HW1 - phasors: a) F = j2 b) F = 3e-j/6 c) F = j2 + 3e-j/6...

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ECE 45 Fall 2007 Homework #1 Due in class on Thursday, October 11 th , 2007 Problem 1 : Kudeki 2.16 (with some modifications) Let A = 3 – j3, B = -1 –j1, and C = 5e -jπ/3 : (a) Find D = AB. Express D in exponential form. (b) Find E = A/B. Express E in rectangular form. (c) Find F = B/C. Express F in exponential form. (d) Find H = (A + B)*. Determine the magnitude |H| and angle <H. Problem 2 : Kudeki 3.19 (a) Show that the following is true: ) 2 cos( 2 2 2 t e e t j t j = + (b) Express the following in terms of a sine function: j e e t j t j 2 4 4 (c) Given that the following is true -4(e j3t + e -j3t ) = Acos(3t + θ) determine the values of A and θ (d) Express the following in terms of a cosine function: P = Re{2e j(π/3) e j5t }
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Problem 3 : Kudeki 4.1 Determine the phasor F for the following sinusoidal functions: a) f(t) = 2cos(2t + π/3) b) f(t) = Asin(wt) c) f(t) = -5sin(πt) Problem 4 : Kudeki 4.2 Find the cosine function f(t) with frequency w = 2 rad/sec corresponding to the following
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Unformatted text preview: phasors: a) F = j2 b) F = 3e-j/6 c) F = j2 + 3e-j/6 Problem 5 : Kudeki 4.6 Using the phasor method, determine the current i(t): 5cos(5t) A 5 1 H i(t) Problem 6 : Kudeki 4.7 (with some modifications) Using the phasor method, determine the phasor voltages V1 , V2 , and V3 . Express these voltages in exponential form. Assuming w = 1 rad/sec, find V1(t), V2(t), and V3(t). Problem 7 : Bandpass Filter Exercise a) Using the phasor method, determine the frequency response H(w) of the system above. Find the magnitude |H(w)| and the phase &lt;H(w) b) Show the following is true: i) |H(w)| = 1 when LC w / 1 = ii) |H(w)| = 0 when w iii) |H(w)| = 0 when w c) Using results from (b), sketch the magnitude plot |H(w)| vs. angular frequency w. 2 V -j 2 1 j2 1e j 90 A V1 V2 V3 C L R + v O (t) - + v i (t) -...
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HW1 - phasors: a) F = j2 b) F = 3e-j/6 c) F = j2 + 3e-j/6...

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