Modeling and analysis on circuit and system level with matlab and simulink

tomcheung

Book1
Circuit Analysis  with MATLAB Applications
Chapter 1
Basic Concepts and Definitions
The Coulomb...................1-1
Electric Current and Ampere........................................................................................................................1-1
Two Terminal Devices...1-4
Voltage (Potential Difference) ......................................................................................................................1-5
Power and Energy...........1-8
Active and Passive Devices ........................................................................................................................ 1-12
Circuits and Networks. 1-12
Active and Passive Networks..................................................................................................................... 1-12
Necessary Conditions for Current Flow .................................................................................................. 1-12
International System of Units .................................................................................................................... 1-13
Sources of Energy........ 1-17
Summary........................ 1-18
Exercises........................ 1-21
Answers to Exercises... 1-25
Chapter 2
Analysis of Simple Circuits
Conventions.....................2-1
Ohm’s Law.......................2-1
Power Absorbed by a Resistor......................................................................................................................2-3
Energy Dissipated by a Resistor ...................................................................................................................2-4
Nodes, Branches, Loops and Meshes..........................................................................................................2-5
Kirchhoff’s Current Law (KCL)...................................................................................................................2-6
Kirchhoff’s Voltage Law (KVL)...................................................................................................................2-7
Analysis of Single Mesh (Loop) Series Circuits....................................................................................... 2-10
Analysis of Single Node-Pair Parallel Circuits......................................................................................... 2-14
Voltage and Current Source Combinations............................................................................................. 2-16
Resistance and Conductance Combinations............................................................................................ 2-18
Voltage Division Expressions.................................................................................................................... 2-22
Current Division Expressions.................................................................................................................... 2-24
Standards for Electrical and Electronic Devices..................................................................................... 2-26
Resistor Color Code .... 2-27
Power Rating of Resistors .......................................................................................................................... 2-28
Temperature Coefficient of Resistance .................................................................................................... 2-29
Ampere Capacity of Wires.......................................................................................................................... 2-30
Current Ratings for Electronic Equipment ............................................................................................. 2-30
Copper Conductor Sizes for Interior Wiring........................................................................................... 2-33
Summary........................ 2-38
Exercises........................ 2-41
Answers to Exercises... 2-50
Chapter 3
Nodal and Mesh Equations - Circuit Theorems
Nodal, Mesh, and Loop Equations ............................................................................................................. 3-1
Analysis with Nodal Equations.................................................................................................................... 3-1
Analysis with Mesh or Loop Equations ..................................................................................................... 3-8
Transformation between Voltage and Current Sources......................................................................... 3-20
Thevenin’s Theorem.... 3-24
Norton’s Theorem....... 3-35
Maximum Power Transfer Theorem ........................................................................................................ 3-38
Linearity......................... 3-39
Superposition Principle ............................................................................................................................... 3-41
Circuits with Non-Linear Devices............................................................................................................. 3-45
Efficiency ...................... 3-47
Regulation ..................... 3-49
Summary........................ 3-49
Exercises........................ 3-52
Answers to Exercises... 3-64
Chapter 4
Introduction to Operational Amplifiers
Signals .............................. 4-1
Amplifiers........................ 4-1
Decibels ........................... 4-2
Bandwidth and Frequency Response.......................................................................................................... 4-4
The Operational Amplifier ........................................................................................................................... 4-5
An Overview of the Op Amp...................................................................................................................... 4-5
Active Filters................. 4-13
Analysis of Op Amp Circuits ..................................................................................................................... 4-16
Input and Output Resistance ..................................................................................................................... 4-28
Summary........................ 4-32
Chapter 5
Inductance and Capacitance
Energy Storage Devices. 5-1
Inductance ....................... 5-1
Power and Energy in an Inductor ............................................................................................................. 5-11
Combinations of Series and Parallel Inductors........................................................................................ 5-14
Capacitance.................... 5-17
Power and Energy in a Capacitor .............................................................................................................. 5-22
Capacitance Combinations ......................................................................................................................... 5-25
Nodal and Mesh Equations in General Terms........................................................................................ 5-28
