Question

A fiberglass (ϵ = 4ϵ₀) radome protecting a microwave antenna is designed as a half-wavelength reflectionless slab at the operating frequency of 12 GHz.

Determine three possible thicknesses (in cm) for this radome.

Answer 1

To find the thicknesses for a fiberglass radome operating at 12 GHz for half-wavelength reflectionless operation, one must calculate the wavelength in the medium and then divide by two for a half-wavelength slab, with options for multiple half-wavelengths.

Step-by-step explanation:

The student has asked to determine three possible thicknesses for a fiberglass radome that is designed as a half-wavelength reflectionless slab at the operating frequency of 12 GHz. To solve this, we first need to find the wavelength in the medium using the formula λ = c / (f ∙ √ε), where c is the speed of light in a vacuum (approximately 3 x 108 m/s), f is the frequency, and ε is the permittivity of the medium (ε = 4ε0 for fiberglass, with ε0 being the permittivity of free space). Next, since the radome is a half-wavelength slab, its thickness is λ/2. After calculations, you can get three different possible thicknesses by considering multiple half-wavelengths (λ/2, 3λ/2, 5λ/2, etc.).