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mid2+sol (1)

# mid2+sol (1) - MIDT-EKM sanncn Midterm Exam 2 of-EElﬁl...

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Unformatted text preview: MIDT-EKM sanncn/ Midterm Exam 2 of-EElﬁl Fall, 2005 Name: Score: Problem #1. (25 points) Perfect Magnetic Conductor (PMC) is a counter-part 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 single-mode 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 _ ‘HW-r 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 cross-section for one needs to insert the probe, assuming 1‘ y / probe Problem #4. (25 points) An air-ﬁlled 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 ...
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