ELE204-MT2(2007-8) - HACETTEPE UNIVERSITY DEPARTMENT OF...

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Unformatted text preview: HACETTEPE UNIVERSITY DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING .; ELE 204 CIRCUIT THEORY - II MIDTERMJI. 8 Ma 2008 Student # : Show all of your steps in detail and present your work CLEARLY. Write your name on all the papers you turn in. Read all questions CAREFULLY, and attempt to solve every part. Write onto the answer sheets, solutions on the question sheets will NOT be graded. 95".“? Q1. i. Find the Laplace transform of the following functions d (Se-2‘ cos 31%), c) x(t) ={ q 3 J, V sint, OSISIZ' a) x(t) =t‘e ' u(t), b) x(t) = E 0, otherwise ii. Find the inverse Laplace transform of the following functions (—7: s/ 2) e s + 2 8 dXs)=——,—, eXs= ,, Xs=——,—7 ) ( s‘+4 ) () (s+l)' f) () s(s‘+4)’ iii. Find x(0) and x(oo) for the following functions 1053+3052+255+50 52+S+1 . 8 g)X(S)=——2—, h)X(S)=2—, 1)X(5)=fi s(s+4)(s +85+100) s +1 s (3—4) iv. Find the impulse response of the following system if the input is x(t) and the output is y(t), j) d? +3Q+2y=ibi+3x dt' dt dt v. Solve the following differential equation using Laplace transform k) d? +8Q+ 25y = 65in 2:, where y(0) = 1, 2(0) = 0. dr dt dz Q2. Consider the circuit in Fig.2, where no energy is initially stored in the components. a) Find the transfer function Vow/[3(5), b) Find the poles and zeros of the transfer function. c) Find the zero—state response of the circuit if the input is is (t) = ((3- 3t cos 2t)u(t) A, d) Find the steady-state response of the circuit if the input is is (t) = (2 cos 2!)u(t) A. Q3. For the circuit given in F ig.3.a, assume that there is no energy stored in the circuit at the time instant when the voltage source is turned on as given in Fig. 3.b. 3) Find the transfer function V0(s)/ V.,.(5) for the circuit, b) Find the impulse response of the circuit, c) Find va(t) for t 2 0+ by using Laplace transform method when the waveform provided in Fig.3.b is applied as the input, d) Determine v00) at I = 2.55ec.s, i.e. vo(2.55ec) 2. .0. 1H fit, Q4. Consider the circuit in Fig. 4.a. The input is i,-(t) and the output is v00). 3) Find the transfer function, H(s), of the circuit, and its poles and zeros, b) What is the impulse response of this circuit? c) Find the output of the circuit for the input given in F ig.4.b. using the convolution integral, d) How long is the memory of the circuit, effectively? What is the weighting of the circuit for a delay of 0.1 secs? 1?. I). 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This note was uploaded on 05/05/2011 for the course ELE 204 taught by Professor Atillayilmaz during the Spring '11 term at Hacettepe Üniversitesi.

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ELE204-MT2(2007-8) - HACETTEPE UNIVERSITY DEPARTMENT OF...

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