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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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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 free-space. 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 X-direction. 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 WIN-L— U+,r+
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O 76/ H"\ DW/q 2 4'0 “Ste $2 mm, b) Show that the time-integrated 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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