Summary........................ 5-29
Exercises ........................ 5-31
Answers to Exercises... 5-36
Chapter 6
Sinusoidal Circuit Analysis
Excitation Functions...... 6-1
Circuit Response to Sinusoidal Inputs ........................................................................................................ 6-1
The Complex Excitation Function.............................................................................................................. 6-3
Phasors in , , and Circuits ................................................................................................................. 6-8
Impedance ..................... 6-14
Admittance .................... 6-17
Summary........................ 6-21
Exercises ........................ 6-25
Answers to Exercises... 6-30
Chapter 7
Phasor Circuit Analysis
Nodal Analysis ................ 7-1
Mesh Analysis ................. 7-5
Application of Superposition Principle....................................................................................................... 7-7
Thevenin’s and Norton’s Theorems ........................................................................................................... 7-8
Phasor Analysis in Amplifier Circuits .......................................................................................................7-12
RL C
Phasor Diagrams .......... 7-15
Electric Filters............... 7-20
Basic Analog Filters ..... 7-21
Active Filter Analysis... 7-26
Summary........................ 7-28
Exercises........................ 7-29
Answers to Exercises... 7-37
Chapter 8
Average and RMS Values, Complex Power, and Instruments
Periodic Time Function 8-1
Average Values ............... 8-2
Effective Values ............. 8-3
Effective (RMS) Value of Sinusoids ........................................................................................................... 8-5
RMS Values of Sinusoids with Different Frequencies ............................................................................. 8-7
Average Power and Power Factor............................................................................................................... 8-9
Average Power in a Resistive Load ........................................................................................................... 8-10
Average Power in Inductive and Capacitive Loads ................................................................................ 8-11
Average Power in Non-Sinusoidal Waveforms.......................................................................................8-14
Lagging and Leading Power Factors......................................................................................................... 8-15
Complex Power - Power Triangle ............................................................................................................. 8-16
Power Factor Correction ............................................................................................................................ 8-18
Instruments ................... 8-21
Summary........................ 8-30
Exercises........................ 8-33
Answers to Exercises... 8-39
Chapter 9
Natural Response
The Natural Response of a Series RL circuit............................................................................................. 9-1
The Natural Response of a Series RC Circuit ......................................................................................... 9-10
Summary........................ 9-17
Exercises........................ 9-19
Answers to Exercises... 9-25
Chapter 10
Forced and Total Response in RL and RC Circuits
The Unit Step Functio10-1
The Unit Ramp Func10-6
The Delta Function......10-8
The Forced and Total Response in an RL Circuit ................................................................................10-14
The Forced and Total Response in an RC Circuit ................................................................................10-21
Summary...................... 10-31
Exercises ...................... 10-33
Answers to Exercises. 10-41

tomcheung

BOOK2
Digital.Circuit.Analysis.and.Design.with.Simulink.Modeling

Digital Circuit Analysis and Design with Simulink ® Modeling i
and Introduction to CPLDs and FPGAs, Second Edition
Copyright © Orchard Publications
1 Common Number Systems and Conversions 1 −1
1.1 Decimal, Binary, Octal, and Hexadecimal Systems ..............................................1 −1
1.2 Binary, Octal, and Hexadecimal to Decimal Conversions ....................................1 −3
1.3 Decimal to Binary, Octal, and Hexadecimal Conversions ....................................1 −3
1.4 Binary −Octal −Hexadecimal Conversions ..............................................................1 −7
1.5 Summary ................................................................................................................1 −9
1.6 Exercises ...............................................................................................................1 −11
1.7 Solutions to End −of −Chapter Exercises ...............................................................1 −12
2 Operations in Binary, Octal, and Hexadecimal Systems 2 −1
2.1 Binary System Operations 2 −1
2.2 Octal System Operations 2 −2
2.3 Hexadecimal System Operations 2 −5
2.4 Complements of Numbers ....................................................................................2 −6
2.4.1 Tens −Complement ......................................................................................2 −7
2.4.2 Nines −Complement ....................................................................................2 −7
2.4.3 Twos −Complement .....................................................................................2 −8
2.4.4 Ones −Complement .....................................................................................2 −9
2.5 Subtraction with Tens −and Twos −Complements .............................................2 −10
2.6 Subtraction with Nines −and Ones −Complements ............................................2 −11
2.7 Summary .............................................................................................................2 −14
2.8 Exercises .............................................................................................................2 −16
2.9 Solutions to End −of −Chapter Exercises .............................................................2 −18
MATLAB Computations: Pages 2 −4, 2 −6, 2 −19 through 2 −21, 2 −23
3 Sign Magnitude and Floating Point Arithmetic 3 −1
3.1 Signed Magnitude of Binary Numbers .................................................................3 −1
3.2 Floating Point Arithmetic ....................................................................................3 −2
3.2.1 The IEEE Single Precision Floating Point Arithmetic ...............................3 −3
3.2.2 The IEEE Double Precision Floating Point Arithmetic .............................3 −7
3.3 Summary ...............................................................................................................3 −9
3.4 Exercises .............................................................................................................3 −10
