ecen3714 network analysis lecture #1 12 january 2015 dr. george scheets

ECEN3714 Network AnalysisLecture #1 12 January 2015Dr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen3714


Goal of this class:Goal of this class:

Builds on Material from ECEN2613 Add to your Circuit Design &

Analysis Tool Set Examine Transform Theory

Laplace Transforms Fourier Series (subset of Fourier Transforms)

Provide a hands-on experience with experiments related to the lectures.

Why bother learning mathfunctions when machines can

do it?

Why bother learning mathfunctions when machines can

do it?

Because you can't always trust those fancy machines.

Because you can't always trust those fancy machines.

Class Home Page

www.okstate.edu/elec-engr/scheets/ecen3714/

Class Home Page

www.okstate.edu/elec-engr/scheets/ecen3714/ECEN Home Page

PeopleScheets

Personal Home Page

http://www.okstate.edu/elec-engr/scheets/ecen3714/







Contact InformationContact Information EMail: [email protected] Phone (405)744-6553 Tentative Office Hours

Monday & Wednesday: 1:00 – 2:00 pm Tuesday & Thursday: 1:00 – 2:30 pm

Lab Teaching Assistant Tristan Underwood [email protected]

GradingGrading Class Work

10 x 10 point Quizzes 2 x 100 point Exams 1 x 150 point Comprehensive Final 450 points Total

Lab Work 10 x 10 point Lab Experiments 1 x 30 point Practical 1 x 30 point Design Project 160 points Total

Overall Class work weighted 1.0, Lab work weighted 1.375 670 points total; 450 + 160*1.375 = 450 + 220

90%, 80%, 70% etc. A/B/C break points will be curved... unless you miss any lab work, then no curve.

Extra CreditExtra Credit

Errors in text, HW solutions, instructor notes, test or quiz solutions, lab manual(20 points max)

Attend IEEE functions (15 points) 3 presentations (3 points apiece + dinner) ECE spring banquet (6 points)

LecturesLectures Quiz or Exam Every Friday

Except: 16 January, 13 March, & 1 May Quizzes

Open book, notes, instructor Tests

Open book & notes Monday & Wednesday

Lectures Feel free to interrupt with pertinent questions or

comment at any time

GradingGrading In Class: Quizzes, Tests, Final Exam

Open Book & Open NotesWARNING! Study for them like they’re closed book!

Ungraded Homework: Assigned most every classNot collectedSolutions ProvidedPayoff: Tests & Quizzes



Review Appendix (Complex Numbers)& Chapter 12.1

Ungraded Homework Problems: None

Why work the ungraded Homework problems?Why work the ungraded Homework problems?

An Analogy: Linear Systems vs. Soccer Reading text = Reading a book about Soccer Looking at the problem solutions =

watching a scrimmage Working the problems =

practicing or playing in a scrimmage Quiz = Exhibition Game or Scrimmage Test = Big Game

To succeed in this class...To succeed in this class...

Show some self-discipline!! Important!!For every hour of class...

... put in 1-2 hours of your own effort.

PROFESSOR'S LAMENTIf you put in the timeYou should do fine.If you don't,You likely won't.

What to study?What to study?

S


S

Readings


S

ReadingsHomework


S

ReadingsHomework

ClassNotes

CheatingCheating Don’t do it!

If caught, expect to get an ‘F’ for the course.

My idol:Judge Isaac ParkerU.S. Court: Western District of Arkansas1875-1896

a.k.a. “Hanging Judge Parker”

Calvin’s Thoughts on Cheating…Calvin’s Thoughts on Cheating…

LabsLabs

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

5 Hertz Square Wave...5 Hertz Square Wave...

1 volt peak, 2 volts peak-to-peak, 0 mean

0

1.5

-1.50 1.0

Generating a Square Wave...Generating a Square Wave...

