For each of the following combinations of parameters, determine if the material is a low-loss dielectric, a quasi-conductor, or

Question

3 years ago

12

For each of the following combinations of parameters, determine if the material is a low-loss dielectric, a quasi-conductor, or

a good conductor, and then calculate α,β,λ,up, and ηc:(a)Glass with μr=1,εr=5, andσ=10−12S/m at 10 GHz.(b)Animal tissue with μr=1,εr=12, and σ=0.3 S/m at 100 MHz.(c)Wood with μr=1,εr=3, and σ=10−4S/m at 1 kHz

Engineering

1 answer:

Alborosie · Answer 1 · 2022-03-27T02:16:25+03:00

Answer:

Glass: Low-Loss dielectric

α = 8.42*10^-11 Np/m

β = 468.3 rad/m

λ = 1.34 cm

up = 1.34*10^8 m/s

ηc = 168.5 Ω

Tissue: Quasi-Conductor

α = 9.75 Np/m

β = 12.16 rad/m

λ = 51.69 cm

up = 0.52*10^8 m/s

ηc = 39.54 + j 31.72 Ω

Wood: Good conductor

α = 6.3*10^-4 Np/m

β = 6.3*10^-4 Np/m

λ = 10 km

up = 0.1*10^8 m/s

ηc = 6.28*( 1 + j )

Explanation:

Given:

Glass with µr = 1, εr = 5, and σ = 10−12 S/m at 10 GHz

Animal tissue with µr = 1, εr = 12, and σ = 0.3 S/m at 100 MHz.

Wood with µr = 1, εr = 3, and σ = 10−4 S/m at 1 kHz

Find:

Determine if the material is a low-loss dielectric, a quasi-conductor, or a good conductor, and then calculate α, β, λ, up, and ηc:

Solution:

- We need to determine the loss tangent to determine category of the medium as follows:

σ / w*εr*εo

Where, w is the angular speed of wave

εo is the permittivity of free space = 10^-9 / 36*pi

- Now we classify as follows:

$Glass = \frac{10^-^1^2 }{2*\pi * 10*10^9 * \frac{5*10^-^9}{36\pi } } = 3.6*10^-^1^3\\\\Tissue = \frac{0.3 }{2*\pi * 100*10^6 * \frac{12*10^-^9}{36\pi } } = 4.5\\\\Wood = \frac{10^-^4 }{2*\pi * 1*10^3 * \frac{3*10^-^9}{36\pi } } = 600\\$