EM2_2005_Mid.pdf - Electromagnetics 11 Midterm...

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Unformatted text preview: Electromagnetics 11 Midterm Exam (10:10am-11:50am) 11/14/2005 :1: gag 20 9} ’ R: 4397* i3]: 5 7% . anew} 100 a} o 1. Finding fields and power flow for a parallel-plate line for specified voltage along the line. A parallel—plate transmission line is made up of perfect conductors of width w = 0.1m and lying in the planes x = 0 and x = 0.01 m. The medium between the conductors is a nonmagnetic (u = u 0), perfect dielectric. For a uniform plane wave propagating along the line, the voltage along the line is given by V(z,t) =10cos(37z><10gt—2772)V Neglecting fringing of fields, find: (a) the electric field intensity Ex(z,t) of the wave; (b) the magnetic field intensity Hy(z,t) of the wave; (c) the current [(2,1) along the line ; and (d) the power flow P(z,t) down the line. 2. Time-domain analysis of a transmission-line system using the bounce-diagram technique. In the system shown in Fig.P2, the switch S is closed at t = 0. Assume Vg(t) to be a direct voltage of 90 V and draw the voltage and current bounce diagrams. From these bounce diagrams, sketch: (a) the line voltage and line current versus t (up to t = 7.25 [1 s) at z = 0, z = I, and z =l/2; and (b) the line voltage and line current versus 2 for t = 1.2 u s andt=3.5us. "X .S' WWW u..U i 90 .0. § , l 1 @2m9 3mm; if i I =l./J,S .//:\\ away W»! fl i=0 . 5:! Figure P2 3. A transmission-line system with inductive discontinuity. In the system shown in Fig.P3, the switch S is closed at t = 0, with the lines uncharged and with zero current in the inductor; Obtain the solution for the line voltage versus time at z = 1+. ,J_ 1/1] ‘T" _ l i 9 ; i ' =‘ w—b— : - 1 1_ W = Z— —_—)— - Figure P3 4. Fig. P4 shows a transmission line system driven by a switching gate. Transmission line 3 (TX 3) is a short stub between transmission line 1 (Txl) and transmission line 2 (Tx2). A capacitive load CL is terminated at the end of Tx2, and the end of Tx3 is open circuit. The per-unit-length coupling inductance and capacitance between Txl (or TxZ) and transmission line 4 (TX4) are Lm and Cm, respectively. As shown in Fig. P4, the characteristic impedances of Txl, Tx2 and Tx4 are all Z0. The characteristic impedance of TX3 is Z]. The delay of Txl, Tx2, Tx3, and Tx4 are 772, 772, 774, and T, reSpectively. The propagation velocity of all transmission lines is V p. a. Assume the initial voltage and current on the transmission line system is both zero, and switch 81 and 82 are opened. At t = 0, S] is closed. Please derive and sketch the voltage waveform Vc(t) on the load CL (point A) forOStSlJST . (The mutual coupling with Tx4 can be ignored here.) b. The timing requirement for the voltage waveform Vc(t) is V50) 2 V”, at 2‘2 T +CLZO. Please design the minimum characteristic impedance of the short stub 21 to satisfy this timing requirement. It is assumed C LZ0< <T /4 . A 32 Z0 , T/2 Zo , T/2 CL Z“ Rem, L". I B n4 Z0 , T Z0 Z0 Figure P4 5. hi the system shown in Fig.P4, after the transmission lines system enters the steady state, the switch 81 is opened and S; is closed simultaneously at time Is. Please derive and sketch the coupling waveform at the near end of Tx4 (point B) forTS S ts TS +T . It is assumed that the system is weakly coupling. 6. In the system shown in Fig. P6, steady-state conditions are established with the switch S closed. At the switch S is opened. a. Find the energy stored in the system at t = 0'. b. Obtain the solutions for the voltages across RL1 and Km for t > O. c. Show that the total energy dissipated in Ru and RL2 for t > 0 is equal to the energy stored in the system at t = 0 R1. |=Zn 2Z0 , T=CZO R.L2=ZZo Figure P6 20f2 Ex W2] Hé T C I NP \ Eli/cg : LEy/Ogm/S =3 : “gr—‘13:; F 17‘; Nib-o . (lira .IJ {LU (/Qflli EKXlu‘gt LYLE) W. 31 ‘ . . , ,2- mxx+Q-\\\\.\<'l‘1 W “L L L \. h ‘ Fin-v , .\ VG .- ‘r :4 w “v —;. ") ‘ I / { ~. I u y {.1 , ,2, 5 .__\ Qf ‘57 f. '5 - ,_._. ..___. m — j ; - 3...»; H x ‘ 7— H? i g ‘4 J'\ L... {1" :1 2L '4‘ 03“; 11- ' {C- 4.1; 7.0 di ‘ Q: 3., \J’c -f'gl) \i 1—: *ANQ 5‘ {L \t , + M JET , mmt Hawk L T: zero. 2T" V0 " 2'“ —‘ 02‘:+AQ ( AL)! V'nLg“: 2 3 ”Z T ’0 | r} E? \l! I ( t .___:l ' “ I“ E ‘00 0’ j \P‘ V3747 9V 7‘ J; iv WE’VE?” <~v"v<> ~ ) 5; Err—w , E we "L E 1% j+€b 3 ‘TfimloV‘iw? Vl+:_.2;g\/ ‘(il/ \E: iLl/i l8! ‘Qm W L S”! ZQIEa E . 9 fl fl We ZVEL Lfig’f‘in ' ‘2 :2 x 2 .V \ 1 \\[4,2 :§ ‘1‘:‘-- '> “v w—w (i {‘57 \ I; r, ‘8 \x ‘ m*-~. i ‘20 ‘15} 19’} ‘3 7 :goV‘H: < 2/5 i‘€)*24’fiv’ 2; 1‘5! , H Li" g ”g W M fiTf) Whig-1 Ve—Xé {dz'n 1 1+: ‘ V0 M Rcfim C! Cnufi‘mg wkmge WE few-E B cow’s/v; {weak «CHM he‘CIKWWWK (N‘Afm‘g- {FW‘M Vf (vak £0vwmok yoMth$ Syrom V+~ mm): 14;, (Wm—WH—flk Mal-3f (twig Hwy] Vut f/ ) f , “J“ ‘1’"?th W0Vea~€ \’V\ m wigfe/M I'W‘?‘ in \— :édkw-“r‘ ‘ 5 "n ~37 r L1 éxéo ;; é \ fi .9 in is v0 *9 , “+1 C -—§'1+ O my: , I / l%v+1 v“ «U0 U- ...
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