ENGI 1100, November 2005 Dr. Dave Shattuck Associate Professor Electrical and Computer Engineering Department Sinusoids, Paradigms and Electronics Phone: (713) Office: Room W326-D3

Introduction I want to talk about what engineers do, and how engineers think about attacking problems. I want to talk about sinusoids. I want to introduce the area called “electronics”.

Introduction to Engineering What is engineering?

Introduction to Engineering Answer: Engineering is Problem Solving.What is engineering? -- Answer: Engineering is Problem Solving. So, what is electrical engineering?So, what is electrical engineering?

Introduction to Engineering What is engineering? -- Answer: Engineering is Problem Solving. Problem solving using electricity, electrical tools and concepts.What is electrical engineering? -- Answer: Problem solving using electricity, electrical tools and concepts. What is science?What is science?

Introduction to Engineering What is engineering? -- Answer: Engineering is Problem Solving. What is electrical engineering? -- Answer: Problem solving using electricity, electrical tools and concepts. Science is knowledge gaining.What is science? – Answer: Science is knowledge gaining.

Introduction to Engineering What is engineering? -- Answer: Engineering is Problem Solving. What is electrical engineering? -- Answer: Problem solving using electricity, electrical tools and concepts. What is science? – Answer: Science is knowledge gaining. So, how can you tell an electrical engineer from a physicist?So, how can you tell an electrical engineer from a physicist?

Introduction to Engineering How can you tell an electrical engineer from a physicist? – Answer: by the goals they work towards. An engineer's goal is to solve problems. A scientist's goal is to learn. However, an engineer needs to learn to be able to solve problems, and a scientist needs to solve problems to learn, so the situation gets muddled. The key is to look at their goals.

Quiz Time: Were the following famous people engineers or scientists? To decide, we need to look at their GOALS! Introduction to Engineering

p He wanted to understand the stars and planets Engineer or Scientist Galileo?  He was a scientist Introduction to Engineering

Engineer or Scientist Leonardo da Vinci?  He was an engineer p He wanted to fly, to paint, to do things Introduction to Engineering

p He wanted to build things, lights, phonographs, etc. Engineer or Scientist Thomas Edison?  He was an engineer Introduction to Engineering

p He wanted to understand how things moved Engineer or Scientist Sir Isaac Newton?  He was a scientist Introduction to Engineering

Engineer or Scientist Albert Einstein?  He was a scientist p He wanted to find the Unified Theory of Everything Introduction to Engineering

Engineer or Scientist Robert Oppenheimer?  He was an engineer  He wanted to build the Atomic Bomb - Manhattan Project Introduction to Engineering

Engineer or Scientist Professor Paul Chu?  He is a scientist p He wants to understand superconductivity Introduction to Engineering

Engineer or Scientist Sir Thomas Crapper?  He was an engineer  He wanted to build a sanitary toilet, which was so important he was knighted Introduction to Engineering

Goal of this lecture: Answer Some Questions Why does a guitar sound different from a violin? Why don’t I sound like Phil Collins? Why don’t I make as much $ as Phil Collins? Why do people talk about audio systems in terms of sinusoids?

Engineering Paradigms We are going to introduce a couple of major engineering paradigms. What are paradigms?

About 20 cents. Get it? “Pair a dimes?” Okay, so it is not very funny…

Engineering Paradigms A paradigm is a way of thinking about something. A paradigm shift is a change in the way we think about something. I want to introduce a couple of engineering paradigm shifts. I will use sinusoids as the basis for this.

Euler’s Relation Who knows Euler’s Relation? To Play = To Lose

NO Wait! To Play = To Lose That was Oiler’s Relation. They are in Tennessee now. They’re called the Titans. This is now an obsolete joke. What is Euler’s Relation?

Euler’s Relation Euler’s Relation is: e j  = cos  + j sin  This means that sinusoids are just complex exponentials. When we solve certain kinds of problems, the solutions turn out to be complex exponentials, or sine waves.

Euler’s Relation Dr. Dave, can you say that again, in English? OK …. Sine waves happen.

Fourier’s Theorem Now, there is a special rule that concerns sinusoids. First, we need to be able to pronounce this. Furrier’s theorem applies in animal husbandry So, pronounce it 4 - E - A !!!

