Fundamentals of Electrical
Engineering I
,© Don Johnson
This work is licensed under a Creative Commons-ShareAlike 4.0 International License
Original source: The Orange Grove
http://florida.theorangegrove.org/og/items/c7d013ec-2b4d-6971-65f9-b1a6af2d9092/
1/
,Contents
Chapter 1 Introduction ..................................................................................................1
1.1 Themes ................................................................................................................................1
1.2 Signals Represent Information ........................................................................................2
1.2.1 Analog Signals..........................................................................................................3
1.2.2 Digital Signals...........................................................................................................4
1.3 Structure of Communication Systems .............................................................................5
1.4 The Fundamental Signal ...................................................................................................7
1.4.1 The Sinusoid ............................................................................................................7
Exercise 1.4.1 ............................................................................................................8
Exercise 1.4.2 ............................................................................................................8
1.4.2 Communicating Information with Signals ............................................................8
1.5 Introduction Problems.......................................................................................................9
1.6 Solutions to Exercises in Chapter 1 ................................................................................10
Chapter 2 Signals and Systems ...................................................................................11
2.1 Complex Numbers ...........................................................................................................11
2.1.1 Definitions ..............................................................................................................11
Exercise 2.1.1 ..........................................................................................................13
Exercise 2.1.2 ..........................................................................................................13
2.1.2 Euler's Formula ......................................................................................................13
2.1.3 Calculating with Complex Numbers....................................................................14
Exercise 2.1.3 .....................................................................................................15
Example 2.1 ............................................................................................................16
2.2 Elemental Signals..............................................................................................................16
2.2.1 Sinusoids ................................................................................................................16
2.2.2 Complex Exponentials ..........................................................................................17
2.2.3 Real Exponentials ..................................................................................................18
2.2.4 Unit Step .................................................................................................................18
2.2.5 Pulse........................................................................................................................20
2.2.6 Square Wave ..........................................................................................................20
2.2.7 Signal Decomposition ...........................................................................................21
Example 2.2 ............................................................................................................21
Exercise 2.3.1 ..........................................................................................................21
2.3 Discrete-Time Signals ......................................................................................................21
2.3.1 Real-and Complex-valued Signals .......................................................................22
2.3.2 Complex Exponentials ..........................................................................................22
2.3.3 Sinusoids ................................................................................................................23
2.3.4 Unit Sample............................................................................................................23
2.3.5 Symbolic-valued Signals .......................................................................................24
2.3.6 Introduction to Systems .......................................................................................24
2.3.6.1 Cascade Interconnection...........................................................................25
2.3.7 Parallel Interconnection .......................................................................................25
2.3.8 Feedback Interconnection....................................................................................26
2.4 Simple Systems ................................................................................................................27
, 2.4.1 Sources ...................................................................................................................27
2.4.2 Amplifiers ...............................................................................................................27
2.4.3 Delay .......................................................................................................................28
2.4.4 Time Reversal.........................................................................................................28
Exercise 2.6.1 ..........................................................................................................28
2.4.5 Derivative Systems and Integrators ...................................................................29
2.4.6 Linear Systems.......................................................................................................29
2.4.7 Time-Invariant Systems ........................................................................................30
2.5 Signals and Systems Problems .......................................................................................32
Problem 2.1: Complex Number Arithmetic ................................................................32
Problem 2.2: Discovering Roots ...................................................................................32
Problem 2.3: Cool Exponentials ...................................................................................32
Problem 2.4: Complex-valued Signals .........................................................................33
Problem 2.5: ...................................................................................................................34
Problem 2.6: ...................................................................................................................35
Problem 2.7: Linear, Time-Invariant Systems .............................................................36
Problem 2.8: Linear Systems ........................................................................................37
Problem 2.9: Communication Channel .......................................................................37
Problem 2.10: Analog Computers ................................................................................38
2.6 Solutions to Exercises in Chapter 2 ................................................................................38
Chapter 3 Analog Signal Processing ...........................................................................40
3.1 Voltage, Current, and Generic Circuit Elements ...........................................................40
Exercise 3.1.1 ..................................................................................................................41
3.2 Ideal Circuit Elements .....................................................................................................41
3.2.1 Resistor ...................................................................................................................42
3.2.2 Capacitor ................................................................................................................42
3.2.3 Inductor ..................................................................................................................43
3.2.4 Sources ...................................................................................................................44
3.3 Ideal and Real-World Circuit Elements ..........................................................................44
3.4 Electric Circuits and Interconnection Laws....................................................................45
3.4.1 Kirchhof's Current Law .........................................................................................46
Exercise 3.4.1 ..........................................................................................................47
3.4.2 Kirchhof's Voltage Law (KVL) ................................................................................47
Exercise 3.4.2 ..........................................................................................................48
3.5 Power Dissipation in Resistor Circuits ...........................................................................48
Exercise 3.5.1 ..................................................................................................................50
Exercise 3.5.2 ..................................................................................................................50
3.6 Series and Parallel Circuits ..............................................................................................50
Exercise 3.6.1 ..................................................................................................................52
Exercise 3.6.2 ..................................................................................................................54
Example 3.1 ....................................................................................................................55
Exercise 3.6.3 ..................................................................................................................56
3.7 Equivalent Circuits: Resistors and Sources....................................................................57
Exercise 3.7.1 ..................................................................................................................59
Example 3.2 ....................................................................................................................59
Exercise 3.7.2 ..................................................................................................................61
