To match the impedance of a 'ground penetrating radar antenna' to the ground, impedance of ground is given by the expression, (if ϵ_r = 14, μ_r = 1, σ = 10⁻² ℧/m, operating frequency = 200 MHz)

Solution:

The impedance with finite conductivity is given by the expression

\(η = \sqrt{jμ ω \over {\sigma+jω ϵ} }\)

where μ = μ₀ μ_r and ϵ = ϵ₀ϵ_r. Hence, we get

\(η = \sqrt{jμ_0μ_r ω \over {\sigma+jω ϵ_0ϵ_r} } = {\sqrt{μ _0 \over ϵ _0}}{\sqrt{jμ_r \over{(\sigma/ ω ϵ_0)+jϵ_r}}}\)

We have \(η_0 = \sqrt{μ_0 \over ϵ_0} = 377 \Omega\) (Impedance of free space), ϵ₀ (permittivity of free space) = 8.85 x 10^-12 F/m, ω = 200 MHz, ϵr = 14, μr = 1 and σ = 10−2 ℧/m. Substituting the values, we get

η = 377\(\rm\sqrt{\frac{j}{0.9+j 14}}\)

Additional Information

• Ground-penetrating radar (GPR)  uses radar pulses to image the subsurface for investigating underground utilities such as metals, soil, etc.
• A GPR transmitter and antenna emit electromagnetic energy into the ground. When the energy encounters a buried object, it may be reflected or refracted, or scattered back to the surface due to the different permittivities. A receiving antenna can then record the variations in the return signal.