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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
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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
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