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A Theory of Antenna Electromagnetic Near Field—Part I

# A Theory of Antenna Electromagnetic Near Field—Part I,10.1109/TAP.2011.2165499,IEEE Transactions on Antennas and Propagation,Said M. Mikki,Yahia M. M.

A Theory of Antenna Electromagnetic Near Field—Part I
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We present in this paper a comprehensive theory of antenna near fields in two parts, highlighting in particular the en- gineering perspective. Part I starts by providing a general concep- tual framework for the more detailed spectral theory to be devel- oped in Part II. This paper proceeds by proposing a general spa- tial description for the electromagnetic field in the antenna exte- rior region based on an asymptotic interpretation of the Wilcox expansion. This description is then extended by constructing the fieldsintheentireexteriordomainbyadirectcomputationstarting from the far-field radiation pattern. This we achieve by deriving the Wilcox expansion from the multipole expansion, which allows us to analyze the energy exchange processes between various re- gions in the antenna surrounding domain, spelling out the effect and contribution of each mode in an analytical fashion. The re- sults are used subsequently to evaluate the reactive energy of ar- bitrary antennas in a complete form written in terms of the TE and TM modes. Finally, the concept of reactive energy is reexam- ined indepth to illustratetheinherent ambiguityof thecircuit total electric and magnetic reactive energies. We conclude that the tra- ditional reactive field concept is inadequate to the characterization of the antenna near field in general.
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## Citation Context (2)

• ...HE RESULTS of the first part of this paper [1] have provided us with an insight into the structure of what we called the near-field shell in the spatial domain...
• ...We have already encountered the term “energy” in our general investigation of the antenna circuit model in [1], where an effective reactive energy was defined in conjunction with the circuit interpretation of the complex Poynting theorem...
• ...The idea was introduced in Part I [1] in the context of the reactive energy, i.e., the energy associated with the circuit model of the antenna input impedance...
• ...As we have already seen in [1], all these calculations of are essentially those related to an equivalent circuit model for the antenna input impedance...
• ...In this section, we synthesize the knowledge that has been achieved in [1], concerning the near field in the spatial domain, and Section II, which focused mainly on the concept of radial streamlines developed from the spectral domain perspective...
• ...The view of the antenna presented in [1] is essentially an exterior region description...
• ...It is for this reason that the analysis in line with Section II is inevitably more difficult than [1]...
• ...only in the exterior region . We then proceed by computing (recursively as in [5] or directly as in [1]) all the vectorial angular functions and starting from the radiation pattern...
• ...Notice first that the reactive energy, as defined in [1], is the form of the total energy expressed through the Wilcox series with the term excluded...
• ...42 This is intuitively clear since, as we have found in Part I [1], higher-order terms in the Wilcox-type expansion correspond to more complex near-field radial structure as we descend from the far zone toward the source region, which in turns necessities the need to include significant short-wavelength components (i.e., large and components)...
• ...43 It is for these reasons that the authors believe the results of this paper to be of direct interest to the antenna engineering community. 44 Cf. Section III and [1]...
• ...49 For the far-field perspective, the reader may refer to the conclusion section in Part I [1]...

### Said M. Mikki, et al. A Theory of Antenna Electromagnetic Near Field—Part II

• ...It turns out that a general theorem (proved in [3]) can be established, which shows that exactly \half" of these layers don’t electromagnetically interact with each other...
• ...Indeed, as we proved in [3], if the integer n + n 0 is odd, then the interactions are identically zero, i.e., hAn;An0i = hBn;Bn0i = 0 for n + n 0 = 2k + 1...
• ...Therefore, the Wilcox series can be derived from the multipole expansion and the exact variation of the angular vector flelds An and Bn are directly determined in terms of the spherical far-fleld modes of the antenna [3]...
• ...However, we make use of the fact proved in [3] stating that the interactions hA0;A1i and hB0;B1i are identically zero...
• ...Moreover, from the results of [3], we now see that total reactive energies (10) are evaluated completely in analytical form and that in principle no computation of inflnite numerical integrals is needed here...
• ...The main insight here is the fact that the same formulas contain information about the mutual dependence of 1) the quality factor Q (through the reactive energy), 2) the size of the antenna (through the dependence on a), and 3) the far-fleld radiation pattern (through the interaction terms and the results of [3].) The derivation above points to the relational structure of the antenna from the engineering point of view in the sense that the ...

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