ECEN3714 Network Analysis Lecture #1 12 January 2015 Dr. George Scheets

Goal of this class: n Builds on Material from ECEN2613 n Add to your Circuit Design & Analysis Tool Set n Examine Transform Theory u Laplace Transforms u Fourier Series (subset of Fourier Transforms) n Provide a hands-on experience with experiments related to the lectures.

Why bother learning math functions when machines can do it?

Because you can't always trust those fancy machines.

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Contact Information n n Phone (405) n Tentative Office Hours u Monday & Wednesday: 1:00 – 2:00 pm u Tuesday & Thursday: 1:00 – 2:30 pm n Lab Teaching Assistant u Tristan Underwood u

Grading n Class Work u 10 x 10 point Quizzes u 2 x 100 point Exams u 1 x 150 point Comprehensive Final u 450 points Total n Lab Work u 10 x 10 point Lab Experiments u 1 x 30 point Practical u 1 x 30 point Design Project u 160 points Total n Overall u Class work weighted 1.0, Lab work weighted u 670 points total; *1.375 = n 90%, 80%, 70% etc. A/B/C break points will be curved... unless you miss any lab work, then no curve.

Extra Credit n Errors in text, HW solutions, instructor notes, test or quiz solutions, lab manual (20 points max) n Attend IEEE functions (15 points) u 3 presentations (3 points apiece + dinner) u ECE spring banquet (6 points)

Lectures n Quiz or Exam Every Friday u Except: 16 January, 13 March, & 1 May n Quizzes u Open book, notes, instructor n Tests u Open book & notes n Monday & Wednesday u Lectures u Feel free to interrupt with pertinent questions or comment at any time

Grading n In Class: Quizzes, Tests, Final Exam Open Book & Open Notes WARNING! Study for them like they’re closed book! n Ungraded Homework: Assigned most every class Not collected Solutions Provided Payoff: Tests & Quizzes

ECEN3714 Network Analysis Lecture #1 12 January 2014 Dr. George Scheets n Review Appendix (Complex Numbers) & Chapter 12.1 n Ungraded Homework Problems: None

Why work the ungraded Homework problems? n An Analogy: Linear Systems vs. Soccer n Reading text = Reading a book about Soccer n Looking at the problem solutions = watching a scrimmage n Working the problems = practicing or playing in a scrimmage n Quiz = Exhibition Game or Scrimmage n Test = Big Game

To succeed in this class... n Show some self-discipline!! Important!! For every hour of class put in 1-2 hours of your own effort. n PROFESSOR'S LAMENT If you put in the time You should do fine. If you don't, You likely won't.

What to study? S

S Readings

What to study? S ReadingsHomework

What to study? S ReadingsHomework Class Notes

Cheating n Don’t do it! If caught, expect to get an ‘F’ for the course. n My idol: Judge Isaac Parker U.S. Court: Western District of Arkansas a.k.a. “Hanging Judge Parker” a.k.a. “Hanging Judge Parker”

Calvin’s Thoughts on Cheating…

Labs n Start at Scheduled Time on Week #2 n But NOT in scheduled place n First 2 Wednesday Labs in EN 510 n First 2 Friday Labs in EN 019

5 Hertz Square Wave... 1 volt peak, 2 volts peak-to-peak, 0 mean

Generating a Square Wave vp 5 Hz 1/3 vp 15 Hz

Generating a Square Wave Hz + 15 Hz

Generating a Square Wave /5 vp 25 Hz Hz + 15 Hz

Generating a Square Wave Hz + 15 Hz + 25 Hz

Generating a Square Wave /7 vp 35 Hz Hz + 15 Hz + 25 Hz

Generating a Square Wave Hz + 15 Hz + 25 Hz + 35 Hz cos2*pi*5t - (1/3)cos2*pi*15t + (1/5)cos2*pi*25t - (1/7)cos2*pi*35t)

Generating a Square Wave... 5 cycle per second square wave generated using first 50 cosines, Absolute Bandwidth = 495 Hertz

Generating a Square Wave... 5 cycle per second square wave generated using first 100 cosines, Absolute Bandwidth = 995 Hertz

