JoyNotes

ECE 27L – Spring 2008 Test 2 Notes Alex Beutel March 31, 2008 Differential equations: dy + ay = b dt s = −a b A= a v(t0 ) − A B= est0 y = A + Best On the test: 1. RC circuits in time 2. RC circuits in frequency domain 3. Frequency response (to periodic input) 4. Fourier series Identities: cos(θ) = cos(−θ) sin(−θ) = − sin(θ) e jθ (1) (2) (3) (4) (5) (6) (7) (8) = Ae jθ+jωt jθ jωt = cos θ + j sin θ jθ A θ = Ae Fourier Series: = Ae e ∞ (9) x(t) = C0 + n=1 Cn cos(nω0 t + θn ) (10) (11) (12) f = a0 + Σai enω0 jt C0 = Cn = Other stuff: f0 = 1 T w = 2πf 1 T 2 T t0 +T vin (t)dt t0 t0 +T t0 vin (t)e−jn T t dt 2π (13) (14) (15) 1 Phasors: ˜ ar =| A | cos θA ˜ ai =| A | sin θA ˜ |A|= θA ˜˜ A×B ˜ A ˜ B a2 + a2 r i −1 ai = tan ( ) ar ˜ || B | (θA + θB ) ˜ =| A ˜ |A| = (θA − θB ) ˜ |B| (16) (17) (18) (19) (20) (21) (22) (23) (24) ˜ ˜ An =| A |n (nθA ) ˜˜ A ± B = (ar ± br ) + j(ai ± bi ) ˜ ˜ A∗ = ar − jai =| A | (−θA ) NOTE: TI-83 / 84 models only interpret eθi in terms of radians, even if the calculator is in degree mode. 2 

Document Info

Posted By:

Alex Beutel

Date:

Sunday, March 30, 2008

School:

Duke University

Class:

ECE 27L

Tags:

• Fourier Series
• Maxwell
• Circuits
• Frequency Response
• Phasors
• Engineering
• ECE

About this Document

This is a review sheet of a few basic ideas for Dr. Ybarra's second exam.