Fourier’s Theorem Any physically realizable waveform can be represented by, and is equivalent to, a summation of sinusoids of different amplitude, frequency and phase. This represented a major paradigm shift in engineering.

Fourier’s Theorem In English this time, Dr. Dave? OK…. You can get any real function by adding up sine waves. This represented a major change in the way we think about problem solving in engineering. We could look at what happens to sine waves, and know what would happen when other signals are used.

Fourier’s Theorem: Answers Question: Why does a guitar sound different from a violin? Answer: Sine wave components in the two instruments are different.

Fourier’s Theorem: Answers Question: Why don’t I sound like Phil Collins? Answer: Sine wave components in the two voices are different.

Fourier’s Theorem: Answers Question: Why don’t I make as much $ as Phil Collins? Equivalent Answer: He can sing. I can’t. Answer: Sine wave components in the two voices are different.

Fourier’s Theorem: Answers Question: Why do people talk about audio systems in terms of sinusoids? Answer: Sine wave components tell us everything we need to know about any signal. Therefore, Fourier’s Theorem allows us to describe and analyze a system without knowing what signals we use it with.

Fourier’s Theorem: Answers Question: Why do we introduce complicated mathematical concepts like Fourier’s Theorem? Answer: To make life hard for engineering students.

Fourier’s Theorem: Answers Question: Why do we introduce complicated mathematical concepts like Fourier’s Theorem? Answer: To make life hard for engineering students. No, this is RONG!

Fourier’s Theorem: Answers Question: Why do we introduce complicated mathematical concepts like Fourier’s Theorem? Answer: These concepts help us to solve problems, and to think about how to solve problems.

Demonstration of Sinusoids Let’s look at a system to send signals around. (Telephone, Radio, etc.)

Application to Electronics Let’s look at a system to send signals around. The telephone: –Converts sound to voltage, with a microphone. –Sends the voltage to the location needed. –Converts voltage to sound, with a speaker.

Send the voltage? How does the voltage get to where we want it? –We need to amplify it, to make it louder. –We need to amplify it, to send it a long way. –We need to deal with noise. –We may need to modulate it to send it through some kinds of channels.

Did I say modulate? In English, please, Dr. Dave! First, the problem: –Sometimes it is kind of awkward to run a wire to the place I want the signal to go. Modulate?

Did I say modulate? In English, please, Dr. Dave! –The problem: Sometimes it is kind of awkward to run a wire to the place I want the signal to go. –The solution: If I stick the wire up in the air, it will send that signal through the air. Modulate?

If I stick a wire up in the air, it will send that signal through the air. –However, to work well, it must be at least 1/10th of a wavelength ( ) long. –At 15 Hertz, the low end of human hearing, that is 0.1 = (0.1)c/f = (0.1)(186,000[miles/s])/(15[s -1 ]) = 1,240 miles in length.

Modulate! Need antennas that are about the length of Texas. Rhode Island would be out of luck. Only one signal can be sent at a time. The strongest signal would win, if you were lucky. Solution: Multiply by sinusoid at some high frequency. Wavelengths are shorter, and I can have lots of signals at once, each with a different frequency sinusoid. The different frequencies are called “stations”.

Modulate!! For example, for radio 740[kHz] –At 740,000[Hertz], we have 0.1 = (0.1)c/f = (0.1)(186,000[miles/s])/(740,000[s -1 ]) = 130 feet in length

Solution: Electronics!! In electronics, we: –Amplify signals (make them bigger). –Deal with noise in signals. –Modulate and demodulate signals. –Fool around with signals, and the devices that allow us to do this fooling around.

Who cares about this stuff? I do, obviously. But that is not really your question. Your question is, why should you care about this? You should only care about this if you are going into electrical engineering. If you are, this is the kind of way you will learn to approach problems. I am showing you electronics as one example. There are many different kinds of problems that Electrical Engineers solve.

Kinds of Problems Electrical and Computer Engineers Solve Communications Electromagnetic Theory Computer Programming Computer Design Computer Systems Signal Analysis Electronics Digital Logic Design Semiconductor Physics Power Generation and Distribution

Conclusions Engineers are problem solvers. Electrical Engineers solve problems using or relating to electricity, and Computer Engineers solve problems using or related to computers. Engineers attack problems using technology, science, and mathematics, because they work.