Transmission through a wall (2/5) In a lossy medium the wavenumber can be written as: k=ωVoee=0√40e0, The complex relative dielectric constant can be written as: ,=e,-je=-j0 E0E0 If the medium is weakly lossy e"<<'. A plane wave propagating through the lossy medium has the expression: E=Ege=Epe(+);with jk-@tjB Thus: 到 Where the series expansion have been truncated at first orderTransmission through a wall (2/5) k = ω µ0ε c = ω µ0ε 0ε r ε r = ε r ′ − jε r ′′ = ε ε 0 − j σ ωε 0 E = E0e− jkr = E0e −(α + jβ )r ; with jk=α+jβ k = ω µ0ε 0ε r = ω µ0ε 0 ε r ′ − jε r ′′ = ω c ε r ′ − jε r ′′ = = ω c ε r ′ 1− j ε r ′′ ε r ′ ≈ ω c ε r ′ 1− j ε r ′′ 2ε r ′ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ In a lossy medium the wavenumber can be written as: The complex relative dielectric constant can be written as: If the medium is weakly lossy ε ” << ε ’. A plane wave propagating through the lossy medium has the expression: Thus: Where the series expansion have been truncated at first order