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# 329sum09he3sol - ECE 329 Hour Exam 3 Aug 3 2009 1 Consider...

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Unformatted text preview: ECE 329 Hour Exam 3 Aug 3, 2009 1. Consider a plane TEM wave propagating in +y direction in free space. The ﬁeld is left—hand circular polarized, and at t = 0 the electric ﬁeld vector on the y = 0 plane is found to be 2071' i V/m. a) (10 pts) Determine the electric ﬁeld phasor E(y) of the wave, E N l /* pA f E:207{Q,Ja>£J(5ll/ m /‘ ‘7‘ "X Ma b) (10 pts) Determine the accompanying I:I(y) phasor. c) (10 pts) Determine the timeaverage Poynting vector, i.e., (E X H) — simplify the result as much asyoucan. (2 M‘ (16%?»- 2W2 W“; : Mme: xgei—m E V H” 0" l l 2. A plane wave ﬁeld E = 20 cos(wt - ﬁz) i: V/m is propagating in free space in the +z direction and is incident on the z = 0 plane which happens to be the boundary of a perfect dielectric having permittivity 960 and permeability no in the region 2 > 0. Determine: a) (IO-pts) The expression for the incident electric ﬁeld in phasor form. N r ’ 20 1(5‘2 A \/ J5? : e >< M . A Kim—«t [7:00 ﬂea? ’3 / (ALW flﬂcﬁo %/ G b) (10 pts) The phasor expressions for the reﬂected and transmitted electric ﬁelds. /( '_ J 0-— .l—( r" {7_ r (; 2 :37! ”lb ; 3 A 3,; , -z:,0,§ (,(+ ,0.g / mm ”‘é’loWo @524 1+3 4 / N 9!. we L: sf" \= min?“\$ 9 «4/ r N ' 10 3? :TE' ’0 5”” W/ 4: c) (10 pts) The phasor expressions for the incident, reﬂective, and transmitted H ﬁelds in A/m units. 3. A generator with internal resistance R9 = 609 and an open circuit output voltage f (t) = 606(t) feeds a T.L. (see the ckt diagram on the left below) that has an unknown characteristic impedance Z, and an unknown resistive load termination RL at an unknown distance, L, from the generator. At a distance 2 = 300 m from the generator, smaller than L, the voltage waveform as a function of time is as plotted below on the right. gcgf§£= 3 7:: 4 V (in Volts at z=300m) 206(t-1) . Shuts evmai Ma; (‘4? ' 7 * HT‘W—H t (HS) 6‘7 -1o/38(t-8) 1%? —105(t-6) a)(5 pts) Determine the impedance of the transmission line, Z0. 20 ZL aoﬁ‘g’oﬂ r 0:; :2 Ma, 7. ,_ “VP/5m» ’ (ma E” 7/10 j ,// CLng 2'6 .. 37’ ;! /‘ / 60%?» @137: E b) (5 pts) Determine the load reﬂection coefﬁcient FL and the load resistance, RL. .. i l7 ZZL’Z" : gL'3O; -L L 7- L aura auzo ”L '“ - , :IOJL, Z.) ZZL— A0 :r-ZL—ao .7 321530 7 h / d) (15 pts) Sketch a bounce diagram using the axes shown below for the voltage waveform V(z, t) for 0 < t < 10 us. Be sure to mark the numerical values for the waveform amplitude in the diagram. Gus ' l t Current (A) z=O z=L a-I—un—u—b z e) (10 pts) What is the algebraic expression for the voltage waveform as a function of (2,15) for the domain 0<z <L and0<t< lOus. W230: 20;“ ’E) - lo £(Jc+ int/us) 'é‘.’ 56% 2% 474;) . . < .w' w WM“ . WWW”. MVm~MMMMTWWWMWWi ...
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