(adsbygoogle = window.adsbygoogle || []).push({}); 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, u_{R}of 2, relative permittivity, ε_{R}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

- n_{i}= sqrt(u_{R}*ε_{R})

-_{wavelength}= λ_{i = }c/(f*n_{i})

- intrinsic impedance = ζ = ζ_{O}*n_{i}

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 - ζ_{O}= 377[Ω], ζ_{SLAB}= 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.

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# Homework Help: Electromagnetics - Plane wave reflections/transmissions

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