Scattering-Matrix Analysis of Linear Periodic Arrays of Short Electric Dipoles
Abstract
The scattering-matrix analysis of linear periodic arrays of electric dipoles given in this report was suggested by the corresponding analysis performed by Yaghjian for linear periodic arrays of electro-acoustic monopole transducers. The extension to electromagnetic antennas reported here requires the use of the more complicated vector spherical wave functions instead of scalar spherical wave functions. However, no new concepts are needed for our treatment. A general vector spherical-wave source scattering-matrix description of electromagnetic antennas is formulated, and reciprocity and power conservation are used to derive relations between the antenna reflection, receiving and scattering coefficients that constitute the scattering matrix. When the antennas are electrically small dipoles only two vector spherical wave modes, one incoming and one outgoing, are required to describe the antennas. The scattering matrix formulation is applied to analyze infinite and finite linear periodic arrays of short electric dipoles perpendicular to the array axis. For an infinite periodic linear array of short dipoles, the scattering-matrix analysis leads to a simple implicit transcendental equation for the propagation constant beta of the traveling wave in terms of the normalized separation distance kd and the phase We of the effective scattering coefficient of the array elements. Interestingly, for certain values of We and kd there can be two different values of beta. The normalized separation distance and phase of the effective scattering coefficient also prove to be the only critical variables in the N x N matrix equation for the N radiation coefficients that is derived for a finite linear array of N electric dipoles. Resonances in the curves of total power radiated versus kd for a finite array excited with one feed element demonstrate the existence of the traveling waves predicted for the corresponding infinite array.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 2004
- Accession Number
- ADA429431
Entities
People
- Arthur Yaghjian
- Robert Shore
Organizations
- Air Force Research Laboratory