Lecture Set 0 – Review part 1 Some important basic materials in electrical engineering

ECE 3340 - Numerical Methods for Electrical and Computer Engineers Credit Hours: 3.0 Lecture Contact Hours: 3    Lab Contact Hours: 0 Prerequisite: ECE 3331 and MATH 3321. Basic linear algebra and numerical methods with electrical engineering applications. Emphasis on use of computer-based solution techniques. MATH 3321 Background math of numerical methods ECE ???? What “electrical engineering applications?” ECE 3331 Basic programming/ coding

ECE 3340 should not be a continuation of ECE 3331 and Math 3321 The whole point is to learn the subjects in order to apply to electrical engineering Hence, we will not learn “numerical methods” in abstract, but in the context of electrical engineering by specific examples. IOW, apply ECE 3331 and Math 3321 to EE subjects.

A review of topics in electrical engineering In preparation for background materials to apply and study ece3340

Topics Periodic phenomena and harmonic functions. Complex number. Basic circuits review 1. Laplace transform. Circuits review 2 and introduction to filters Fourier series and Fourier transform Frequency analysis – power spectral density. We will learn and put to practice “Numerical Methods” via these topical examples

Topic: Periodic Phenomena and Mathematical Tools to Study Them

Unit 1

Question 1 We will study periodic phenomena in time. Things that happen regularly and repeat themselves after some period of time. Give an example of periodic phenomena that you know. Score 5

Discussion here is an example of Houston average monthly temperature. It is periodic from year to year. here is an example of day to day temperature: it goes up during the day and goes down at night. Although there is some fluctuation, the trend is periodic

Discussion: Here is an example of one of the longest ecological study of predator and prey dynamic. Note how the populations of the lynx and the hare went up and down periodically over nearly a 90-year period. But there seems to be a time lag between them. The lynx population tended to rise a bit later than that of the hare and when the hare population dropped, it also followed. Why? http://www.okc.cc.ok.us/biologylabs/Images/Homeostasis%20Images/lynx-hare.jpg

Discussion: The sun has spots with 11-years cycle. http://upload.wikimedia.org/wikipedia/commons/2/28/Sunspot_Numbers.png

Circadian cycle (or rhythm) is common in many living things on earth Circadian cycle (or rhythm) is common in many living things on earth. We have a 24-hr internal clock in our body. But it needs daylight to synchronize. Even bacteria have it. Here is an example of a cyanobacterium species that emits light with 24-hr cycle, even in darkness. Discussion:

Question 2 Now, let’s get more examples. Find what you can online or wherever. You get points for each correct example. Find up to 3. Score 10

Discussion: Let’s test our concept. Which of the following examples do you think periodic and which is not.

Question 3 Human population, periodic or non-periodic Score 12

Question 4 Our heart beats Score 14

You must have seen the Foucault pendulum in museum You must have seen the Foucault pendulum in museum. It appears to be periodic. But is it absolutely periodic in one fixed vertical plane? (in other words, does it swing in just one vertical plane?) Question 5 http://www.google.com/doodles/leon-foucaults-194th-birthday Score 16

Question 6 Stock market: periodic or non-periodic Score 18

Discussion: Critical thinking: The concept of periodicity in science is not the same as that in math with rigorous definition.

Question 7 Now, let’s look for some periodic phenomena closer to home, like right here in this class room, right now. Find some examples here and now.

Question 8 Write the most general mathematical function that you can think of to describe all periodic phenomena that we have seen so far.

Demo:

Question 1 How do we describe the voltage signal as a function of time mathematically? Write a formula and plot it Score 25

Discussion: If our whistling can be recorded as a sine (or cosine) signal, can we do the reverse: can the signal we plot also be played to generate sound. Tutorial in Mathematica

Another experiments. How would you plots these two signals Question 2 Another experiments. How would you plots these two signals

Discussion: 𝑇= 2𝜋  Period 𝑉=cos⁡(𝑡) 𝑇= 1 𝒇 𝑉=cos⁡(𝟐 𝝅𝒇𝑡)

Unit 2

Continued from the last time

Question 3

Discussion: 𝑉=𝐀 cos⁡(𝑡)

Discussion: The answer is: G, or E, or B. But it depends on which shadow or projection that you look at.

Question 4 Which one is periodic and which one is not? (a) (b)

Discussion: Use your imagination, what does this animation remind you of? Score 50

Discussion:

Question 5 Let’s project the shadow of the planet on a wall as shown. Write a mathematical expression (function) to describe the shadow position (the red line) on the wall as a function of time? Score 55

What is the relationship of the shadow frequency vs the angular (rotational) speed of the blue planet? Question 6 𝑓= 1 𝑇 = 𝜔 2𝜋 Score 60

Now, let’s look at the shadow position on a different wall (the blue line). What is the function for this? You have to be specific and write out the whole expression, amplitude, frequency included). Question 7

Discussion

Discussion Score 65

Discussion: Sine can be made into cosine and vice versa if only we can “slide” it as shown below. But how?

Mathematica app demo Question 8 𝑉=𝐀 cos⁡(𝑡+) Slide the phase back and forth to see the translation of the function.

𝑉=𝐀 cos⁡(𝑡+) 𝑉=𝐀 cos⁡(2 𝜋𝑓𝑡+) Amplitude Frequency Phase Discussion: Just remember 3 things: Amplitude Frequency Phase 𝑉=𝐀 cos⁡(𝑡+) 𝑉=𝐀 cos⁡(2 𝜋𝑓𝑡+)

Write expressions to describe the motions (position vs Write expressions to describe the motions (position vs. time) of Red, Green, and Blue dots on each respective axis. Question 9 Score 75 𝑉=𝐀 cos⁡(2 𝜋𝑓𝑡+)

Discussion: Score 80

Discussion: Now we look at Green, We don’t care about the absolute phase. But this Green phase has to be correct relative to what we pick for Red. Look at the orange/purple axes. They are rotated by 2Pi/3 relative to the vertical/horizontal axes. 2𝜋 3 Score 100 Discussion:

Question 10 Name an application for this

Question 10 Name an application for this Score 105

Question 11 Search online for a mechanical device that uses 3-phase AC 3-phase motor 3-cylinder engine Score 110

Additional examples of phase devices

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