Plane Wave Propagation in Lossy Media Asst Prof
- Slides: 32
Plane Wave Propagation in Lossy Media Asst. Prof. Dr. Özgür Tamer
Lossy Media A lossy dielectric is a medium in which an EM wave loses power as it propagates due to poor conduction. A lossy dielectric is a partially conducting medium
Lossy Media In a lossless dielectric medium, the relative permittivity εr is real, For non-magnetic materials, the relative permeability μr =1 For lossy media permittivity is a complex number
Lossy Media In a lossy medium
Loss Tangent is called the loss tangent › The complex permittivity can be written as
Loss Tangent Current Terms
Helmholtz’s equation By replacing k with kc, all the previous results derived for lossless media are applicable to lossy media. But since kc is a complex number, the plane wave will experience loss when it propagates.
Helmholtz’s equation γ is known as the complex propagation constant › solutions with the +α constant have been discarded as they imply waves with increasing amplitudes which is impossible
Complex Propagation
Complex Propagation The general form of a plane wave in a lossy medium is
Complex Propagation
Complex Propagation
Good Conductor Loss tangent for a good conductor is;
Good Conductor In a good conductor, the intrinsic impedance ηc is a complex number, meaning that the electric and magnetic fields are not in phase as in the case of a lossless medium.
Good Conductor Phase velocity and wavelength
Good Conductor H and E inside a good conductor
Good Conductor Skin Depth › Because of the attenuation constant α, the wave amplitude becomes smaller when it propagates through a good conductor. › amplitude of a travelling plane wave decreases by a factor of e-1 = 0. 368 = 36. 8% is called the skin depth
Skin Depth
Skin Depth
Skin Depth For copper σ = 5. 8 × 107 S/m and μr =1
Skin Depth
Low Loss Dielectrics For a low loss dielectric loss tangent satisfies
Low Loss Dielectrics
Low Loss Dielectrics A skin depth δ can be similarly defined as in the good conductor case:
Example 1 The electric field intensity of a linearly polarised uniform plane wave propagating in the +z direction in seawater is E = x 100 cos(107 πt) at z=0. The constitutive parameters of seawater are εr = 72, μr = 1, and σ = 4 S/m.
Determine the attenuation constant, intrinsic impedance, phase velocity, wavelength, and skin depth.
Write expressions for H(z, t) and E(z, t).
Find the distance z 1 at which the amplitude of the electric field is 1% of its value at z = 0.
Compute the skin depth at a frequency of 1 GHz.
find the power densities at distances of skin depth z = δ and z = 0.
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