j. rutkowski - circuit theory, Elektronika
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CIRCUIT THEORY
Jerzy RUTKOWSKI
Institute of Electronics
Gliwice
Silesian University of Technology
16.06.2006
LIST OF CONTENT
PREFACE ..................................................................................6
1. INTRODUCTION TO CIRCUIT THEORY ..............................8
1.1 CIRCUIT VARIABLES - BASIC TERMS and DEFINITIONS................................... 8
1.2 CLASSIFICATION of CIRCUIT THEORY PROBLEMS ......................................... 13
2. DC ANALYSIS .....................................................................15
2.1 CIRCUIT ELEMENTS ................................................................................................... 15
CLASSIFICATION ............................................................................................................. 15
PASSIVE TWO-TERMINAL ELEMENTS........................................................................ 17
Resistor............................................................................................................................. 17
Voltmeter.......................................................................................................................... 18
Ammeter........................................................................................................................... 19
ACTIVE TWO-TERMINAL ELEMENTS ......................................................................... 19
Voltage source.................................................................................................................. 19
Current source .................................................................................................................. 20
2.2 CIRCUIT DIAGRAM and KIRCHHOFF’s LAWS..................................................... 23
CIRCUIT DIAGRAM.......................................................................................................... 23
KIRCHHOFF’S LAWS ....................................................................................................... 25
2.3 ANALYSIS of COMPLEX CIRCUITS ......................................................................... 30
GENERALIZED KIRCHHOFF’S ANALYSIS .................................................................. 30
NODE VOLTAGE (NODAL) ANALYSIS ........................................................................ 32
2.4 ENERGY/POWER CONSERVATION PRINCIPLE .................................................. 38
2.5 TWO-TERMINAL SUBCIRCUIT, THEVENIN’s/NORTON’s THEOREM ........... 40
PASSIVE TWO-TERMINAL SUBCIRCUIT..................................................................... 40
Series connection of resistors, Voltage divider ................................................................ 40
Parallel connection of resistors, Current divider .............................................................. 41
ACTIVE TWO-TERMINAL SUBCIRCUIT ...................................................................... 43
Thevenin’s theorem.......................................................................................................... 44
Norton’s theorem.............................................................................................................. 44
Practical sources ............................................................................................................... 47
2.6 MAXIMUM POWER TRANSFER THEOREM.......................................................... 53
2.7 TRANSFER FUNCTION, SUPERPOSITION PRINCIPLE ...................................... 57
TRANSFER FUNCTION .................................................................................................... 57
One-dimensional case ...................................................................................................... 57
Multi-dimensional case .................................................................................................... 58
Multi-dimensional case .................................................................................................... 58
SUPERPOSITION PRINCIPLE .......................................................................................... 58
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2.8 SEPARATION PRINCIPLE (SOURCE SUBSTITUTION THEOREM) ................. 64
2.9 MULTI-TERMINAL ELEMENTS................................................................................ 67
ELEMENT DESCRIPTION – CONDUCTANCE MATRIX ............................................. 67
Passive multi-terminal element ........................................................................................ 67
Two-terminal element (one-port)............................................................................................................ 68
Three-terminal element........................................................................................................................... 68
Two-port ................................................................................................................................................. 70
Active multi-terminal element ......................................................................................... 71
OTHER MATRICES OF MULTI-TERMINAL ELEMENT .............................................. 72
ANALYSIS OF CIRCUITS WITH MULTI-TERMINAL ELEMENT(S) ......................... 74
2.10 DEPENDENT (CONTROLLED) ELEMENTS .......................................................... 78
Arbitrary dependent element - description....................................................................... 78
Controlled sources - description....................................................................................... 78
Use of controlled sources to element modeling ............................................................... 79
Transistor ................................................................................................................................................ 79
Operational amplifier .............................................................................................................................. 80
Arbitrary three-terminal or two-port element ......................................................................................... 81
Analysis of circuits containing controlled sources........................................................... 81
2.11 DESIGN TOLERANCES, SENSITIVITY ANALYSIS ............................................. 85
Designation of the maximum design deviation of circuit variable .................................. 87
Worst case
analysis................................................................................................................................. 87
Sensitivity analysis ................................................................................................................................. 88
Designation of parameter design tolerances..................................................................... 90
2.12 ANALYSIS OF NONLINEAR CIRCUITS ................................................................. 93
GRAPHICAL ANALYSIS .................................................................................................. 94
Series connection of elements................................................................................................................. 94
Parallel connection of elements .............................................................................................................. 95
Single-loop circuit .................................................................................................................................. 96
Circuit with one nonlinear element ......................................................................................................... 96
ANALYSIS BASED ON PWL APPROXIMATION.......................................................... 98
ANALYSIS BASED ON NEWTON-RAPHSON ITERATION SCHEME ..................... 100
2.13 NETWORK ANALOGIES – MAGNETIC CIRCUITS........................................... 106
3. TRANSIENT ANALYSIS....................................................111
3.1 KIRCHHOFF’S LAWS and PASSIVE ELEMENT LAWS...................................... 111
KIRCHHOFF’S LAWS ..................................................................................................... 111
PASSIVE ELEMENT LAWS............................................................................................ 112
Resistor........................................................................................................................... 112
Capacitor ........................................................................................................................ 114
Coil (Inductor)................................................................................................................ 117
Passive elements – Summary ......................................................................................... 120
3.2 TRANSIENT ANALYSIS in CIRCUITS with STEP EXCITATION ...................... 125