Engineering I
,© Don Johnson
This work is licensed under a Creative Commons-ShareAlike 4.0 International License
Original source: The Orange Grove
http://florida.theorangegrove.org/og/items/c7d013ec-2b4d-6971-65f9-b1a6af2d9092/
1/
,Contents
Chapter 1 Introduction ..................................................................................................1
1.1 Themes ................................................................................................................................1
1.2 Signals Represent Information ........................................................................................2
1.2.1 Analog Signals..........................................................................................................3
1.2.2 Digital Signals...........................................................................................................4
1.3 Structure of Communication Systems .............................................................................5
1.4 The Fundamental Signal ...................................................................................................7
1.4.1 The Sinusoid ............................................................................................................7
Exercise 1.4.1 ............................................................................................................8
Exercise 1.4.2 ............................................................................................................8
1.4.2 Communicating Information with Signals ............................................................8
1.5 Introduction Problems.......................................................................................................9
1.6 Solutions to Exercises in Chapter 1 ................................................................................10
Chapter 2 Signals and Systems ...................................................................................11
2.1 Complex Numbers ...........................................................................................................11
2.1.1 Definitions ..............................................................................................................11
Exercise 2.1.1 ..........................................................................................................13
Exercise 2.1.2 ..........................................................................................................13
2.1.2 Euler's Formula ......................................................................................................13
2.1.3 Calculating with Complex Numbers....................................................................14
Exercise 2.1.3 .....................................................................................................15
Example 2.1 ............................................................................................................16
2.2 Elemental Signals..............................................................................................................16
2.2.1 Sinusoids ................................................................................................................16
2.2.2 Complex Exponentials ..........................................................................................17
2.2.3 Real Exponentials ..................................................................................................18
2.2.4 Unit Step .................................................................................................................18
2.2.5 Pulse........................................................................................................................20
2.2.6 Square Wave ..........................................................................................................20
2.2.7 Signal Decomposition ...........................................................................................21
Example 2.2 ............................................................................................................21
Exercise 2.3.1 ..........................................................................................................21
2.3 Discrete-Time Signals ......................................................................................................21
2.3.1 Real-and Complex-valued Signals .......................................................................22
2.3.2 Complex Exponentials ..........................................................................................22
2.3.3 Sinusoids ................................................................................................................23
2.3.4 Unit Sample............................................................................................................23
2.3.5 Symbolic-valued Signals .......................................................................................24
2.3.6 Introduction to Systems .......................................................................................24
2.3.6.1 Cascade Interconnection...........................................................................25
2.3.7 Parallel Interconnection .......................................................................................25
2.3.8 Feedback Interconnection....................................................................................26
2.4 Simple Systems ................................................................................................................27
, 2.4.1 Sources ...................................................................................................................27
2.4.2 Amplifiers ...............................................................................................................27
2.4.3 Delay .......................................................................................................................28
2.4.4 Time Reversal.........................................................................................................28
Exercise 2.6.1 ..........................................................................................................28
2.4.5 Derivative Systems and Integrators ...................................................................29
2.4.6 Linear Systems.......................................................................................................29
2.4.7 Time-Invariant Systems ........................................................................................30
2.5 Signals and Systems Problems .......................................................................................32
Problem 2.1: Complex Number Arithmetic ................................................................32
Problem 2.2: Discovering Roots ...................................................................................32
Problem 2.3: Cool Exponentials ...................................................................................32
Problem 2.4: Complex-valued Signals .........................................................................33
Problem 2.5: ...................................................................................................................34
Problem 2.6: ...................................................................................................................35
Problem 2.7: Linear, Time-Invariant Systems .............................................................36
Problem 2.8: Linear Systems ........................................................................................37
Problem 2.9: Communication Channel .......................................................................37
Problem 2.10: Analog Computers ................................................................................38
2.6 Solutions to Exercises in Chapter 2 ................................................................................38
Chapter 3 Analog Signal Processing ...........................................................................40
3.1 Voltage, Current, and Generic Circuit Elements ...........................................................40
Exercise 3.1.1 ..................................................................................................................41
3.2 Ideal Circuit Elements .....................................................................................................41
3.2.1 Resistor ...................................................................................................................42
3.2.2 Capacitor ................................................................................................................42
3.2.3 Inductor ..................................................................................................................43
3.2.4 Sources ...................................................................................................................44
3.3 Ideal and Real-World Circuit Elements ..........................................................................44
3.4 Electric Circuits and Interconnection Laws....................................................................45
3.4.1 Kirchhof's Current Law .........................................................................................46
Exercise 3.4.1 ..........................................................................................................47
3.4.2 Kirchhof's Voltage Law (KVL) ................................................................................47
Exercise 3.4.2 ..........................................................................................................48
3.5 Power Dissipation in Resistor Circuits ...........................................................................48
Exercise 3.5.1 ..................................................................................................................50
Exercise 3.5.2 ..................................................................................................................50
3.6 Series and Parallel Circuits ..............................................................................................50
Exercise 3.6.1 ..................................................................................................................52
Exercise 3.6.2 ..................................................................................................................54
Example 3.1 ....................................................................................................................55
Exercise 3.6.3 ..................................................................................................................56
3.7 Equivalent Circuits: Resistors and Sources....................................................................57
Exercise 3.7.1 ..................................................................................................................59
Example 3.2 ....................................................................................................................59
Exercise 3.7.2 ..................................................................................................................61