0

1.5

-1.50 1.0

0

1.5

-1.50 1.0

1 vp5 Hz

1/3 vp15 Hz


0

1.5

-1.50 1.0

5 Hz+

15 Hz


0

1.5

-1.50 1.0

1/5 vp25 Hz

0

1.5

-1.50 1.0

5 Hz+

15 Hz


0

1.5

-1.50 1.0

5 Hz+

15 Hz+

25 Hz


0

1.5

-1.50 1.0

1/7 vp35 Hz

0

1.5

-1.50 1.0

5 Hz+

15 Hz+

25 Hz


0

1.5

-1.50 1.0

5 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)


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

0

1.5

-1.50 1.0


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

0

1.5

-1.50 1.0

Sines & CosinesSines & Cosines Can be used to construct any time domain

waveform x(t) = ∑ [ aicos(2πfit) + bisin(2πfit) ] cosines & sines are 90 degrees apart

cos(2πft) + j sin(2πft) Phasor

ejπft = cos(2πft) + j sin(2πft) cos(2πft) = Real {ejπft } sin(2πft) = Imaginary {ejπft } Wikipedia Example

http://en.wikipedia.org/wiki/Phasor

Phasor ProjectionPhasor Projection

Projection on Real Axis = Cosine

Projection on Imaginary Axis = Sine

Snapshot after 1 phasor revolution



Read 13.1 – 13.4 Ungraded Homework Problems

12.1, 2, & 3

OSI IEEEOSI IEEE

January General Meeting 5:50-6:30 pm, Wednesday, 21 January ES201b

Reps from Grand River Dam will present Operate 3 dams, 2 lakes, Salina Pump Storage

Dinner will be served All are invited

Complex NumbersRectangular & Polar Coordinates

Complex NumbersRectangular & 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…Last Time…

Two complex numbers

x = 7 + j4 = 8.062 / 29.74o = 8.062ej0.1652π

y = 2 – j4 = 4.472/ - 63.43o = 4.472e-j0.3524π

Pierre-SimonMarquis de LaplacePierre-SimonMarquis de Laplace Born 1749 Died 1827 French Mathematician

& Astronomer Previously, you've had y(t) = function{ x(t) }

Solved in time domain (derivatives?, integrals?) In 1785, Laplace noticed it's frequently easier

to solve these via x(t) → X(s) →Y(s) → y(t) transform massage transform



Problems: 13.2, 4, & 6

OSI IEEEOSI IEEE

January General Meeting 5:50-6:30 pm, Wednesday, 21 January ES201b

Reps from Grand River Dam will present Operate 3 dams, 2 lakes, Salina Pump Storage

Dinner will be served + 3 pts extra credit All are invited

Time BoundsTime Bounds

None Specified?Assume 0- < t < ∞ = 0 < t < ∞ (Default bounds for this class)

Assume time function = 0 where not specified

Example: x(t) = 7t; t > 3Assume x(t) = 0 when t < 3

Laplace TransformLaplace Transform

F(s) = f(t) e-st dt

0-

∞

"s" is a complex number = σ + jω

Fourier Transform is similar σ = 0 Lower Bound = -∞

CorrelationCorrelation

Provides a measure of how "alike" x(t) and y(t) are

If integral evaluates positive x(t1) and y(t1) tend to be doing same thing

t1 an arbitrary time if x(t1) is positive, y(t1) tends to be positive if x(t1) is negative, y(t1) tends to be negative

x(t) y(t) dt

CorrelationCorrelation

If integral evaluates negative x(t1) and y(t1) tend to be doing the opposite

If evaluates = 0 x(t) & y(t) are not related (uncorrelated)

no predictability

x(t) y(t) dt

Laplace TransformLaplace Transform

F(s) = f(t) e-st dt

0-

∞

Laplace Transform of f(t) = e-2tLaplace Transform of f(t) = e-2t

F(s) = e-2t e-st dt

0-

∞

Laplace Transform of e-2tLaplace Transform of e-2t

F(0) = e-2t e-0t dt

0-

∞


t

e-0t = u(t)

t

e-2t

This evaluates to F(0) = 1/2


F(2) = e-2t e-2t dt

0-

∞

F(s) = e-2t e-2t dt

0-

∞


t

e-2t

Product is e-4t, which has area F(2) = 1/4.

t

e-st evaluated at s = 2Ideally, these twowaveforms would have the highest + correlation.

Laplace Transformis an imperfectcorrelator.

Normalized EnergyNormalized Energy

e-2t e-st dt

∞

0-

e-st dt

∞

0-

NE(s) =

Normalized Energy PlotNormalized Energy Plot

s

NE(s) = s0.5/(s+2)

.354

0 2 Peak is at s = 2.

Correlation & Laplace Transform Correlation & Laplace Transform

Somewhat similar

x(t) y(t) dt

ecen3714 network analysis lecture #1 12 january 2015 dr. george scheets

Documents

n phone

ecen2613 n

n builds

u lectures u

points u

grading n class work

n quizzes u open book

points total n lab work