3.5 Solutions to End −of −Chapter Exercises .............................................................3 −11
4 Binary Codes 4 −1
4.1 Encoding ................................................................................................................ 4 −1
4.1.1 Binary Coded Decimal (BCD) .................................................................... 4 −1
4.1.2 The Excess −3 Code ..................................................................................... 4 −2
4.1.3 The 2*421 Code .......................................................................................... 4 −3
4.1.4 The Gray Code ............................................................................................ 4 −4
4.2 The American Standard Code for Information Interchange (ASCII) Code ........ 4 −5
4.3 The Extended Binary Coded Decimal Interchange Code (EBCDIC) .................. 4 −8
4.4 Parity Bits .............................................................................................................. 4 −8
4.5 Error Detecting and Correcting Codes ................................................................. 4 −9
4.6 Cyclic Codes .......................................................................................................... 4 −9
4.7 Summary .............................................................................................................. 4 −14
4.8 Exercises .............................................................................................................. 4 −16
4.9 Solutions to End −of −Chapter Exercises .............................................................. 4 −17
5 Fundamentals of Boolean Algebra 5 −1
5.1 Basic Logic Operations .......................................................................................... 5 −1
5.2 Fundamentals of Boolean Algebra ........................................................................ 5 −1
5.2.1 Postulates ..................................................................................................... 5 −1
5.2.2 Theorems ..................................................................................................... 5 −2
5.3. Truth Tables 5 −3
5.4 Summary ................................................................................................................ 5 −5
5.5 Exercises ................................................................................................................ 5 −7
5.6 Solutions to End −of −Chapter Exercises ................................................................ 5 −8
6 Minterms and Maxterms 6 −1
6.1 Minterms .................................................................................................................6 −1
6.2 Maxterms ................................................................................................................6 −2
6.3 Conversion from One Standard Form to Another .................................................6 −3
6.4 Properties of Minterms and Maxterms ...................................................................6 −4
6.5 Summary .................................................................................................................6 −9
6.6 Exercises ................................................................................................................6 −10
6.7 Solutions to End −of −Chapter Exercises ...............................................................6 −12
7 Combinational Logic Circuits 7 −1
7.1 Implementation of Logic Diagrams from Boolean Expressions ..............................7 −1
7.2 Obtaining Boolean Expressions from Logic Diagrams ........................................ 7 −10
7.3 Input and Output Waveforms ............................................................................. 7 −11
7.4 Karnaugh Maps .................................................................................................... 7 −13
Digital Circuit Analysis and Design with Simulink ® Modeling iii
and Introduction to CPLDs and FPGAs, Second Edition
Copyright © Orchard Publications
7.4.1 K −map of Two Variables ............................................................................ 7 −14
7.4.2 K −map of Three Variables ......................................................................... 7 −15
7.4.3 K −map of Four Variables ............................................................................ 7 −15
7.4.4 General Procedures for Using a K −map of n Squares ................................ 7 −17
7.4.5 Don’t Care Conditions ............................................................................... 7 −20
7.5 Design of Common Logic Circuits ........................................................................ 7 −21
7.5.1 Parity Generators/Checkers ....................................................................... 7 −22
7.5.2 Digital Encoders ......................................................................................... 7 −27
7.5.3 Decimal −to −BCD Encoder ......................................................................... 7 −31
7.5.4 Digital Decoders ......................................................................................... 7 −37
7.5.5 Equality Comparators ................................................................................. 7 −40
7.5.6 Multiplexers and Demultiplexers ............................................................... 7 −44
7.5.7 Arithmetic Adder and Subtractor Logic Circuits ...................................... 7 −52
7.6 Summary ............................................................................................................... 7 −63
7.7 Exercises ................................................................................................................ 7 −65
7.8 Solutions to End −of −Chapter Exercises ............................................................... 7 −68
Simulink Modeling: Pages 7 −3, 7 −12, 7 −25, 7 −29 through 7 −30, 7 −47, 7 −50,
7 −56 through 7 −60
8 Sequential Logic Circuits 8 −1
8.1 Introduction to Sequential Circuits ........................................................................ 8 −1
8.2 Set −Reset (SR) Flip Flop ........................................................................................ 8 −1
8.3 Data (D) Flip Flop ..................................................................................................8 −4
8.4 JK Flip Flop .............................................................................................................8 −5
8.5 Toggle (T) Flip Flop ................................................................................................8 −6
8.6 Flip Flop Triggering .................................................................................................8 −7
8.7 Edge −Triggered Flip Flops ...................................................................................... 8 −8
8.8 Master / Slave Flip Flops ......................................................................................... 8 −8
8.9 Conversion from One Type of Flip Flop to Another ............................................ 8 −11
8.10 Analysis of Synchronous Sequential Circuits ....................................................... 8 −13
