Abstract
This paper proposes new closed expressions of self-impedance using the Method of Moments with the Point Matching Procedure and piecewise constant and linear basis functions in different configurations, which allow saving computing time for the solution of wire antennas with complex geometries. The new expressions have complexity O(1) with well-defined theoretical bound errors. They were compared with an adaptive numerical integration. We obtain an accuracy between 7 and 16 digits depending on the chosen basis function and segmentation used. Besides, the computing time involved in the calculation of the self-impedance terms was evaluated and compared with the time required by the adaptative quadrature integration solution of the same problem. Expressions have a run-time bounded between 50 and 200 times faster than an adaptive numerical integration assuming full computation of all constant of the expressions.
Highlights
The radiation and scattering produced by antennas is the foundation of modern wireless communications
The unknown current I (s0 ) is found through the solution of the Electric Field Integral Equation (EFIE) [21,22,23], which is expressed by published maps and institutional affil
It is possible to find closed expressions for the self-impedance using piecewise constant and linear basis functions in useful configurations applied for straight wire antennas with size 8a ≤ L ≤ 0.1λ
Summary
The radiation and scattering produced by antennas is the foundation of modern wireless communications. The closed expressions allow saving computing time for the solution of complex problems, in the design of arbitrary wire geometries. Closed expressions for self-impedances allow reducing the numerical error of the solution of (5) because [ Z pq ] M× M is a nearly-diagonal dominant matrix. The authors of [43] use the additive separation technique to find a closed self-impedance using the Maclaurin series approximation of R−5 e− jkR and the piecewise constant basis function with an observation point z p located at the middle of the segment ∆. It is possible to find closed expressions for the self-impedance using piecewise constant and linear basis functions in useful configurations applied for straight wire antennas with size 8a ≤ L ≤ 0.1λ. The last sections present the conclusions, future work and appendices
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