FORCED RESPONSE ....................................................................................................... 126
1
st
order circuit – time-domain method .......................................................................... 126
1
st
order circuit –
s
-domain method................................................................................ 129
1
st
order circuit – boundary values based method .......................................................... 132
3
2
nd
order circuit –
s
-domain method............................................................................... 136
NATURAL RESPONSE.................................................................................................... 142
COMPLETE RESPONSE: NATURAL RESPONSE + FORCED RESPONSE............... 147
3.3 TRANSIENT ANALYSIS in CIRCUITS with ARBITRARY EXCITATION ........ 156
TRANSFER FUNCTION – PROPERTIES and SELECTED EXAMPLES..................... 156
Properties........................................................................................................................ 157
Transfer functions of selected circuits............................................................................ 158
Integrator .............................................................................................................................................. 158
Differentiator ........................................................................................................................................ 160
TRANSFER FUNCTION BASED TRANSIENT ANALYSIS - EXAMPLES................ 161
Practical step ......................................................................................................................................... 163
Practical pulse ....................................................................................................................................... 163
4. AC STEADY-STATE ANALYSIS.......................................170
4.1 ALTERNATING CURRENT – RMS VALUE, PHASOR NOTATION .................. 170
4.2 PHASOR ANALYSIS .................................................................................................... 173
KIRCHHOFF’S LAWS ..................................................................................................... 173
ELEMENT LAWS ............................................................................................................. 173
Resistor........................................................................................................................... 173
Inductor .......................................................................................................................... 174
Capacitor ........................................................................................................................ 175
GENERAL TWO-TERMINAL PHASOR CIRCUIT, PHASOR IMPEDANCE ............. 175
ALGORITHM OF AC STEADY-STATE ANALYSIS .................................................... 180
4.3 AC STEADY-STATE POWER .................................................................................... 185
MEASURES OF POWER ................................................................................................. 185
Instantaneous power ....................................................................................................... 185
Average or real power .................................................................................................... 185
Apparent power .............................................................................................................. 187
Reactive power ............................................................................................................... 188
Complex power .............................................................................................................. 189
MAXIMUM POWER TRANSFER................................................................................... 189
4.4 FREQUENCY CHARACTERISTICS OF TWO-TERMINAL SUBCIRCUIT ...... 192
IDEAL ELEMENTS – SUMMARY ................................................................................. 192
Resistor........................................................................................................................... 192
Inductor .......................................................................................................................... 193
Capacitor ........................................................................................................................ 195
PRACTICAL COIL and PRACTICAL CAPACITOR...................................................... 197
RESONANT CIRCUITS ................................................................................................... 200
Series-resonant circuit
RLC
............................................................................................ 201
Parallel-resonant circuit
RLC
......................................................................................... 206
Complex-resonant circuit ............................................................................................... 208
4.5 TRANSFER FUNCTION IN FREQUENCY DOMAIN-FREQUENCY RESPONSE
................................................................................................................................................ 212
BODE (LOGARITHMIC) PLOT ...................................................................................... 214
FILTERS ............................................................................................................................ 217
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Low-Pass Filter - LPF .................................................................................................... 218
High-Pass Filter - HPF ................................................................................................... 218
Band-Pass Filter - BPF ................................................................................................... 219
Band-Stop Filter - BSF................................................................................................... 220
4.6 ANALYSIS OF CIRCUIT RESPONSE WHEN ONE CIRCUIT CONSTANT
VARIES................................................................................................................................. 223
4.7 MUTUAL INDUCTANCE AND TRANSFORMERS................................................ 226
MUTUAL INDUCTANCE – BASIC TRANSFORMER ................................................. 226
IDEAL TRANSFORMER ................................................................................................. 231
PRACTICAL TRANSFORMER MODELED with IDEAL TRANSFORMER ............... 234
4.8 THREE-PHASE CIRCUITS......................................................................................... 237
WYE-WYE SYSTEMS ..................................................................................................... 238
DELTA-DELTA and WYE-DELTA SYSTEMS .............................................................. 243
COMBINATIONAL SYSTEMS ....................................................................................... 244
POWER IN THREE-PHASE SYSTEMS.......................................................................... 244
5 TRANSMISSION LINE........................................................247
5.1 INTRODUCTION .......................................................................................................... 247
5.2 TRANSIENT ANALYSIS ............................................................................................. 249
5.3 AC ANALYSIS – STANDING WAVES ...................................................................... 264
MATCHED LOAD LINE .................................................................................................. 265
ARBITRARY TERMINATION ........................................................................................ 266
Open-circuited line ......................................................................................................... 268
Short-circuited line ......................................................................................................... 269
TRANSMISSION LINE as CIRCUIT ELEMENT, INPUT IMPEDANCE ..................... 269
APPENDIX A - LAPLACE TRANSFORM .............................275
DEFINITION ..................................................................................................................... 275
PROPERTIES .................................................................................................................... 275
INVERSE TRANSFORMATION - HEAVISIDE’S FORMULA .................................... 276
LAPLACE TRANSFORM DICTIONARY....................................................................... 277
APPENDIX B – COMPLEX NUMBERS.................................283
APPENDIX C – TERMS AND CONCEPTS ...........................288
REFERENCES .......................................................................306
INDEX.....................................................................................307
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