8.11 Design of Synchronous Counters ......................................................................... 8 −23
8.12 Registers ................................................................................................................ 8 −28
8.13 Ring Counters ....................................................................................................... 8 −34
8.14 Ring Oscillators ..................................................................................................... 8 −37
8.15 Summary ............................................................................................................... 8 −39
8.16 Exercises ................................................................................................................ 8 −42
8.17 Solutions to End −of −Chapter Exercises ............................................................... 8 −45
9 Memory Devices 9 −1
9.1 Random −Access Memory (RAM) ......................................................................... 9 −1
9.2 Read −Only Memory (ROM) ..................................................................................9 −3
9.3 Programmable Read −Only Memory (PROM) .......................................................9 −7
9.4 Erasable Programmable Read −Only Memory (EPROM) ......................................9 −9
9.5 Electrically −Erasable Programmable Read −Only Memory (EEPROM) ..............9 −10
9.6 Flash Memory .......................................................................................................9 −10
9.7 Memory Sticks ......................................................................................................9 −10
9.8 Cache Memory .....................................................................................................9 −11
9.9 Virtual Memory ....................................................................................................9 −11
9.10 Scratch Pad Memory ............................................................................................9 −12
9.11 The Simulink Memory Block ...............................................................................9 −12
9.12 Summary ..............................................................................................................9 −14
9.13 Exercises ...............................................................................................................9 −16
9.14 Solutions to End −of −Chapter Exercises ...............................................................9 −17
Simulink Modeling: Pages 9 −6, 9 −12
10 Advanced Arithmetic and Logic Operations 10 −1
10.1 Computers Defined .............................................................................................10 −1
10.2 Basic Digital Computer System Organization and Operation ............................10 −2
10.3 Parallel Adder .....................................................................................................10 −4
10.4 Serial Adder ........................................................................................................10 −5
10.5 Overflow Conditions ...........................................................................................10 −6
10.6 High-Speed Addition and Subtraction ...............................................................10 −9
10.7 Binary Multiplication ........................................................................................10 −10
10.8 Binary Division ..................................................................................................10 −13
10.9 Logic Operations of the ALU ...........................................................................10 −14
10.10 Other ALU functions ........................................................................................10 −15
10.11 Logic and Bit Operations with Simulink Blocks ...............................................10 −16
10.11.1 The Logical Operator Block ..............................................................10 −16
10.11.2 The Relational Operator Block .........................................................10 −16
10.11.3 The Interval Test Block .....................................................................10 −17
10.11.4 The Interval Test Dynamic Block .....................................................10 −18
10.11.5 The Combinatorial Logic Block ........................................................10 −19
10.11.6 The Compare to Zero Block ..............................................................10 −24
10.11.7 The Compare to Constant Block ......................................................10 −25
10.11.8 The Bit Set Block ..............................................................................10 −26
10.11.9 The Clear Bit Block ...........................................................................10 −27
10.11.10 The Bitwise Operator Block ..............................................................10 −28
Digital Circuit Analysis and Design with Simulink ® Modeling v
and Introduction to CPLDs and FPGAs, Second Edition
Copyright © Orchard Publications
10.11.11 The Shift Arithmetic Block .............................................................. 10 −31
10.11.12 The Extract Bits Block ..................................................................... 10 −32
10.12 Summary 10 −34
10.13 Exercises ........................................................................................................... 10 −36
10.14 Solutions to End −of −Chapter Exercises .......................................................... 10 −37
Simulink Modeling: Pages 10 −16 through 10 −33
11 Introduction to Field Programmable Devices 11 −1
11.1 Programmable Logic Arrays (PLAs) .................................................................. 11 −1
11.2 Programmable Array Logic (PAL) .....................................................................11 −5
11.3 Complex Programmable Logic Devices (CPLDs) 11 −6
11.3.1 The Altera MAX 7000 Family of CPLDs .............................................11 −7
11.3.2 The AMD Mach Family of CPLDs .....................................................11 −13
11.3.3 The Lattice Family of CPLDs ..............................................................11 −15
11.3.4 Cypress Flash370 Family of CPLDs .....................................................11 −16
11.3.5 Xilinx XC9500 Family of CPLDs ........................................................11 −21
11.3.6 CPLD Applications .............................................................................11 −31
11.4 Field Programmable Gate Arrays (FPGAs) .....................................................11 −37
11.4.1 SRAM −Based FPGA Architecture .....................................................11 −38
11.4.2 Xilinx FPGAs ......................................................................................11 −38
11.4.3 Atmel FPGAs ......................................................................................11 −41
11.4.5 Altera FPGAs ......................................................................................11 −42
11.4.6 Lattice FPGAs .....................................................................................11 −43
