EMSP 24gennaio2023 Sol

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Electromagnetics and Signal Processing for Spaceborne Applications – EM part January 24th, 2023 1 2 3 4 do not write above Problem 1 Consider the plane sinusoidal wave depicted below hitting the interface between two lossless media, whose EM characteristics are reported in the figure. The incidence angle is  = 35° as shown below. The wave frequency is f = 1 GHz. The incident electric field in medium 1 at the origin of the system is: 𝐸⃗ 𝑖(0,0,0) = 𝑗𝜇 𝑦 V/m For this scenario, calculate: a) The reflection coefficient at the interface. b) The power density flowing in the z direction in the second medium. c) The absolute value of the total electric field in point A(x = 1, y = 2, z = -1). Solution: a) The wave is TE. To calculate the reflection coefficient, first, let us calculate the refraction angle, which is obtained from the Snell’s law: == 1472.1sinsinsin 22211  nn evanescent wave SURNAME AND NAME ____________________________________________________ ID NUMBER ___________________________________________________________ SIGNATURE ___________________________________________________________ z 0 1 x 2 A The wave is evanescent, which implies that the absolute value of the reflection coefficient is 1, i.e. all the power density is reflected. For the detailed calculation of the reflection coefficient , we s tart from the intrinsic impedances: 1.230cos 1 4 1 01 ==  TE Ω ( ) 6.6705622.0sin1cos 20 2 2 0 2 02 jj TETE == − ==      Ω Note that this mathematical solution is picked to achieve a physical solution for the wave equation in the second medium. Finally, the reflection coefficient is: 6140789012 12 . + j. TETE TETE =+ −=   b) As the wave is e vanescent wave, no power density will travel in the z direction in the second medium. c) The total electric…