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Dave ShattuckUniversity of Houston
ENGI 1100, November 2005
Dr. Dave ShattuckAssociate Professor
Electrical and Computer Engineering Department
Sinusoids, Paradigms and Sinusoids, Paradigms and ElectronicsElectronics
Email: Shattuck@uh.eduPhone: (713) 743-4422
Office: Room W326-D3
Dave ShattuckUniversity of Houston
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”.
Dave ShattuckUniversity of Houston
Introduction to Engineering
• What is engineering?
Dave ShattuckUniversity of Houston
Introduction to Engineering
• What is engineering? -- Answer: Answer: Engineering is Problem Solving.Engineering is Problem Solving.
• So, what is electrical engineering?So, what is electrical engineering?
Dave ShattuckUniversity of Houston
Introduction to Engineering
• What is engineering? -- Answer: Engineering is Problem Solving.
• What is electrical engineering? -- Answer: Problem solving using Problem solving using electricity, electrical tools and electricity, electrical tools and concepts.concepts.
• What is science?What is science?
Dave ShattuckUniversity of Houston
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 Science is knowledge gaining.knowledge gaining.
Dave ShattuckUniversity of Houston
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 So, how can you tell an electrical engineer from a physicist?from a physicist?
Dave ShattuckUniversity of Houston
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
He wanted to understand He wanted to understand the stars and planetsthe stars and planets
Engineer or Scientist
Galileo?
He was a scientistHe was a scientist
Introduction to Engineering
Engineer or ScientistLeonardo da Vinci?
He was an engineerHe was an engineer
He wanted to fly, to He wanted to fly, to paint, to do thingspaint, to do things
Introduction to Engineering
He wanted to build He wanted to build things, lights, phonographs, things, lights, phonographs, etc.etc.
Engineer or Scientist
Thomas Edison?
He was an engineerHe was an engineer
Introduction to Engineering
He wanted to understand He wanted to understand how things movedhow things moved
Engineer or Scientist
Sir Isaac Newton?
He was a scientistHe was a scientist
Introduction to Engineering
Engineer or Scientist
Albert Einstein?
He was a scientistHe was a scientist
He wanted to find the He wanted to find the Unified Theory of EverythingUnified Theory of Everything
Introduction to Engineering
Engineer or Scientist
Robert Oppenheimer?
He was an engineerHe was an engineer
He wanted to build the He wanted to build the Atomic Bomb - Manhattan Atomic Bomb - Manhattan ProjectProject
Introduction to Engineering
Engineer or Scientist
Professor Paul Chu?
He is a scientistHe is a scientist
He wants to understand He wants to understand superconductivitysuperconductivity
Introduction to Engineering
Engineer or Scientist
Sir Thomas Crapper?
He was an engineerHe was an engineer
He wanted to buildHe wanted to build a sanitary toilet, which a sanitary toilet, which was so important he was knightedwas so important he was knighted
Introduction to Engineering
Dave ShattuckUniversity of Houston 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?
Dave ShattuckUniversity of Houston
Engineering Paradigms
• We are going to introduce a couple of major engineering paradigms.
• What are paradigms?
Dave ShattuckUniversity of Houston
What are paradigms?
About 20 cents.
Get it? “Pair a dimes?” Okay, so it is not very funny…
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
Euler’s Relation
• Who knows Euler’s Relation?
To Play = To Lose
Dave ShattuckUniversity of Houston
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?
Dave ShattuckUniversity of Houston
Euler’s Relation
• Euler’s Relation is:
ej= 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.
Dave ShattuckUniversity of Houston
Euler’s Relation
• Dr. Dave, can you say that again, in English? OK ….
• Sine waves happen.
Dave ShattuckUniversity of Houston
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 !!!
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
Fourier’s Theorem: Answers
• Question: Why does a guitar sound different from a violin?
• Answer: Sine wave components in the two instruments are different.
Dave ShattuckUniversity of Houston
Fourier’s Theorem: Answers
• Question: Why don’t I sound like Phil Collins?
• Answer: Sine wave components in the two voices are different.
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
Fourier’s Theorem: Answers
• Question: Why do we introduce complicated mathematical concepts like Fourier’s Theorem?
•Answer: To make life hard for engineering students.
Dave ShattuckUniversity of Houston
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!No, this is RONG!
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
Demonstration of Sinusoids
• Let’s look at a system to send signals around. (Telephone, Radio, etc.)
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
• 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?
Dave ShattuckUniversity of Houston
• 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?
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
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”.
Dave ShattuckUniversity of Houston
Modulate!!
• For example, for radio station @ 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
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston
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.
Dave ShattuckUniversity of Houston 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
Dave ShattuckUniversity of Houston
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.
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