SJSU EE 140 - soln140_MT2_S15 (3 pages)

EE140 Mid Term 2 Dr Ray Kwok Student Name Last First r 1 35 pts A plane wave in air with E y 5 sin t 3 z 4 x V m is incident upon the planar surface of a dielectric material with r 2 25 occupying the half space x 0 Write the full expression for the reflected H field and the transmitted E field n1 Ei r k i 3 z 4 x n2 k1 3 2 4 2 5 ki incidence ck1 1 5 10 9 Hi transmission i x r Hr 3 4 n1 sin i n2 sin t tan i t O Et kt z reflection 3 1 1 5 sin t 5 t 23 6 o Ht kr Er n2 r 2 2 25 1 5 n1 cos i n2 cos t 1 4 5 1 5 cos 23 6 o 0 264 n1 cos i n2 cos t 1 4 5 1 5 cos 23 6 o r E H r z cos r x sin r oi sin t k1 z sin r x cos r o r 0 264 5 H r z 4 5 x 3 5 sin t 5 z 3 5 x 4 5 377 r 9 H r z 2 8 x 2 1 sin 1 5 10 t 3 z 4 x mA m 1 1 0 264 0 736 k2 r Et r Et r Et k o n2 5 1 5 7 5 y Eoi sin t k 2 x cos t z sin t y 0 736 5 sin t 7 5 x cos 23 6 o z sin 23 6 o 9 y 3 68 sin 1 5 10 t 6 87 x 3 z V m EE140 2 Mid Term 2 Dr Ray Kwok 35pts Two 90 45 45o prisms shown in Figure are made of lossless glass with n 1 5 What power in dB is the transmitted signal through the bottom prism The normally incident signal is a 15 9 GHz unpolarized continuous electromagnetic wave At the first air glass interface normal incident 1 n1 n2 1 1 5 0 2 n1 n2 1 1 5 Inside of the prism nglass sin C nair sin 90o 1 5 sin C 1 P C 41 8o At the last glass air interface normal incident again Total reflection or both polarization 2 n2 n1 1 5 1 0 2 n2 n1 1 5 1 Total power transmitted to the bottom is P 1 1 1 1 0 2 2 2 2 2 2 2 4 0 849 84 9 0 71dB Note The polarization here doesn t do anything since both polarizations have the same reflection transmission properties EE140 3 Mid Term 2 Dr Ray Kwok 30 pts It is extremely difficult to communicate with an underwater object by air Suppose a helicopter is sending a perpendicularly polarized 10 kHz signal to wake up the Black Box at the bottom of an ocean 8 km deep what strong a signal must it send if the Box has a sensitivity to receive 100 dBm signal And how close to the Box must the signal enter the water Use r 81 r 1 4 S m for seawater The following would guide you through your estimation a What is the critical angle Remember this is a lossy medium b From a calculate where should the signal enter the water c What is the transmitted power in dB right beneath the surface assuming normal incident d What is the attenuation in dB of the signal going through 8 km of sea water e If the receiver were to detect a 100 dBm of signal how strong a signal in W must the helicopter send a tan z y 4 8 9 10 4 4 2 10 81 10 9 36 Good conductor 2 k1 0 40 2 104 2 1 10 4 c 3 108 k1 sin 1 k 2 sin 2 k2 0 4 sin C 2 1 10 4 sin 90o C 0 03o 5 3 10 4 radians b y 8km tan C 4m c 2 1 j 1 j 0 4 1 j 0 1 0 14 45 o 4 2 1 1 j 0 1 377 0 9995 0 03 o 2 1 1 j 0 1 377 2 0 9989 99 89 0 11 transmitted 10log 0 0011 29 6 dB d Attenuation 8 686 r 27795 dB e 100 29 6 27795 27895 dBm 27725 dBW 102772 W 2 10 4 4 10 7 4 0 40 2