders, lattices, bridged-T circuits, etc.
As indicated earlier, although the words circuit and system are synonymous and will be used interchangeably
throughout the text, the terms circuit theory and system theory sometimes denote different points of view in
the study of circuits or systems. Roughly speaking, circuit theory is mainly concerned with interconnections of
components (circuit topology) within a given system, whereas system theory attempts to attain generality by
means of abstraction through a generalized (input-output state) model.
One of the goals of this section is to present a unified treatment on the study of linear circuits and systems.
That is, while the study of linear circuits with regard to their topological properties is treated as an important
phase of the entire development of the theory, a generality can be attained from such a study.
The subject of circuit theory can be divided into two main parts, namely, analysis and synthesis. In a broad
sense, analysis may be defined as “the separating of any material or abstract entity [system] into its constituent
elements;” on the other hand, synthesis is “the combining of the constituent elements of separate materials or
abstract entities into a single or unified entity [system].”
2
It is worth noting that in an analysis problem, the solution is always unique no matter how difficult it may
be, whereas in a synthesis problem there might exist an infinite number of solutions or, sometimes, none at all!
It should also be noted that in some network theory texts the words synthesis and design might be used
interchangeably throughout the entire discussion of the subject. However, the term synthesis is generally used
to describe analytical procedures that can usually be carried out step by step, whereas the term design includes
practical (design) procedures (such as trial-and-error techniques which are based, to a great extent, on the
experience of the designer) as well as analytical methods.
In analyzing the behavior of a given physical system, the first step is to establish a mathematical model. This
model is usually in the form of a set of either differential or difference equations (or a combination of them),
1
Circuit topology or graph theory deals with the way in which the circuit elements are interconnected. A detailed discussion
on elementary applied graph theory is given in Chapter 3.6.
2
The definitions of analysis and synthesis are quoted directly from The Random House Dictionary of the English Language,
2nd ed., Unabridged, New York: Random House, 1987.
T
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the solution of which accurately describes the motion of the physical systems. There is, of course, no exception
to this in the field of electrical engineering. A physical electrical system such as an amplifier circuit, for example,
is first represented by a circuit drawn on paper. The circuit is composed of resistors, capacitors, inductors, and
voltage and/or current sources,
1
and each of these circuit elements is given a symbol together with a mathe-
matical expression (i.e., the voltage-current or simply v-i relation) relating its terminal voltage and current at
every instant of time. Once the network and the v-i relation for each element is specified, Kirchhoff’s voltage
and current laws can be applied, possibly together with the physical principles to be introduced in Chapter 3.1,
to establish the mathematical model in the form of differential equations.
In Section I, focus is on analysis only (leaving coverage of synthesis and design to Section III, “Electronics”).
Specifically, the passive circuit elements—resistors, capacitors, inductors, transformers, and fuses—as well as
voltage and current sources (active elements) are discussed. This is followed by a brief discussion on the elements
of linear circuit analysis. Next, some popularly used passive filters and nonlinear circuits are introduced. Then,
Laplace transform, state variables, z-transform, and T and p configurations are covered. Finally, transfer
functions, frequency response, and stability analysis are discussed.
Nomenclature
1
Here, of course, active elements such as transistors are represented by their equivalent circuits as combinations of resistors
and dependent sources.
Symbol Quantity Unit
A area m
2
B magnetic flux density Tesla
C capacitance F
e induced voltage V
e dielectric constant F/m
e ripple factor
f frequency Hz
F force Newton
f magnetic flux weber
I current A
J Jacobian
k Boltzmann constant 1.38 ′ 10
–23
J/K
k dielectric coefficient
K coupling coefficient
L inductance H
l eigenvalue
M mutual inductance H
n turns ratio
n filter order
Symbol Quantity Unit
w angular frequency rad/s
P power W
PF power factor
q charge C
Q selectivity
R resistance W
R(T) temperature coefficient W/°C
of resistance
r resistivity Wm
s Laplace operator
t damping factor
q phase angle degree
v velocity m/s
V voltage V
W energy J
X reactance W
Y admittance S
Z impedance W
? 2000 by CRC Press LLC
