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Unformatted text preview: a, Mia Name ECE604
Midterm Exam #3
April 15, 2009 Notes:
0 4 problems, 50 minutes.
0 A formula sheet is supplied separately or attached at back.
0 You are also allowed your formula sheet: two sides at 8 1/2” X 11” 0 Please put your name on each page. Power reflectance (R) Name Problem 1. 25 points Consider a smooth planar interface between two transparent materials with it = uo. One material
is air (n = 1); the other material has unknown refractive index n (n > 1). The power reflectance is
sketched below for both polarizations as a function of incidence angle. The order of the
materials is not specified at this point. a) Is the light incident from air into the unknown material or from the unknown material
into air? How do you know? the WM 4%er we a 4% i when 5% ‘3»: ‘3 a: a a. @m l’\ t liWﬁL’lC I iI'\ [goo Far/kl ‘5 (bCCZCﬂA 3’)
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reﬂectance data. Give a number for the refractive index of the unknown material. ‘im 6ch l EM elm U A lc; m: (m M11“ incident angle Workspace for Problem 1 on next page Name Problem 1 Additional Worksheet Name Problem 2. 25 points A voltage source with RS = 509 series impedance drives a transmission line (TL) system at 3 GHz. As shown, the source is connected to the left end of TLl with characteristic impedance
21 = 509 and length (11 = 1 meter. At the right end of the TL1, two more transmission lines, TL2
and TL3 are connected in parallel. The characteristic impedances, lengths, and load resistors are
as shown. All TL’s are air—filled; that is, the propagation velocity is the speed of light (3 x 108
m/sec). a) For R2 = 1009, specify values of d2 and d3 that minimize the power in the negative travelling
wave in TL1. b) For R2 = 259, specify values of d2 and d3 that minimize the power in the negative travelling
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metallic rectangular waveguide. In particular, list three distinct ways in which the properties of
the field (including its propagation) are fundamentally different for the waveguide solutions
compared to the (lowest—order) transmission line solution. Your answers should be short but clear. You may assume that both transmission line and waveguide are lossless, air—filled, and
constructed from perfectly conducting metal. /( 5 144 c: [a g s ‘ rM» {14"}; €154 $4: altk1,. [0‘71 ; / H as”.
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(at z = O) as: EZ =E0 sin[m—TCX—]sin Ex = —jﬁ[m_n]/kg E0 003(m_nx]3in a b a a b By: —jB[—n—7E]/kg Eosin mnx]cos[rm—y Hx= jwe[£l£]/kg 13()six1{“‘—TEx cos Pit—y—
b a b b a b (a, 13) (a=30cm) x=a Fig 1 In this problem we consider the TM” mode (m = 1, n = 1). Assume the waveguide is air—filled,
the metal plates are perfect conductors, and the waveguide dimensions are a = 30 cm, b = 15 cm. superposition of various plane waves. The operating frequency is 2 GHz.
i) How many plane waves are required? a) Within the region 0 S x S a, 0 S y S b, theFl‘Mu Eolution may be considered as the ii) If the various plane waves have the form e_jk'? (in phasor notation), completely ' specify the k vector for each of the plane waves. 7 '
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