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# solution_to_last_part_questions - 14 15 For the...

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Unformatted text preview: 14 15. For the transmission line shown below, M4 {_.________._........v.,-inwW7”, Zin ’ Z0 = 50 Q 100 Q (10pts) The input impedance Zin is 10 o “ ' “V ’ (a) "my? (“:27 44" j} Zﬂﬂﬁ / i (b) 100 Q X: QM x: g; a (c) 50 Q I (d) 5 Q (e) oo W (t) 0 Q one of the above iv 12:; g}. (10pts) The reﬂection coefﬁcient F at the load is (a) 0 —1/3 ("@318 Eli) 42/3 (e) 2/3 (1‘) None of the above fem W Va.) ﬂint; ‘7’“ SW} 15 (20 pts) 16. A type of transmission line is the planar line consisting of two plates of width w and separation d. In between the two plates is free space. (a) Determine the characteristic impedance Z0. (Assuming w >> (1, and ﬁelds are conﬁned in between the two plates) (b) If the transmission line is operating at 1 GHZ, and the transmission line is of length 75 mm, determine the input impedance of the transmission line if it is shorted at the far end (2 = 75mm). W <—-————-———> z = 75 mm Z = 0 (i [g £20 2:, (,j-vllz.xc‘/L.e;.amt,"’{VL’ﬂwCR, {’3 F" («CM 4"”3’: 517’ 7/19. , C é, X 1)" A I, . v- “ 52,1" L’w-ff- v ‘T‘i’x‘iw/ f >4? I”v [yr-ﬂap? ‘ If) g M, @f l ﬁnk, “w” “ﬁx”! 5’, 4%mwywm [If bfgcyi‘i/L ,1 4-, \ W a )Lbclél x x/ L! z c: 2:» é; 45M” ’ I x w“? I] k l (y 14,5”. M13: w b w W W m {1 £3 may \ V0,.) V ﬂaw s, - t W j]; >wig§ m I i: i e r ‘ All." “(Jug/w ; m ‘ 3% 71bit]? (lb; I? j,- ' J 1 v if k f I [20% (I “7 J w iii/Wig: , g, j 6 ‘ f ‘ C7: \ Wi/ A > w ‘ X “I l i, a“ ’7 WE??? f} Claw; gall“ X mm 1 ‘ gX £564)? A 4 I 'w/ 6m)”. 14 For the shon-cirouited transmission line shown, the input impeganqe is Zia =0 a=wn Zm -—-> WWW“ w ‘ ' Cannot be infonnation. determined from the (20 pts.) 20. A plane wave E = e'jkz 21K in a medium with relative dielectric constant 4 is normally incident in the +z—direction on an interface with free space, the 2:0 plane. Region 1 8 =480 (5 pts.) The total electric ﬁeld in the incident half~space is: E) None of the above. J. U (5 pts.) The electric ﬁeld in the transmission region half space, with k0 the free-space wave number, is 1 r 4 -' IE2)=—-e “2 ax W?” W, A?!“ 1‘ E2 =_2_ejkaz ax 3 ' 1 h f / 3 E2 =[ejkoz + Ee-Jknz) ax :3 E2 = -e"*"‘ ax ' 3 ‘ f? 4 _ Ez = 38W ax . ,‘ None of the above. J. U Km \ (15 pts) 14. The region of space for z < 0 is filled with a dielectric of dielectric constant; (er/The region for z > 0 is free space. The electric field for z < 0 is given by E = (ZOe'jp‘ —10e“’”‘);2-ax . . . 9 __ V 5+ I: M (5 Pts) What is the standing wave ratio. I ,5 k wigmmiwiw % x Mr; ww /' Q (5 pts) What is the reflection coefficient? ‘4'“? ,1 W .v m... 24;» i (5 pts) Give an expression for the magnetic field for z < 0. a.» (20 pts) 15. Answer the following question for an electric ﬁeld that is described by E(x,t) = SOCosKSJr x1014s‘1)t+ (—ZﬂG—x107m")x]az K The electric ﬁeld is a wave propagating in the MX direction (:E:§irection +21z direction -az direction it is not propagating, it is a standing wave The wavelength of the wave is 2.5 x 10‘7m ~75— x107m 2.5 WWM ‘5 x lO'j-ﬁm The frequency of the wave in radians per second is, \ 2 x 10%“ ,__,r.3,2le§sT‘.l ., N ’31: x 10143:”; 3‘— ><107s'l 2.5 sumgwxmw ;f‘:\g/:f3 S ”' 'emggnitude of the velocity of the wave is z ><108 4"3\ mmﬂwws‘mm) 3X108% :1» (MW; 1 x 107 _Fl_’l_ [4,, 2.5 s The maximum value the electric field can obtain is, awmpﬁmmw . V ‘x 30- ~- (wwm~/ : 151’. m r sol m 475 (5 pts.) 22. A wave has E = aZ co{27r x10°t — Tx) V/m. Circle the comect answers. 00 Direction of propagation: @ +y +2 -x —y -z Temporal period (seconds): 27r><106 106 (27t x 10")-l Phase constant' 4% —-l-- ' 300 6 Phase velocity: c ...
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solution_to_last_part_questions - 14 15 For the...

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