11.4.7 Antifuse-Based FPGAs ........................................................................11 −44
11.4.8 Actel FPGAs .......................................................................................11 −44
11.4.8 QuickLogic FPGAs .............................................................................11 −50
11.5 FPGA Block Configuration −Xilinx FPGA Resources ...................................11 −52
11.6 The CPLD versus FPGA Trade −Off ................................................................11 −59
11.7 What is Next ....................................................................................................11 −59
11.8 Summary ..........................................................................................................11 −62
11.9 Exercises ...........................................................................................................11 −64
11.10 Solutions to End −of −Chapter Exercises ...........................................................11 −66

tomcheung

Digital.Circuit.Analysis.and.Design.with.Simulink.Modeling.part2

tomcheung

Digital.Circuit.Analysis.and.Design.with.Simulink.Modeling.par3

tomcheung

BOOK3
Signals and Systems - with MATLAB Computing and Simulink Modeling

1 Elementary Signals 1 −1
1.1 Signals Described in Math Form .............................................................................1 −1
1.2 The Unit Step Function ..........................................................................................1 −2
1.3 The Unit Ramp Function ......................................................................................1 −10
1.4 The Delta Function ............................................................................................... 1 −11
1.4.1 The Sampling Property of the Delta Function ............................................1 −12
1.4.2 The Sifting Property of the Delta Function ................................................1 −13
1.5 Higher Order Delta Functions...............................................................................1 −14
1.6 Summary ................................................................................................................1 −22
1.7 Exercises.................................................................................................................1 −23
1.8 Solutions to End −of −Chapter Exercises ................................................................1 −24
MATLAB Computing
Pages 1 −20, 1 −21
Simulink Modeling
Page 1 −18
2 The Laplace Transformation 2 −1
2.1 Definition of the Laplace Transformation...............................................................2 −1
2.2 Properties and Theorems of the Laplace Transform ...............................................2 −2
2.2.1 Linearity Property ........................................................................................2 −3
2.2.2 Time Shifting Property .................................................................................2 −3
2.2.3 Frequency Shifting Property ........................................................................2 −4
2.2.4 Scaling Property ...........................................................................................2 −4
2.2.5 Differentiation in Time Domain Property ...................................................2 −4
2.2.6 Differentiation in Complex Frequency Domain Property ...........................2 −6
2.2.7 Integration in Time Domain Property .........................................................2 −6
2.2.8 Integration in Complex Frequency Domain Property .................................2 −8
2.2.9 Time Periodicity Property ............................................................................2 −8
2.2.10 Initial Value Theorem..................................................................................2 −9
2.2.11 Final Value Theorem .................................................................................2 −10
2.2.12 Convolution in Time Domain Property.....................................................2 −11
2.2.13 Convolution in Complex Frequency Domain Property.............................2 −12
2.3 The Laplace Transform of Common Functions of Time.......................................2 −14
2.3.1 The Laplace Transform of the Unit Step Function ..........................2 −14
2.3.2 The Laplace Transform of the Ramp Function ................................2 −14
2.3.3 The Laplace Transform of ..............................................................2 −15
t n u 0 t ()
2.3.4 The Laplace Transform of the Delta Function ................................. 2 −18
2.3.5 The Laplace Transform of the Delayed Delta Function .............. 2 −18
2.3.6 The Laplace Transform of .......................................................... 2 −19
2.3.7 The Laplace Transform of ....................................................... 2 −19
2.3.8 The Laplace Transform of ......................................................... 2 −20
2.3.9 The Laplace Transform of ......................................................... 2 −20
2.3.10 The Laplace Transform of ................................................. 2 −21
2.3.11 The Laplace Transform of ................................................. 2 −22
2.4 The Laplace Transform of Common Waveforms .................................................. 2 −23
2.4.1 The Laplace Transform of a Pulse............................................................... 2 −23
2.4.2 The Laplace Transform of a Linear Segment .............................................. 2 −23
2.4.3 The Laplace Transform of a Triangular Waveform .................................... 2 −24
2.4.4 The Laplace Transform of a Rectangular Periodic Waveform.................... 2 −25
2.4.5 The Laplace Transform of a Half −Rectified Sine Waveform ..................... 2 −26
2.5 Using MATLAB for Finding the Laplace Transforms of Time Functions ............ 2 −27
2.6 Summary ................................................................................................................ 2 −28
2.7 Exercises................................................................................................................. 2 −31
The Laplace Transform of a Sawtooth Periodic Waveform ............................... 2 −32
The Laplace Transform of a Full −Rectified Sine Waveform.............................. 2 −32
2.8 Solutions to End −of −Chapter Exercises................................................................. 2 −33
3 The Inverse Laplace Transform 3 −1
3.1 The Inverse Laplace Transform Integral ..................................................................3 −1
3.2 Partial Fraction Expansion........................................................................................3 −1
3.2.1 Distinct Poles..................................................................................................3 −2
3.2.2 Complex Poles ................................................................................................3 −5
3.2.3 Multiple (Repeated) Poles..............................................................................3 −8
3.3 Case where F(s) is Improper Rational Function.....................................................3 −13
