This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MIDTEKM sanncn/ Midterm Exam 2 ofEElﬁl Fall, 2005
Name:
Score: Problem #1. (25 points) Perfect Magnetic Conductor (PMC) is a counterpart of Perfect
Electrical Conductor under the dual relationship of electric ﬁeld and magnetic ﬁeld. For
PMC, it satisﬁes the boundary condition that the tangential magnetic ﬁeld and normal
electric ﬁeld must equal to zero. For an air ﬁlled waveguide shown as below, the top and
bottom of the waveguide 15 made of PEG, while the two sides are made of PMC The
dimensions are a=5cm, b=3cm. (a) Find the dominant mode propagating in this
waveguide? (b) If this waveguide supports TEM mode, what is the characteristic
impedance? (1:) To keep the singlemode operation, how should one limit the operating frequency? (d) If the waveguide is completely ﬁlled with a medium with dielectric
constant of 4, answer question (c) again. ' lie/tax
PEC r) M‘s wavesﬁg’ql ads as a, ”fafw me :Ib @ :Flale mammal: M “‘3‘ a 0351, Us TE“
(a>bl ._ not Wﬁ GED Charadeﬁs’hb‘ ‘Wémqlf _ ‘ meﬁ fﬁ‘ (ODS MOALKS ﬂwmlia a; ma 3’“ .. 33191
aeeihnﬁwiamw ifs—Hm We 4'?
. . .n _ w :1 Gla—_
s m can) in“ i 0 i
._ . a 3 11ng
A _ ‘HWr WW 3? 'Ttl: _. 13“ :ﬁr ll: lglxbiiD—l
: are 6‘12 Problem #2. (25 Points) A rectangular wavegoide has a length a = 5cm and width b =
3cm. (1) Find the cutoff frequencies for the lowest four modes including both TM and TE modes and sort them in order (2) What is the phase constant ,6 , guiding wavelength 3. , the phase velocity vJ3 and group velocity vs for the dominant mode at 3.5 GHZ. (3) Consider a signal propagates along the waveguide with two frequency components at
respectively 3.5GHz and 4.0 GHZ. They have the same phase at the excitation position;
ﬁnd out how much phase difference between these two components at the observation
position which is about 5 cm away from the excitation plane. (4) If a lOns wide pulse
modulated on a carrier of 5.5 GHz is transmitted in the waveguide, at what distance from
the excitation plane you may observe two separate pulses? TE; 1%: c. :5on _ 361,: g
03' 92a; lxﬁxldl
3
" . _£_ M;[email protected]
*Ttoi ‘ 19C ‘ Zb F ls5xloﬂl __\
t _ C i 5x103 . £66412®
1E” ‘ it" F I 5 xt_{_o:_,,__.,,. mush.“ _ _ racism” 1 W W 5 @ssaaa.
XlO .._ I , 1,2 2) ﬁﬁ/ Clmoawt MAL, u; 'lEfostéh—tm <9 I) 61 3E gmf— {‘5 64cm S
c“ : 5x10 .1 5.81,;{03 [rm/5.
l (in/18))" 0 .SIS 1  g
1C"L 39:1) : (5x10%)_ 'H:*_l.5‘l'§kl0 rel/36>
I 3 5,811me ' ‘ Problem ii 3 (25 points) One needs to nude
ctor devices. For example, if we excite a‘ particular waveguide mode'or mount semicondu
ite the TEzl mode like in the insert a current probe into a rectangular waveguide to exc
be is at the maximum B ﬁeld in the following ﬁgure, we have to make sure the pro
direction of probing. ' '
on the crosssection for
one needs to insert the probe, assuming 1‘ y / probe Problem #4. (25 points) An airﬁlled rectangular cavity has a dimension a = 5 cm, b = 3
cm, d=5.5cm, (I) Find the lowest resonance frequency and mode of this cavity. (2) Find
the resonant frequency again if the cavity is completely ﬁlled with a medium with
dielectric constant s,=4 (3) What are the guide wavelengths for the above two cases. (4) If
the cavity is ﬁlled partially with the same ”medium in Z direction to tune the resonant
frequency as shown in the ﬁgure, from equal phase analysis, choose the minimum length
we should ﬁll in order to have a TE“. mode to resonate at 6GHz. hp”. LLE
muWIml n. ma
_ _ My? UMW 2%. n. L 3W
m, u a. “a, WWII]!
y? Mira”. ﬁ ndwxw
tnm,uim_. . mm
3.9 «W @241
poﬂwﬂéwﬁ 4 SWUmp ”PEI h
Twin. 1%. F 5! ﬁx? LEW 2‘ Q mp u. o. 3 033 ...
View
Full Document
 Spring '09
 WANG
 Electromagnet

Click to edit the document details