Time-domain Green's function for an infinite sequentially excited periodic line array of dipoles

Felsen, Leopold B.; Capolino, Filippo

doi:10.1109/8.865225

Cited by 26 publications

(59 citation statements)

References 18 publications

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“…Here, bold face symbols define vector quantities and , , denote unit vectors along , , , respectively. The FW-based modal FD and TD fields due to the array are related by the Fourier transform pair (1) in which can be either a scalar or a vector quantity; a caret denotes time-dependent quantities.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…In (4), is the impressed phase speed along . Here, we treat the case which implies excitation phase speeds (and corresponding projected phase speeds and ) larger than the ambient wavespeed [1], [3]. The nonphased case corresponds to simultaneous excitation of all the dipoles.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…We have previously investigated canonical TD dipole-excited Green's functions (GF) for infinite [1] and truncated [2] periodic line arrays, and for infinite [3] and semi-infinite [4] periodic planar arrays. The radiated field there has been expressed and parameterized in terms of a few TD Floquet waves (FWs).…”

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confidence: 99%

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Network Oriented Dyadic Time Domain Green's Function for a Sequentially Excited Infinite Planar Array of Dipoles in Free Space

Capolino

Felsen²,

Villa³

2007

IEEE Trans. Antennas Propagat.

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Abstract-During the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas, infinite periodic structures, frequency selective surfaces and related applications, with emphasis on gaining physical insight into the phenomenology of short-pulse radiation. The present contribution shows the current status of our network-oriented dyadic time domain Green's function (TD-GF) for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short-pulsed radiation by infinite periodic arrays. The dispersive effects of the TD-Floquet waves (FW) and the consequences of a TE and TM field decomposition are discussed in details. In this network formulation, the equivalent TD transmission line (TL) voltages and currents excited by equivalent TD current generators are determined. An expression for the TM voltage TL-GF is provided for the first time in terms of incomplete Lipschitz-Hankel integrals and Bessel functions together with some remarks for its evaluation. As shown in previous publications for the scalar potentials, real-TD physical observables are determined by pairing TD Floquet waves with positive and negative indices. It is shown that the vectorial TD radiated field is reconstructed at any time with the superposition of a few TD-FWs.

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Section: Statement Of the Problemmentioning

confidence: 99%

Section: Statement Of the Problemmentioning

confidence: 99%

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Network Oriented Dyadic Time Domain Green's Function for a Sequentially Excited Infinite Planar Array of Dipoles in Free Space

Capolino

Felsen²,

Villa³

2007

IEEE Trans. Antennas Propagat.

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“…To this end, in what follows, we extend the Floquet-based frequency-domain analysis in [29], [30], for infinite and semi-infinite periodic phased arrays of dipoles, to the quasiperiodic modified-Fibonacci case. As in [29], [30], attention is restricted to the zdirected vector potential A(r) = A(r)u z , with r ≡ (z, ρ) and with u z denoting a z-directed unit vector, from which all field quantities of interest can be computed. Whenever applicable, partial results from [29], [30] are recalled and used, without going into the details of the technical derivations.…”

Section: Radiated Fieldmentioning

confidence: 99%

“…extending the Floquet-based parameterization of infinite and semi-infinite time-harmonic periodic arrays in [29], [30] to the case of two-scale quasiperiodic arrays. Next, the inherent degree of freedom in the choice of the ratio between the two scales can be used to study the "transition" from periodic (d 1 = d 2 ) to quasiperiodic (d 1 = d 2 ) order, so as to better understand the quasiperiodicity-induced footprints in the wave dynamics.…”

Section: Introductionmentioning

confidence: 99%

Parameterizing quasi-periodicity: generalized Poisson summation and its application to modified-Fibonacci antenna arrays

Galdi

Castaldi

Pierro

et al. 2005

IEEE Trans. Antennas Propagat.

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The fairly recent discovery of "quasicrystals", whose X-ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of "aperiodic order". Within the context of the radiation properties of antenna arrays, an instructive novel (canonical) example of wave interactions with quasiperiodic order is illustrated here for one-dimensional (1-D) array configurations based on the "modifiedFibonacci" sequence, with utilization of a two-scale generalization of the standard Poisson summation formula for periodic arrays. This allows for a "quasi-Floquet" analytic parameterization of the radiated field, which provides instructive insights into some of the basic wave mechanisms associated with quasiperiodic order, highlighting similarities and differences with the periodic case. Examples are shown for quasiperiodic infinite and spatially-truncated arrays, with brief discussion of computational issues and potential applications.

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Analysis of periodic line arrays of phased dipoles with band-limited excitations

Uluisik

2016

Int J RF and Microwave Comp Aid Eng

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Radiation from periodic line arrays of sequentially excited electric current dipoles is investigated in time domain. The time domain Floquet wave representations are reviewed for a semi-infinite line array. In this study, the excitation function is chosen as a normalized Rayleigh pulse which does not contain significant low frequency components. The Floquet wave representation for band limited excitations includes a time consuming convolution operation which has to be performed numerically. To avoid the numerical convolution the normalized Rayleigh pulse is represented approximately via a set of linear/ quadratic functions. This results in substantial reduction in the computation time since the convolution can be calculated analytically. V C 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:342-348, 2016.

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Time-domain Green's function for an infinite sequentially excited periodic line array of dipoles

Cited by 26 publications

References 18 publications

Network Oriented Dyadic Time Domain Green's Function for a Sequentially Excited Infinite Planar Array of Dipoles in Free Space

Network Oriented Dyadic Time Domain Green's Function for a Sequentially Excited Infinite Planar Array of Dipoles in Free Space

Parameterizing quasi-periodicity: generalized Poisson summation and its application to modified-Fibonacci antenna arrays

Analysis of periodic line arrays of phased dipoles with band-limited excitations

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