3.4 Alternate Method of Partial Fraction Expansion...................................................3 −15
3.5 Summary .................................................................................................................3 −19
3.6 Exercises..................................................................................................................3 −21
3.7 Solutions to End −of −Chapter Exercises .................................................................3 −22
MATLAB Computing
Pages 3 −3, 3 −4, 3 −5, 3 −6, 3 −8, 3 −10, 3 −12, 3 −13, 3 −1 4, 3 −22
4 Circuit Analysis with Laplace Transforms 4 −1
4.1 Circuit Transformation from Time to Complex Frequency.................................... 4 −1
4.1.1 Resistive Network Transformation ............................................................... 4 −1
4.1.2 Inductive Network Transformation .............................................................. 4 −1
4.1.3 Capacitive Network Transformation ............................................................ 4 −1
4.2 Complex Impedance Z(s).........................................................................................4 −8
4.3 Complex Admittance Y(s) .....................................................................................4 −11
4.4 Transfer Functions .................................................................................................4 −13
4.5 Using the Simulink Transfer Fcn Block.................................................................4 −17
4.6 Summary.................................................................................................................4 −20
4.7 Exercises .................................................................................................................4 −21
4.8 Solutions to End −of −Chapter Exercises.................................................................4 −24
5 State Variables and State Equations 5 −1
5.1 Expressing Differential Equations in State Equation Form................................... 5 −1
5.2 Solution of Single State Equations ........................................................................ 5 −6
5.3 The State Transition Matrix ................................................................................. 5 −9
5.4 Computation of the State Transition Matrix ...................................................... 5 −11
5.4.1 Distinct Eigenvalues ................................................................................. 5 −11
5.4.2 Multiple (Repeated) Eigenvalues ............................................................. 5 −15
5.5 Eigenvectors......................................................................................................... 5 −18
5.6 Circuit Analysis with State Variables.................................................................. 5 −22
5.7 Relationship between State Equations and Laplace Transform.......................... 5 −30
5.8 Summary.............................................................................................................. 5 −38
5.9 Exercises .............................................................................................................. 5 −41
5.10 Solutions to End −of −Chapter Exercises .............................................................. 5 −43
MATLAB Computing
Pages 5 −14, 5 −15, 5 −18, 5 −26, 5 −36, 5 −48, 5 −51
Simulink Modeling
Pages 5 −27, 5 −37, 5 −45
6 The Impulse Response and Convolution 6 −1
6.1 The Impulse Response in Time Domain ................................................................ 6 −1
6.2 Even and Odd Functions of Time .......................................................................... 6 −4
6.3 Convolution ............................................................................................................ 6 −7
6.4 Graphical Evaluation of the Convolution Integral................................................. 6 −8
6.5 Circuit Analysis with the Convolution Integral ................................................... 6 −18
6.6 Summary ............................................................................................................... 6 −21
6.7 Exercises................................................................................................................ 6 −23
6.8 Solutions to End −of −Chapter Exercises................................................................ 6 −25
MATLAB Applications
Pages 6 −12, 6 −15, 6 −30
7 Fourier Series 7 −1
7.1 Wave Analysis......................................................................................................... 7 −1
7.2 Evaluation of the Coefficients................................................................................. 7 −2
7.3 Symmetry in Trigonometric Fourier Series ............................................................. 7 −6
7.3.1 Symmetry in Square Waveform..................................................................... 7 −8
7.3.2 Symmetry in Square Waveform with Ordinate Axis Shifted........................ 7 −8
7.3.3 Symmetry in Sawtooth Waveform................................................................. 7 −9
7.3.4 Symmetry in Triangular Waveform............................................................... 7 −9
7.3.5 Symmetry in Fundamental, Second, and Third Harmonics........................ 7 −10
7.4 Trigonometric Form of Fourier Series for Common Waveforms.......................... 7 −10
7.4.1 Trigonometric Fourier Series for Square Waveform................................... 7 −11
7.4.2 Trigonometric Fourier Series for Sawtooth Waveform............................... 7 −14
7.4.3 Trigonometric Fourier Series for Triangular Waveform ............................. 7 −16
7.4.4 Trigonometric Fourier Series for Half −Wave Rectifier Waveform............. 7 −17
7.4.5 Trigonometric Fourier Series for Full −Wave Rectifier Waveform.............. 7 −20
7.5 Gibbs Phenomenon ............................................................................................... 7 −24
7.6 Alternate Forms of the Trigonometric Fourier Series .......................................... 7 −24
7.7 Circuit Analysis with Trigonometric Fourier Series............................................. 7 −28
7.8 The Exponential Form of the Fourier Series ........................................................ 7 −31
7.9 Symmetry in Exponential Fourier Series .............................................................. 7 −33
7.9.1 Even Functions ........................................................................................... 7 −33
7.9.2 Odd Functions ............................................................................................ 7 −34
7.9.3 Half-Wave Symmetry ................................................................................. 7 −34
7.9.4 No Symmetry .............................................................................................. 7 −34
7.9.5 Relation of to ................................................................................ 7 −34
7.10 Line Spectra.......................................................................................................... 7 −36
7.11 Computation of RMS Values from Fourier Series................................................ 7 −41
