EE140 Mid-Term 2 Dr. Ray Kwok incidence transmission reflection θθθθi θθθθr θt n1 n2 Ei ki Hi Et kt Ht Er kr Hr x z O Student Name: (Last) ____________________ (First) ______________________________ 1. [35 pts] A plane wave in air with V/m, is incident upon the planar surface of a dielectric material with εr = 2.25, occupying the half-space x > 0. Write the full expression for the reflected H field and the transmitted E field. )43sin(5ˆxztyE −−=ωrotttiiinnckkxzk6.23sin)5.1(53)1(sinsin43tan105.1543ˆ4ˆ32191221====⋅===+=+=θθθθθωr( )[ ]( ) ( )[ ])43105.1sin()1.2ˆ8.2ˆ()5/4()5/3(5sin377)5(264.0))5/3(ˆ5/4ˆ(cossinsin)sinˆcosˆ(264.06.23cos)5.1()5/4)(1(6.23cos)5.1()5/4)(1(coscoscoscos5.125.291212122xztxzHxztxzHxzktExzHnnnnnrrrrooirrrootitir+−⋅+=−−−−−=−−Γ−−=−=+−=+−=Γ===⊥⊥rrrωθθωηθθθθθθεmA/m ( )[ ]( )( )[ ]( )zxtyEzxtyEzxktEyEnkktootttoito387.6105.1sin68.3ˆ)6.23sin6.23cos(5.7sin5736.0ˆ)sincos(sinˆ5.7)5.1(5736.0264.0119222−−⋅=+−=+−=====−=Γ+=⊥⊥⊥rrrωθθωττV/mEE140 Mid-Term 2 Dr. Ray Kwok P = ? 2. [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. oCCoairCglassnn8.411sin5.190sinsin===θθθ2.05.115.1121211−=+−=−−=ΓnnnnAt the first air-glass interface, normal incident Inside of the prism: At the last glass-air interface, normal incident again. ()()dBP 71.0%9.84849.0)2.01(1142222221−===−=Γ−Γ−=Total power transmitted to the bottom is: Note: The polarization here doesn’t do anything since both polarizations have the same reflection / transmission properties. Total reflection or both polarization 2.015.115.112122+=+−=−−=ΓnnnnEE140 Mid-Term 2 Dr. Ray Kwok y z 3. [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 εr = 81, µr = 1, σ = 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) ( )( )( )( )( )( )40.0241041022109.836/10811024tan74494=⋅==⋅===−−ππωµσαππωεσδGood conductor ( )radianskkckkoCoC44221148421103.503.090sin101.2sin4.0sinsin101.210310240.0−−−⋅==⋅==⋅=⋅=====θθθθπωαβ(b) 0.11% transmitted = 10log(0.0011) = -29.6 dB (c) ( ) ( ) ( )( )( )%89.999989.003.09995.03771.013771.014514.01.0144.011212122==Γ∠=++−+=+−=Γ∠=+=+=+=oojjjjjηηηησαηmkmyC4tan)8( ==∆θ(d) Attenuation = -8.686 αr = -27795 dB !!!! (e) -100 + 29.6 + 27795 = 27895 dBm = 27725 dBW = 102772