Sines & Cosines n Can be used to construct any time domain waveform n x(t) = ∑ [ a i cos(2πf i t) + b i sin(2πf i t) ] n cosines & sines are 90 degrees apart cos(2πft) + j sin(2πft) n Phasor e jπft = cos(2πft) + j sin(2πft) n cos(2πft) = Real {e jπft } n sin(2πft) = Imaginary {e jπft } n Wikipedia Example Wikipedia Example Wikipedia Example

Phasor Projection n Projection on Real Axis = Cosine n Projection on Imaginary Axis = Sine Snapshot after 1 phasor revolution

ECEN3714 Network Analysis Lecture #2 14 January 2015 Dr. George Scheets n Read 13.1 – 13.4 n Ungraded Homework Problems 12.1, 2, & 3

OSI IEEE n January General Meeting n 5:50-6:30 pm, Wednesday, 21 January n ES201b n Reps from Grand River Dam will present u Operate 3 dams, 2 lakes, Salina Pump Storage n Dinner will be served n All are invited

Complex Numbers Rectangular & Polar Coordinates Easiest to use... Addition (x+y)Rectangular Subtraction (x-y)Rectangular Multiplication (x*y)Rectangular or Polar Division (x/y)Polar 3 ways to represent a complex number Ex) 9 + j9 = 81 / 45o = 81ejπ/4

Last Time… n Two complex numbers x = 7 + j4 = / o = 8.062e j0.1652π y = 2 – j4 = 4.472/ o = 4.472e -j0.3524π y = 2 – j4 = 4.472/ o = 4.472e -j0.3524π

Pierre-Simon Marquis de Laplace n Born 1749 n Died 1827 n French Mathematician & Astronomer n Previously, you've had y(t) = function{ x(t) } u Solved in time domain (derivatives?, integrals?) n In 1785, Laplace noticed it's frequently easier to solve these via x(t) → X(s) →Y(s) → y(t) transform massage transform

ECEN3714 Network Analysis Lecture #3 16 January 2015 Dr. George Scheets n Problems: 13.2, 4, & 6

OSI IEEE n January General Meeting n 5:50-6:30 pm, Wednesday, 21 January n ES201b n Reps from Grand River Dam will present u Operate 3 dams, 2 lakes, Salina Pump Storage n Dinner will be served + 3 pts extra credit n All are invited

Time Bounds n None Specified? Assume 0 - < t < ∞ = 0 < t < ∞ u (Default bounds for this class) n Assume time function = 0 where not specified u Example: x(t) = 7t; t > 3 Assume x(t) = 0 when t 3 Assume x(t) = 0 when t < 3

Laplace Transform F(s) = f(t) e -st dt 0-0- ∞ "s" is a complex number = σ + jω Fourier Transform is similar σ = 0 Lower Bound = -∞

Correlation n Provides a measure of how "alike" x(t) and y(t) are n If integral evaluates positive u x(t1) and y(t1) tend to be doing same thing t1 an arbitrary time u if x(t1) is positive, y(t1) tends to be positive u if x(t1) is negative, y(t1) tends to be negative x(t) y(t) dt

Correlation n If integral evaluates negative u x(t1) and y(t1) tend to be doing the opposite n If evaluates = 0 u x(t) & y(t) are not related (uncorrelated) no predictability x(t) y(t) dt

Laplace Transform F(s) = f(t) e -st dt 0-0- ∞

Laplace Transform of f(t) = e -2t F(s) = e -2t e -st dt 0-0- ∞

Laplace Transform of e -2t F(0) = e -2t e -0t dt 0-0- ∞

Laplace Transform of e -2t t e -0t = u(t) t e -2t n This evaluates to F(0) = 1/2

Laplace Transform of e -2t F(2) = e -2t e -2t dt 0-0- ∞ F(s) = e -2t e -2t dt 0-0- ∞

Laplace Transform of e -2t t e -2t n Product is e -4t, which has area F(2) = 1/4. t e -st evaluated at s = 2 Ideally, these two waveforms would have the highest + correlation. Laplace Transform is an imperfect correlator.

Normalized Energy e -2t e -st dt ∞ 0-0- e -st dt ∞ 0-0- NE(s) =

Normalized Energy Plot s NE(s) = s 0.5 /(s+2) Peak is at s = 2.

Correlation & Laplace Transform n Somewhat similar x(t) y(t) dt