7.12 Computation of Average Power from Fourier Series ........................................... 7 −44
7.13 Evaluation of Fourier Coefficients Using Excel® ................................................ 7 −46
7.14 Evaluation of Fourier Coefficients Using MATLAB® ........................................ 7 −47
7.15 Summary............................................................................................................... 7 −50
7.16 Exercises ............................................................................................................... 7 −53
7.17 Solutions to End −of −Chapter Exercises ............................................................... 7 −55
8 The Fourier Transform 8 −1
8.1 Definition and Special Forms ................................................................................ 8 −1
8.2 Special Forms of the Fourier Transform................................................................ 8 −2
8.2.1 Real Time Functions.................................................................................. 8 −3
8.2.2 Imaginary Time Functions ......................................................................... 8 −6
8.3 Properties and Theorems of the Fourier Transform.............................................. 8 −9
8.3.1 Linearity...................................................................................................... 8 −9
8.3.2 Symmetry.................................................................................................... 8 −9
8.3.3 Time Scaling............................................................................................. 8 −10
8.3.4 Time Shifting............................................................................................ 8 −11
8.3.5 Frequency Shifting ................................................................................... 8 −11
8.3.6 Time Differentiation ................................................................................ 8 −12
8.3.7 Frequency Differentiation ........................................................................ 8 −13
8.3.8 Time Integration ...................................................................................... 8 −13
8.3.9 Conjugate Time and Frequency Functions.............................................. 8 −13
8.3.10 Time Convolution .................................................................................... 8 −14
8.3.11 Frequency Convolution............................................................................ 8 −15
8.3.12 Area Under ........................................................................................ 8 −15
8.3.13 Area Under ...................................................................................... 8 −15
8.3.14 Parseval’s Theorem................................................................................... 8 −16
8.4 Fourier Transform Pairs of Common Functions.................................................. 8 −18
8.4.1 The Delta Function Pair .......................................................................... 8 −18
8.4.2 The Constant Function Pair .................................................................... 8 −18
8.4.3 The Cosine Function Pair ........................................................................ 8 −19
8.4.4 The Sine Function Pair............................................................................. 8 −20
8.4.5 The Signum Function Pair........................................................................ 8 −20
8.4.6 The Unit Step Function Pair .................................................................... 8 −22
8.4.7 The Function Pair .................................................................... 8 −24
8.4.8 The Function Pair ............................................................... 8 −24
8.4.9 The Function Pair ............................................................... 8 −25
8.5 Derivation of the Fourier Transform from the Laplace Transform .................... 8 −25
8.6 Fourier Transforms of Common Waveforms ...................................................... 8 −27
8.6.1 The Transform of ....................................... 8 −27
8.6.2 The Transform of ........................................... 8 −28
8.6.3 The Transform of ........... 8 −29
8.6.4 The Transform of .............................. 8 −30
8.6.5 The Transform of a Periodic Time Function with Period T..................... 8 −31
8.6.6 The Transform of the Periodic Time Function .... 8 −32
8.7 Using MATLAB for Finding the Fourier Transform of Time Functions............ 8 −33
8.8 The System Function and Applications to Circuit Analysis ............................... 8 −34
8.9 Summary.............................................................................................................. 8 −42
8.10 Exercises............................................................................................................... 8 −47
8.11 Solutions to End −of −Chapter Exercises .............................................................. 8 −49
MATLAB Computing
Pages 8 −33, 8 −34, 8 −50, 8 −54, 8 −55, 8 −56, 8 −59, 8 −60
9 Discrete −Time Systems and the Z Transform 9 −1
9.1 Definition and Special Forms of the Z Transform............................................... 9 −1
9.2 Properties and Theorems of the Z Transform...................................................... 9 −3
9.2.1 Linearity ..................................................................................................... 9 −3
9.2.2 Shift of in the Discrete −Time Domain ..................................... 9 −3
9.2.3 Right Shift in the Discrete −Time Domain ................................................ 9 −4
9.2.4 Left Shift in the Discrete −Time Domain................................................... 9 −5
9.2.5 Multiplication by in the Discrete −Time Domain................................. 9 −6
9.2.6 Multiplication by in the Discrete −Time Domain ........................... 9 −6
9.2.7 Multiplication by and in the Discrete −Time Domain ..................... 9 −6
9.2.8 Summation in the Discrete −Time Domain ............................................... 9 −7
9.2.9 Convolution in the Discrete −Time Domain ............................................. 9 −8
9.2.10 Convolution in the Discrete −Frequency Domain ..................................... 9 −9
9.2.11 Initial Value Theorem ............................................................................... 9 −9
9.2.12 Final Value Theorem............................................................................... 9 −10
9.3 The Z Transform of Common Discrete −Time Functions.................................. 9 −11
9.3.1 The Transform of the Geometric Sequence.............................................9 −11
9.3.2 The Transform of the Discrete −Time Unit Step Function ......................9 −14
9.3.3 The Transform of the Discrete −Time Exponential Sequence .................9 −16
9.3.4 The Transform of the Discrete −Time Cosine and Sine Functions ..........9 −16
9.3.5 The Transform of the Discrete −Time Unit Ramp Function....................9 −18
