ECEN3714 Network AnalysisLecture #39 20 April 2015Dr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen3714

ECEN3714 Network AnalysisLecture #39 20 April 2015Dr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen3714

Problems: 15.6, 8, 22 Quiz #10 this Friday (Fourier Series)

ECEN3714 Network AnalysisLecture #40 22 April 2015Dr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen3714

ECEN3714 Network AnalysisLecture #40 22 April 2015Dr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen3714

Problems: 15.6, 8, 22 Problems: 15.20, 26, 34 Quiz #10 this Friday (Fourier Series) Quiz #9 Results

Hi = 10.0, Low = 2.0, Ave = 6.46Standard Deviation = 2.78

Fourier SeriesFourier Series

an = 2/T f(t) cos(nωot) dt

0

a3 tells how alike f(t) and cos(3ωot) are

Over one period, T 1/T = average 2 = scaling factor to get power correct

T

Fourier SeriesFourier Series

bn = 2/T f(t) sin(nωot) dt

0

b3 tells how alike f(t) and sin(3ωot) are

Over one period, T 1/T = average 2 = scaling factor to get power correct

T

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

0

1.5

-1.50 1.0

5 Hz+

15 Hz+

25 Hz+

35 Hz

(1) cos2*pi*5t - (1/3)cos2*pi*15t + (1/5)cos2*pi*25t + (1/7)cos2*pi*35t) (π/4)

( ) terms are an

5 Hz is the Fundamental FrequencyThis waveform has 3rd, 5th, and 7th harmonics.

Fourier TransformFourier Transform

F(ω) = f(t) e-jωt dt- ∞

∞

F(ω) tells how much of e-jωt is in f(t) F(3) tells how alike f(t) and e-j3t are

Over the time interval -∞ to +∞ Where e-j3t = cos(3t) + jsin(3t)

Got a Laplace Transform?Got a Laplace Transform?

Re(s) = σ

Im(s) = jω

|V(s)|

The Fourier Transform of x(t) is on the jω axis.*

*Provided x(t) = 0; t < 0

Laplace → FourierLaplace → Fourier Replace "s" with "jω"

0 < t < ∞

-∞ < t < ∞

Source: Basic Engineering Circuit Analysis, 10th Edition, J. David Irwin & R. Mark Nelms, Wiley, 2011

Source: Basic Engineering Circuit Analysis, 10th Edition, J. David Irwin & R. Mark Nelms, Wiley, 2011

Fourier Transform PropertiesFourier Transform Properties

Source: Basic Engineering Circuit Analysis, 10th Edition, J. David Irwin & R. Mark Nelms, Wiley, 2011

Bad Opamp Circuit #1Bad Opamp Circuit #1

source: Horowitz & Hill, THE ART OF ELECTRONICS, 1990

Bad Opamp Circuit #2Bad Opamp Circuit #2

source: Horowitz & Hill, THE ART OF ELECTRONICS, 1990