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