test1_SPRING06

# test1_SPRING06 - ECE 220 Exam#1 Spring 2006 Section 002...

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Unformatted text preview: ECE 220 Exam #1 Spring 2006 Section 002 Student Name: K E \r LAST NAME (PRINT) FIRST NAME (PRINT) (SIGNATURE) By signing I am stating that I have taken this exam in accordance with the NCSU honor code. Show all work — no credit for answer only Spring 2006 ECE 220 Exam 1 1 1. Unit Step and Unit Pulse Functions 21. Consider the signal s(t) below. Graph the signal 31 (I) = s(0.5t + 2) on the axis provided. s(t) b. Graph the signal S1(t) = s(—t + 3) on the axis provided. s(t) Spring 2006 ECE 220 Exam 1 2 c. Consider the signal p(t) below. Write the mathematical expression for a 250Hz clock signal made from these pulses. Plt) “ t(msec) d. Represent the following signal, s(t) , as a sequence of UNIT STEP functions u (t i to) . s(t)=u(t+2)—3u(t+1)+4u(t—1)—2u(t—2)—u(t—3)+u(t—4) Spring 2006 ECE 220 Exam 1 3 2. Sinusoids: a. Given the sine wave below, write a mathematical expression for it in terms of amplitude, frequency and phase? s(t) =105in(21t +1 4 4 MSea b. Use Euler’s identity to verify the following trigonometric identity: c0s(a + [5) = cos(a) cos(/o’) — sin(a) sin([3’) j(a+/3) + e—j(a+/3‘) 2 RHS = cos(a) cos(/3’) — sin(a) sin([3’) eja+e-/a ejﬁ+e-/ﬂ eja_e-/a e/ﬂ __e-J/3 LHS =cos(a+/3) = e 2 2 2 j 2 j ej(a+/J’) +e-j(a+/J‘) ej(a+/)’) +e—/(a+ﬂ) = + 4 4 (a+ﬂ) ~J(a+/J’) e’ +e c. 21 =1— j, 22 = 4ej§ , find 21 —22 in Cartesian (rectangular) form. JE.2 21 —z2 =1—j—4(7+j—i—) = (1—2ﬁ)—j(1+2\/§) Spring 2006 ECE 220 Exam 1 4 3. Matrices: a. Given the circuit below, write the mesh equations in matrix form and solve for 11 and 12 20 2045119 6(11—12): 0 911—612 2 20 6(12-11)+212+10=0 611—812 =10 | ———9 l [9 4‘ 20l -gklmz [9 —6‘ 20 l 6 —8 10_| 0 —4 —10/3J gkﬁkl 9 0 25 l 151/: 1 0 25/9l 0 —4 —10/3_| 0 1 5/6J b. A similar circuit with variables for one of the voltage sources and one of the components produces the following system of equations. Determine the values of a and I) such that the system has no solution. x1+ax2=3 2x1—6x22b 1 3 1 a 19—6]1 (—2a—6)x2=b—6 2 —6 bJ 0 —2a—6 Spring 2006 ECE 220 Exam 1 5 4. Draw the complex numbers and the result on the compass graphs below. For full credit you must mark and label the plot accordingly. The result should be written next to the arrow in exponential form. a. (2+j2)+(2—j2)=? 17 180' 1— '3 b. e 2+e’”- 180' Spring 2006 ECE 220 Exam 1 C. (1+j)(2—j2) 2? 2%+%+L 180' Spring 2006 ECE 220 Exam 1 ...
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## This note was uploaded on 03/30/2009 for the course ECE 220 taught by Professor Nilson during the Spring '08 term at N.C. State.

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test1_SPRING06 - ECE 220 Exam#1 Spring 2006 Section 002...

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