SEMI-ANALYTICAL FORMULATION FOR A UNIFIED TIME AND FREQUENCY ANTENNA CHARACTERIZATION
Keywords:SEM, FDTD, Effective Height, Matrix Pencil
The definition of parameters that characterize the radiation of electric and magnetic fields for antennas in the time and frequency domain on an unified representation is proposed. Â The formulation uses a straightforward semi-analytical formulation that can be subsequently applied on the analysis of excited antennas for an arbitrary source with temporal behavior. The effective height is a parameter for antenna analysis defined for quantities in far field region and can be used as a transfer function of the antenna. This transfer function can be described through the antenna singularities which can be obtained by singularity expansion. The Singularity Expansion Method (SEM) is capable to model an electromagnetic quantity with the singularities extracted by the current densities of an arbitrary object. This work proposes that the singularities are extracted by the Matrix Pencil method applied on the current densities. The current densities are obtained numerically through the method of the Finite Differences in the Time Domain (FDTD) for wired log-periodic antenna and, after the singularities are obtained, the formulation of the semi-analytical effective height equation is written. To validate the presented method, a formulation of the time-domain radiation pattern is presented and a corresponding frequency-domain radiation pattern is also presented using Parseval's theorem.
Electromagnetics. CRC Press, Boca Raton, 1993.
 S. Licul, “Ultra-wideband antenna characterization and measurements,” Ph.D. dissertation,
Faculty of the Virginia Polytechnic Institute & State University, 2004.
 S. T. M. Gonçalves, “Caracterização temporal de antenas refletoras para faixas de frequência
ultra-largas,” Master’s thesis, Universidade Federal de Minas Gerais, 2005.
 A. Shlivinski, E. Heyman, and R. Kastner, “Antenna characterization in the time domain,”
IEEE Transactions on Antennas and Propagation, vol. 45, no. 7, pp. 1140–1149, Jul. 1997.
 K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s
equations in isotropic media,” IEEE Transaction on Antennas and Propagation, vol. AP–14, no. 3,
pp. 302–307, 1966.
 C. E. Baum, “The singularity expansion method,” Transient Electromagnetics Fields, 1976,
L. B. Felsen (editor), Berlin: Springer-Verlag.
 G. Marrocco and M. Ciattaglia, “Ultrawide-band modeling of transient radiation from
aperture antennas,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 9, pp. 2341–2347,
 R. S. Adve, T. K. Sarkar, O. M. C. Pereira-Filho, and S. M. Rao, “Extrapolation of timedomain responses from three-dimensional conducting objects utilizing the matrix pencil technique,”
IEEE Transactions on Antennas and Propagation, vol. 45, no. 1, pp. 147–156, Jan. 1997.
 D. Caratelli and A. Yarovoy, “Unified time- and frequency-domain approach for accurate
modeling of electromagnetic radiation processes in ultrawideband antennas,” IEEE Transactions on
Antennas and Propagation, vol. 58, no. 10, pp. 3239–3255, Oct. 2010.
 C. E. Baum, “Singularity expansion of electromagnetic fields and potentials radiated from
antennas or scattered from objects in free space,” May 1973, Sensor and simulation notes, Air Force
 S. T. M. Gonçalves, “Caracterização unificada de antenas nos domínios do tempo e
frequência”, Ph.D. dissertation, Universidade Federal de Minas Gerais, Sep. 2010.
 J. Chauveau, N. de Beaucoudrey, and J. Saillard, “Selection of contribuiting natural poles for
the characterizationa of perfectly conducting targets in resonance region,” IEEE Transactions on
Antennas and Propagation, vol. 55, no. 9, pp. 2610–2617, Sep. 2007.
 A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time
Domain Method, 2nd ed. Artech House, Boston, 2000.
 A. Voors, “Nec based antenna modeler and optimizer,” http://www.qsl.net/4nec2/, last access
in April 2015.