test1_SPRING06

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

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Page1 / 7

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online