ECEN3714 Network Analysis Lecture #39 20 April 2015 Dr. George Scheets n Problems: 15.6, 8, 22 n Quiz #10 this Friday (Fourier Series)

ECEN3714 Network Analysis Lecture #40 22 April 2015 Dr. George Scheets n Problems: 15.6, 8, 22 n Problems: 15.20, 26, 34 n Quiz #10 this Friday (Fourier Series) n Quiz #9 Results Hi = 10.0, Low = 2.0, Ave = 6.46 Standard Deviation = 2.78

Fourier Series a n = 2/T f(t) cos(nω o t) dt 0 n a 3 tells how alike f(t) and n a 3 tells how alike f(t) and cos(3ω o t) are u Over one period, T u 1/T = average u 2 = scaling factor to get power correct T

Fourier Series b n = 2/T f(t) sin(nω o t) dt 0 n b 3 tells how alike f(t) and sin n b 3 tells how alike f(t) and sin (3ω o t) are u Over one period, T u 1/T = average u 2 = scaling factor to get power correct T

Generating a Square Wave 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 a n 5 Hz is the Fundamental Frequency This waveform has 3rd, 5th, and 7th harmonics.

Fourier Transform F(ω) = f(t) e -jωt dt - ∞ ∞ n F(ω) tells how much of e -jωt is in f(t) n F(3) tells how alike f(t) and e -j3t are u Over the time interval - u Over the time interval - ∞ to +∞ u u Where e -j3t = cos(3t) + jsin(3t)

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 → Fourier n Replace "s" with "jω" 0 < t < ∞ -∞ < t < ∞ Source: Basic Engineering Circuit Analysis, 10th Edition, J. David Irwin & R. Mark Nelms, Wiley, 2011

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

Bad Opamp Circuit #1 source: Horowitz & Hill, THE ART OF ELECTRONICS, 1990

Bad Opamp Circuit #2 source: Horowitz & Hill, THE ART OF ELECTRONICS, 1990