Question

A dielectric medium has a dielectric constant εᵣ = 2.1 - j0.1 and conductivity σ = 0.4 Siemens/meter. Write down the effective dielectric function of the medium at the frequency of 3 GHz.

Answer 1

To find the effective dielectric function of the medium at a frequency of 3 GHz, we can use the formula ε' = εᵣ - j(σ/ω), where ε' is the complex dielectric constant, εᵣ is the real part of the dielectric constant, j is the imaginary unit, σ is the conductivity, and ω is the angular frequency.

Step-by-step explanation:

The effective dielectric function of a medium at a given frequency is determined by its dielectric constant and conductivity. To find the effective dielectric function at a frequency of 3 GHz, we can use the formula:

ε' = εᵣ - j(σ/ω)

where ε' is the complex dielectric constant, εᵣ is the real part of the dielectric constant, j is the imaginary unit, σ is the conductivity, and ω is the angular frequency.

Plugging in the values εᵣ = 2.1, σ = 0.4 S/m, and ω = 2πf = 6π × 10^9 rad/s, we can calculate ε' = 2.1 - j(0.4/6π) = 2.1 - j(0.0667).