ECE108HW%235Sol_06

# ECE108HW%235Sol_06 - ECE 108 Hw#5 Solution 1. Problem 3.22...

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ECE 108 Hw#5 — Solution 1. Problem 3.22 (a) Fig (b) Here 0 2 6 and 63 T π ω == = Then () ( ) ( ) ( ) 666 6 2( 1 ) 1 2 f tt t t t δδδ δ =+ −+ −− +− and () 22 0 11 66 1 1 6 6 cos 2 cos 33 oo o o o o jk jk jk jk k jk jk jk jk o Xe e e e ee e e kk ωω =− Hence ( ) [] 0 2 1 cos 2 cos 3 32 cos cos for 0 k o o SS X jk k k ππ =       0 1 2 X =

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2 3.22 (a) Figure (c) in the textbook. Here 0 2 3 and 3 T π ω == Then () () () ( ) 2 33 2 2 dxt d gt f tt t dt dt δδ = −+ + Therefore 0 0 0 00 2 3 22 0 0 1 1 19 1 for 0 4 1 2 jk k jk k k jk jk kk k Fe F e G jk jk GF ee X k jk k k k X ωω =− + = = =
3 2. Given the RC circuit shown (a) Determine the Transfer Function of the System, assuming the input is and the output ( ) i vt is ( ) 0 First write the differential equation () () () 0 0 1 t dv t i d i t C Cd t ττ −∞ =⇒ = 1 t i v t Ri t i d C τ −∞ =+ Substitute the expression for i ( t ) into the second equation ( ) 00 0 0 1 t i dv t dv dv t vt RC C d RC dt C d dt −∞ Put this differential equation in standard form 0 0 1 i dv t vt vt dt RC += Then 11 1 1 1 Hs RC s s RC == + +

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4 (b) For , determine the Amplitude and Phase Characteristic of this system 0 2 ω π = () 0 0 11 2 Hj k jk j k == ++ () () 0 22 1 0 1 14 tan 2 H k k kk θ ωπ = + =− (c) Plot the Amplitude and Phase Characteristic for the values 0 for 0, 1, 2 = =±± (d) If the input is a pulse train as shown below, determine the Fourier Coefficients of the output signal
5 00 0 1 0 11 4 44 1 4 2s i n

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## This note was uploaded on 10/24/2009 for the course ECE 108 taught by Professor Li during the Spring '08 term at Lehigh University .

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ECE108HW%235Sol_06 - ECE 108 Hw#5 Solution 1. Problem 3.22...

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