Prelim 1

# Prelim 1 - ECE 486 Prelim#1 Spring 2006 l(9 points An...

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Unformatted text preview: ECE 486 Prelim #1 Spring 2006 l. (9 points) An aireﬁlled rectangular waveguide with dimensions (Land 13 satisfying 1) < a, < 2b is to be used at 2 GHZ in the TEN) mode. If the operating frequency is to be at least 20% higher than the cutoff frequency and at least 20% lower than the cutoﬂ3 of the next higher mode, a) Determine the acceptable ranges of values for a and b. b) For the values of a, and b With the smallest allowed ratio of (1/ I), ﬁnd the wave phase velocity, guide wavelength, and impedance. 4' : M. M '1. K '1. r’N m. Q 2: Jk;3* EX ‘T “*9 .xl a + ‘ OM\M“ \ 0 O ‘ V1" war-\- IA 2- Ida“ 57. Tu“) éomw-OK'K 1' 42‘: a L/o... , he. “‘3"? \3 150‘ L ‘Fcr {k ‘— i ll "" "' K 2. 6H .9!- .1 z A I: 4 2’ b 0.23 6\. > 6" (M \a L. L CM ﬁ.\\$b hLAQL-h l‘ ‘ 'u: «at: an; EPY~§CM 5‘; ‘3 cm F: )«ZuF; v ___E'__.__—— 4’ : «7—,.- : r-iz ‘3 l . 2‘ u .. a “La/r? “9"" ’ “35 '3 (5 ) \ Z 5 3 (-6,?— 1 (M 1-3 c 3% r" a l 3“, 4 .,— I-‘(L (3?? 1L} era/e Q J______ 2. (8 points) A wave with a frequency of 200 MHZ propagates in a circular waveguide with a radius of 7 cm ﬁlled with distilled water (E = 8160). Note that this waveguide has somehow been specially constructed in such a way that TE modes cannot exist within it. a) Determine the mode that is propagating. b) What is the highest frequency wave that will excite only a single propagating mode in this waveguide? c) Write the expression for E3 or Hz (whichever is relevant) for the 200 MHZ wave. Make a sketch showing how the expression you wrote varies across the waveguide aperture. (1) Suppose the water is pumped out of the waveguide, leaving behind a vacuum. Will the 200 MHZ wave still propagate? Below are listed the ith zeros of Jn(:r) and Just), which may be useful. L... am) 420:) =1 11:2 n=0 n=1 n=2 5 IE 0 3:5 l=1 3.832 1.841 3054 1:2 5.520 .016 8.417 122 7.016 5.331 6.706 bx XW‘ , IGJ‘TM I» 2w T bk, c/Ct £°J""“o\ = ”‘2 Hr‘ra er- a. more nus‘r Tb'E THM a Lt) TM“ L‘ic Mu% b iJEWT "We ego-rah Hung Z sink-15% CI 6-}; d 3" (xai’: \ c2. lM\0§-T' ¢ dep l m 9° r \ 0k \ 3. (8 points) The electric ﬁeld for a particular mode in an air—ﬁlled parallel-plate waveguide with a plate separation of 3 cm is given by: E41}, 2) : 106760“ sin(1007rz) kV/m a) What is this mode? b) What is the Operating frequency? 0) What is the highest order mode of the same type (TM or TE) that will propagate at this frequency? V1453cn~ e M g: Ex war-wit: Te Habﬁ 2 mar k=j=looﬂ =bv~=3 Maﬁa. 2 E 3:99“ 33:93?“ (56W3L= gooTFA-b __ LAT/4,1" C f 3 (EL n'ﬁ' 51> TE. 115?, Pumnanﬁa m" .1 can ...
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• Spring '06
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