EBOOK - Linear Circuit Theory - Matrices in Computer Applications (Jiri Vlach)

EBOOK - Lý thuyết mạch tuyến tính - Ma trận trong các ứng dụng máy tính - Tác giả: Jiri Vlach (463 Trang).

Circuit theory, developed in the twentieth century, supports today a huge industrial section of analog networks. Most designs are done by computers, but the need to thoroughly understand the theory remains.
In about five hundred pages, this book introduces most subjects of the linear circuit theory. Some methods, like the Laplace transformation, sensitivities, active network design and modified nodal formulation, will be taught in later years and the student can keep the book throughout the undergraduate program.
Emphasis of the book is on solving small examples by hand, because only practice leads to understanding and knowledge. Almost all problems in the book lead to only two or three linear equations. A complete solutions manual is available.
The style of explanation is also important and here is what makes this book different.
Solutions by matrix algebra are started in the third chapter. First year students, most likely, have not heard about matrices, so we start with an absolute minimum: how to write two or three linear equations in matrix form, how to evaluate their determinants and how to apply the Cramer’s rule. This can be taught in a one hour lecture. Additional subjects of the matrix algebra can be taught later or left to mathematics courses. Cramer’s rule avoids divisions and fractions of the elimination method and is suitable for up to four linear equations. Matrices have to be used for more omplicated problems anyway and the students will be acquainted with their use.

1. BASIC CONCEPTS ...........................................................................................  1
Introduction ......................................................................................................  1
1.1. Voltages and currents ................................................................................  1
1.2. Network elements .....................................................................................  4
1.2.1. Independent voltage and current sources ........................................  4
1.2.2 Resistor .............................................................................................  5
1.2.3. Capacitor ..........................................................................................  6
1.2.4. Inductor ............................................................................................  6
1.2.5. Dependent sources ...........................................................................  7
1.2.6. Transformer  ....................................................................................  8
1.2.7. Operational amplifier .......................................................................  8
1.2.8. Other elements .................................................................................  9
1.2.9. Units and their prefixes  ...................................................................  9
1.2.10. Examples of networks  ..................................................................  10
1.3. Independent voltage and current sources ..................................................  11
1.4. Resistors and Ohm’slaw  ..........................................................................  16
1.5. Power and energy .....................................................................................  18
1.6. Kirchhoff’sLaws .......................................................................................  20
1.6.1. Kirchhoff current law ......................................................................  21
1.6.2. Kirchhof voltage law .......................................................................  22
1.7. Connections of resistors ............................................................................  25
Problems  .........................................................................................................  32

2. NODAL AND MESH ANALYSIS ....................................................................  38
Introduction  .....................................................................................................  38
2.1. Nodal analysis ...........................................................................................  38
2.2. Mesh analysis ............................................................................................  45
Problems  .........................................................................................................  50
3. MATRIX METHODS .........................................................................................  54
Inroduction  ......................................................................................................  54
3.1. Linear equations in matrix form ...............................................................  54
3.2. Determinants .............................................................................................  57
3.3. Matrix inversion  .......................................................................................  59
3.4. Cramer’srule  .............................................................................................  62
3.5. Expansion of determinants .......................................................................  66
3.6. Solutions of resistive networks  ................................................................  69
Problems  .........................................................................................................  75
4. DEPENDENT SOURCES ..................................................................................  79
Introduction ......................................................................................................  79
4.1. Voltage controlled current source .............................................................  79
4.2. Current controlled voltage source .............................................................  85
4.3. Current controlled current source .............................................................  91
4.4. Voltage controlled voltage source .............................................................  96
4.5. Summary of dependent sources ................................................................  102

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EBOOK - Lý thuyết mạch tuyến tính - Ma trận trong các ứng dụng máy tính - Tác giả: Jiri Vlach (463 Trang).

Circuit theory, developed in the twentieth century, supports today a huge industrial section of analog networks. Most designs are done by computers, but the need to thoroughly understand the theory remains.
In about five hundred pages, this book introduces most subjects of the linear circuit theory. Some methods, like the Laplace transformation, sensitivities, active network design and modified nodal formulation, will be taught in later years and the student can keep the book throughout the undergraduate program.
Emphasis of the book is on solving small examples by hand, because only practice leads to understanding and knowledge. Almost all problems in the book lead to only two or three linear equations. A complete solutions manual is available.
The style of explanation is also important and here is what makes this book different.
Solutions by matrix algebra are started in the third chapter. First year students, most likely, have not heard about matrices, so we start with an absolute minimum: how to write two or three linear equations in matrix form, how to evaluate their determinants and how to apply the Cramer’s rule. This can be taught in a one hour lecture. Additional subjects of the matrix algebra can be taught later or left to mathematics courses. Cramer’s rule avoids divisions and fractions of the elimination method and is suitable for up to four linear equations. Matrices have to be used for more omplicated problems anyway and the students will be acquainted with their use.

1. BASIC CONCEPTS ...........................................................................................  1
Introduction ......................................................................................................  1
1.1. Voltages and currents ................................................................................  1
1.2. Network elements .....................................................................................  4
1.2.1. Independent voltage and current sources ........................................  4
1.2.2 Resistor .............................................................................................  5
1.2.3. Capacitor ..........................................................................................  6
1.2.4. Inductor ............................................................................................  6
1.2.5. Dependent sources ...........................................................................  7
1.2.6. Transformer  ....................................................................................  8
1.2.7. Operational amplifier .......................................................................  8
1.2.8. Other elements .................................................................................  9
1.2.9. Units and their prefixes  ...................................................................  9
1.2.10. Examples of networks  ..................................................................  10
1.3. Independent voltage and current sources ..................................................  11
1.4. Resistors and Ohm’slaw  ..........................................................................  16
1.5. Power and energy .....................................................................................  18
1.6. Kirchhoff’sLaws .......................................................................................  20
1.6.1. Kirchhoff current law ......................................................................  21
1.6.2. Kirchhof voltage law .......................................................................  22
1.7. Connections of resistors ............................................................................  25
Problems  .........................................................................................................  32

2. NODAL AND MESH ANALYSIS ....................................................................  38
Introduction  .....................................................................................................  38
2.1. Nodal analysis ...........................................................................................  38
2.2. Mesh analysis ............................................................................................  45
Problems  .........................................................................................................  50
3. MATRIX METHODS .........................................................................................  54
Inroduction  ......................................................................................................  54
3.1. Linear equations in matrix form ...............................................................  54
3.2. Determinants .............................................................................................  57
3.3. Matrix inversion  .......................................................................................  59
3.4. Cramer’srule  .............................................................................................  62
3.5. Expansion of determinants .......................................................................  66
3.6. Solutions of resistive networks  ................................................................  69
Problems  .........................................................................................................  75
4. DEPENDENT SOURCES ..................................................................................  79
Introduction ......................................................................................................  79
4.1. Voltage controlled current source .............................................................  79
4.2. Current controlled voltage source .............................................................  85
4.3. Current controlled current source .............................................................  91
4.4. Voltage controlled voltage source .............................................................  96
4.5. Summary of dependent sources ................................................................  102

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