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Electromagnetics - Plane wave reflections/transmissions

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data
    A 1 GHz plane wave is free space is normally incident on a finite-width, lossless dielectric slab (relative permeability, uR of 2, relative permittivity, εR of 18, slab of length l).

    Determine the narrowest slab length for which 57.14% of power is reflected and the reflected signal has a phase angle of -160.89 degrees with respect to incident signal.


    2. Relevant equations
    - ni = sqrt(uRR)
    - wavelength = λi = c/(f*ni)
    - intrinsic impedance = ζ = ζO*ni


    3. The attempt at a solution
    - Knowing the dielectric values for air and the slab, I know the index of refraction for air is simply 1. The dielectric exhibits an index of 6.

    - I also know the intrinsic impedances of the two dielectrics as well - ζO = 377[Ω], ζSLAB = 125.67[Ω]

    -Wavelength of free space is 0.30[m], whereas the wavelength within the slab is 0.05[m].

    - I also know that the reflection coefficient is equal to 0.5714.

    From these small steps I have completed, I hope I have gotten closer to the answer. Thank you for all help in advance! It is most appreciated.
     
  2. jcsd
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