EBOOK - The Electrical Engineering Handbook (Richard C. Dorf )

THIS SECTION PROVIDES A BRIEF REVIEW of the definitions and fundamental concepts used in the study of linear circuits and systems. We can describe a circuitor 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 linearcircuit can be described by a set of linear (differential) equations; otherwise it is a nonlinear circuit. A time-invariantcircuit or system implies that none of the components of the circuit have parameters that vary with time; otherwise it is a time-variantsystem.

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 lumpedcircuit; otherwise it is referred to as a distributedcircuit.
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-portare commonly used in circuit theory. Another method of classification is based on circuit configurations (topology), 1 which gives rise to such terms as ladders, lattices, bridged-T circuits,etc.
As indicated earlier, although the words circuitand systemare synonymous and will be used interchangeably throughout the text, the terms circuit theoryand system theorysometimes denote different points of view in the study of circuits or systems. Roughly speaking, circuit theoryis mainly concerned with interconnections of components (circuit topology) within a given system, whereas system theoryattempts 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, analysismay be defined as “the separating of any material or abstract entity [system] into its constituent elements;” on the other hand, synthesisis “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 uniqueno 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 synthesisand designmight be used interchangeably throughout the entire discussion of the subject. However, the term synthesisis generally used to describe analyticalprocedures that can usually be carried out step by step, whereas the term designincludes 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.

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
9 T-PEquivalent 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

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THIS SECTION PROVIDES A BRIEF REVIEW of the definitions and fundamental concepts used in the study of linear circuits and systems. We can describe a circuitor 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 linearcircuit can be described by a set of linear (differential) equations; otherwise it is a nonlinear circuit. A time-invariantcircuit or system implies that none of the components of the circuit have parameters that vary with time; otherwise it is a time-variantsystem.

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 lumpedcircuit; otherwise it is referred to as a distributedcircuit.
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-portare commonly used in circuit theory. Another method of classification is based on circuit configurations (topology), 1 which gives rise to such terms as ladders, lattices, bridged-T circuits,etc.
As indicated earlier, although the words circuitand systemare synonymous and will be used interchangeably throughout the text, the terms circuit theoryand system theorysometimes denote different points of view in the study of circuits or systems. Roughly speaking, circuit theoryis mainly concerned with interconnections of components (circuit topology) within a given system, whereas system theoryattempts 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, analysismay be defined as “the separating of any material or abstract entity [system] into its constituent elements;” on the other hand, synthesisis “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 uniqueno 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 synthesisand designmight be used interchangeably throughout the entire discussion of the subject. However, the term synthesisis generally used to describe analyticalprocedures that can usually be carried out step by step, whereas the term designincludes 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.

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
9 T-PEquivalent 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

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Chuyên mục: C. Bài giảng C. Bài giảng chuyên ngành Điện - Điện tử (Electrical & Electronic) C. Bài giảng kỹ thuật