9.4 Computation of the Z Transform with Contour Integration .............................9 −20
9.5 Transformation Between s −and z −Domains .......................................................9 −22
9.6 The Inverse Z Transform ...................................................................................9 −25
9.6.1 Partial Fraction Expansion ..................................................................... 9 −25
9.6.2 The Inversion Integral............................................................................ 9 −32
9.6.3 Long Division of Polynomials ................................................................ 9 −36
9.7 The Transfer Function of Discrete −Time Systems ............................................ 9 −38
9.8 State Equations for Discrete −Time Systems ...................................................... 9 −45
9.9 Summary............................................................................................................. 9 −48
9.10 Exercises ............................................................................................................. 9 −53
9.11 Solutions to End −of −Chapter Exercises ............................................................. 9 −55
MATLAB Computing
Pages 9 −35, 9 −37, 9 −38, 9 −41, 9 −42, 9 −59, 9 −61
Simulink Modeling
Page 9 −44
Excel Plots
Pages 9 −35, 9 −44
10 The DFT and the FFT Algorithm 10 −1
10.1 The Discrete Fourier Transform (DFT) ............................................................10 −1
10.2 Even and Odd Properties of the DFT................................................................10 −9
10.3 Common Properties and Theorems of the DFT .............................................. 10 −10
10.3.1 Linearity ...............................................................................................10 −10
10.3.2 Time Shift ............................................................................................10 −11
10.3.3 Frequency Shift ....................................................................................10 −12
10.3.4 Time Convolution ...............................................................................10 −12
10.3.5 Frequency Convolution .......................................................................10 −13
10.4 The Sampling Theorem ...................................................................................10 −13
10.5 Number of Operations Required to Compute the DFT ..................................10 −16
10.6 The Fast Fourier Transform (FFT)..................................................................10 −17
10.7 Summary...........................................................................................................10 −28
10.8 Exercises ...........................................................................................................10 −31
10.9 Solutions to End −of −Chapter Exercises...........................................................10 −33
MATLAB Computing
Pages 10 −5, 10 −7, 10 −34
Excel Analysis ToolPak
Pages 10 −6, 10 −8
11 Analog and Digital Filters
11.1 Filter Types and Classifications......................................................................... 11 −1
11.2 Basic Analog Filters........................................................................................... 11 −2
11.2.1 RC Low &#8722ass Filter ............................................................................... 11 −2
11.2.2 RC High &#8722ass Filter .............................................................................. 11 −4
11.2.3 RLC Band &#8722ass Filter.............................................................................11 −7
11.2.4 RLC Band −Elimination Filter ................................................................11 −8
11.3 Low −Pass Analog Filter Prototypes ..................................................................11 −10
11.3.1 Butterworth Analog Low −Pass Filter Design .......................................11 −14
11.3.2 Chebyshev Type I Analog Low −Pass Filter Design..............................11 −25
11.3.3 Chebyshev Type II Analog Low −Pass Filter Design ............................11 −38
11.3.4 Elliptic Analog Low −Pass Filter Design ...............................................11 −39
11.4 High −Pass, Band −Pass, and Band −Elimination Filter Design..........................11 −41
11.5 Digital Filters ....................................................................................................11 −51
11.6 Digital Filter Design with Simulink..................................................................11 −70
11.6.1 The Direct Form I Realization of a Digital Filter.................................11 −70
11.6.2 The Direct Form II Realization of a Digital Filter................................11 −71
11.6.3 The Series Form Realization of a Digital Filter ....................................11 −73
11.6.4 The Parallel Form Realization of a Digital Filter .................................11 −75
11.6.5 The Digital Filter Design Block............................................................11 −78
11.7 Summary...........................................................................................................11 −87
11.8 Exercises ...........................................................................................................11 −91
11.9 Solutions to End −of −Chapter Exercises ...........................................................11 −97
MATLAB Computing
Pages 11 −3, 11 −4, 11 −6, 11 −7, 11 −9, 11 −15, 11 −19, 11 −23, 11 −24, 11 −31,
11 −35, 11 −36, 11 −37, 11 −38, 11 −40, 11 −41, 11 −42, 11 −43, 11 −45, 11 −46,
11 −48, 11 −50, 11 −55, 11 −56, 11 −57, 11 −60, 11 −62, 11 −64, 11 −67, 11 −68,
and 11 −97 through 11 −106
Simulink Modeling
Pages 11 −71, 11 −74, 11 −77, 11 −78, 11 −80, 11 −82, 11 −83, 11 −84
A Introduction to MATLAB A −1
A.1 MATLAB® and Simulink®........................................................................... A −1
A.2 Command Window ......................................................................................... A −1
A.3 Roots of Polynomials ....................................................................................... A −3
A.4 Polynomial Construction from Known Roots ................................................. A −4
A.5 Evaluation of a Polynomial at Specified Values .............................................. A −6
A.6 Rational Polynomials ....................................................................................... A −8
A.7 Using MATLAB to Make Plots..................................................................... A −10
A.8 Subplots ......................................................................................................... A −18
A.9 Multiplication, Division, and Exponentiation .............................................. A −18
A.10 Script and Function Files .............................................................................. A −26
A.11 Display Formats ............................................................................................. A −31

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Signals and Systems - with MATLAB Computing and Simulink Modeling part2

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