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Electromagnetic Fields
Published in Christos Christopoulos, Principles and Techniques of Electromagnetic Compatibility, 2022
It is clear that Zw differs from the intrinsic impedance of the medium Z0 both in magnitude and in phase. Since βr=ωμεr=2πfr/u=2πr/λ, it follows that when r ≫ λ (far-field region), 1/(βr) → 0 and | Zw | → Z0 as expected. Very near to the dipole (r ≪ λ), the wave impedance is Zw ≃ Z0 λ/2πr and hence much larger than Z0. This implies that the electric field component is larger than would be expected for a radiation field. At a distance r = λ/2π, the wave impedance has equal real and reactive (capacitive) parts. The reactive part is due to the storage of energy in the near field. This is reasonable since the dipole described operates primarily by separating electric charges and by setting up potential differences. Near this electric dipole, the character of the source is reflected in the EM wave properties. In the far-field region, however, there is nothing in the field properties to identify the character of its source. The wave impedance is important as wave reflection and penetration are both determined by impedance differences along the path of propagation.
Guided Wave Propagation and Transmission Lines
Published in Mike Golio, Commercial Wireless Circuits and Components Handbook, 2018
W.R. Deal, V. Radisic, Y. Qian, T. Itoh
The wave impedance of the waveguide is given by the ratio of the magnitudes of the transverse electric and magnetic field components, which will be constant across the cross-section of the waveguide. For a given mode, the wave impedance for the TE and TM modes are given as: () ZTE=ETHT=jωμμ () ZTM=ETHT=γjωε
Maxwell’s theory of electromagnetism
Published in Edward J. Rothwell, Michael J. Cloud, Electromagnetics, 2018
Edward J. Rothwell, Michael J. Cloud
where η=μ0/(ϵ0ϵr) $ \eta =\sqrt{\mu _0/(\epsilon _0\epsilon _r)} $ is a wave impedance with units of ohms.
Rigorous electromagnetic scattering solution of a PEMC strip placed at interface of dielectric-chiral media using Kobayashi Potential
Published in Waves in Random and Complex Media, 2022
Hossein Davoudabadifarahani, Behbod Ghalamkari
In these equations, is the incident angle,, and is the intrinsic wave impedance of the dielectric; and are the permeability and permittivity of the dielectric, respectively. Wave number of the dielectric is represented as and . Coefficients and are constants; denotes transverse magnetic polarized (TM) wave, while denotes transverse electric polarized (TE) wave.
Investigating space harmonics’ behavior on modulated reactance surfaces
Published in Waves in Random and Complex Media, 2021
Nasser Montaseri, Alireza Mallahzadeh
It is well-known that uniform reactance surfaces can support surface waves [8]. The wave propagation along various reactance surfaces has numerous electromagnetic applications. In Figure 1, the surface impedance, , is shown in the plane and can generally be expressed as [17]: where is the wave impedance in free space, represents the normalized average surface reactance, and denotes the reactance surface’s period. Also, s are the known modulation indices such that is absolutely convergent. It is supposed that there would be no variation along the (). Besides, the harmonic time dependence is assumed throughout this paper.
Broad band absorber based on cascaded metamaterial layers including graphene
Published in Waves in Random and Complex Media, 2018
Yi-Chi Zhang, Yun-Tuan Fang, Qiang Cai
where is the wave impedance in free space. When we put kz,2 into the Equation (13), the impedance will become –Z. For isotropic material layer with a constant permittivity εiso we can still use Equations (18)–20) to describe the two wave vector components and the wave impedance in the layer by setting εxx = εyy = εzz = εiso, εxz = εzx = 0. For example, for air with εiso = 1 we obtain: