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Unformatted text preview: Notes: ECE604
Midterm Exam #2
April 8, 2004 4 problems
Formula sheets (3 pages) is supplied separately or attached at back. You are also allowed your own one—sided 8 1/2” X 11” formula sheet Please put your name on each page. SOIDJW‘“ Name Problem 1. 20 points A pair of circular perfectly conducting plates of radius a are separated by a distance d << 21 to
form a circular capacitor. Discuss the conditions under which it is valid to write the fields within the capacitor as E — —Y&—z sin (0t, H~ 0. 53,44}
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/ M ) 5001‘ ”ﬂtﬂL .9 ?dw'a’l st" 74"” “M” W” 7; MHA ion/wk Name Problem 2. 20 points (2 parts) An ideal lossless transmission line is terminated by a load impedance ZL equal to half the
characteristic impedance Z0 of the transmission line, i.e., ZL = 20/2. An additional impedance
with value ZQ is placed across the line a distance D in front of the load impedance. Transmission line Sinusoidal
signal
generator Characteristic ' l4— D——> v '
impedance Z0  ' (a) Let D = M4, where )t is the wavelength at a certain fixed frequency (00. What value of
ZQ can be used to eliminate reﬂections on the generator side of ZQ at frequency (00? 2 a EL 1/141» W‘—
(1” 2L. k? \\ 2%0 3 %& ( Sc @717” (b) Suppose the frequency is now increased to 20%. If the distance D and additional impedance ZQ are the same as from part (a), what fraction of the incident power is now
reﬂected back toward the generator? ‘ Mob/91)) Mme‘VL (“*M‘” 349mm Name Problem 3. 30 points (3 parts) Consider a time—harmonic (elm) uniform plane wave propagating in freespace. In phasor notation the electric field is written
E=Eo(jﬁ+z)e—jﬁy (1)
where E0 is a constant and B = 0) M080 . (a) Is the wave linearly polarized, circularly polarized, or elliptically polarized? Justify your
answer. (No credit without justification.) ﬁat/W“ Name (b) Referring to figure 4.1 below, the wave of eq. (1) is incident at oblique incidence (9 #2 0)
onto a dielectric medium with 8 = 880 and u = 2M0 . transmitted Is the reﬂected wave linearly, circularly, or elliptically polarized? Justify your answer,
but no need for detailed numerical calculation. 4% 37/0, “Ha. “TE all TM “We;
(0'35“ Mrowk‘ :0 ‘Q‘ 4"“) gnaw Name (c) Referring to Fig. 4.2, the wave of eq. (1) is incident at normal incidence (6 = 0) onto a
dielectric medium characterized by e = 880, u = Zuo. The boundary between the air and
dielectric medium is coated with a thin wire screen which is perfectly conducting in the z—direction and perfectly insulating in the Xdirection. The spacing between the
individual wires in the screen is much less than the wavelength of the plane wave. dielectric
IL: 2‘10
' a: 820
wire
screen
incident wave (normal incidence) Fig. 4.2 Is the reﬂected wave linearly, circularly, or elliptically polarized? How about for the
transmitted wave? ' Justify your answers, but no need for detailed numerical calculation. C‘i’M‘t) TLuX QDlGA’D‘“
50$Aqbwb‘f‘” ’Zﬁt f“ 3 ma,» Name Problem 4. 30 points (3 parts) switch eluses atif i=0: ' " ﬂ t, Z RL V T "isﬁiiséibnlii‘iéﬂ. " ' o z=w A transmission line has characteristic impedance ZO = 509, phase velocity u = c/2, and length
w = 3 meters. Initially it is charged up to a voltage V0 = 10 volts and then left open—circuited at
both ends. At t = O a switch suddenly closes connecting it to a load resistor RL at one end. ‘ a) Assume that the load resistor is matched to the characteristic impedance (RL = 20). Give
the current in the load as a function of time. J an ‘heammswm (his. Tiugiautmfu’ ILZO _pt,\ﬁz.o. ‘ \ Q hu‘vld WINL— U+,r+
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O 76/ H"\ DW/q 2 4'0 “Ste $2 mm, b) Show that the timeintegrated current passing through the load in (a) is equal to the total
charge stored on the top half of the line pn'or to the closing of the switch. .__ h 1:270 01 to” ‘ _ Lg \ \ .‘ ﬂ
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Name c) Now assume that RL = 259. Sketch the voltage waveform at the midpoint of the line (2 = w/Z) as a function of time. Be sure to indicate the values of the appropriate voltage
amplitudes and transition times. \> I”. f:0+) U? v°+ VrUr'5/u) V
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 Electromagnet

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