RADIOENGINEERING, VOL. 19, NO. 1, APRIL 2010 105 Multicriteria Optimization of Antennas in Time-Domain Jaroslav LÁČÍK 1 , Ioan E. LAGER 2 , Zbyněk RAIDA 1 1 Dept. of Radio Electronics, Brno University of Technology, Purkyňova 118, 612 00 Brno, Czech Republic 2 International Res. Centre for Telecomm. and Radar, Delft Univ. of Tech., Mekelweg 4, 2628 CD Delft, the Netherlands lacik@feec.vutbr.cz, i.e.lager@tudelft.nl, raida@feec.vutbr.cz Abstract. An original approach to the time-domain multi- criteria optimization of antennas is presented. For a given excitation pulse, the time-domain objective function takes the “time-domain impedance matching”, distortion of responses at the feeding point and in a desired radiating direction (with respect to the excitation pulse), and the radiated energy in the desired direction into account. The objective function is tested on the optimization of a bow-tie antenna using the particle swarm optimization. The proposed approach is suitable for the design of broadband antennas. Keywords Multicriteria optimization, particle swarm optimi- zation (PSO), time domain integral equation (TDIE). 1. Introduction The time-domain integral equation (TDIE) method has become a popular tool applied to the numerical analysis of electromagnetic radiation and scattering [1]-[4]. Essentially, if broadband information is desired, the time- domain solution of electromagnetic problems is more efficient than the frequency-domain one. For the analysis of antennas in the transmitting mode, the structure is excited by a desired voltage pulse at the feeding point of the antenna in order to find the transient response of the current. In case of antennas in the receiving mode, the goal is the same, but the whole structure is excited by the incident wave. Due to the frequency-domain nature of antenna parameters, time responses of computed quantities have to be converted to the frequency-domain, where the objective function is formulated. However, in order to avoid the Fourier transformation of the time response at each step of an optimization procedure, the objective function is more conveniently defined in the time-domain. Following this principle, the objective function is formulated in [5] in the time-domain, taking only matching of an antenna to the desired excitation pulse into account. Other important phenomena (such as the influence of a feeding line of an antenna, the antenna radiation), are not considered. In this paper, the multicriteria objective function for the optimization of antennas directly in the time-domain is discussed. The proposed approach is suitable for the design of broadband antennas. 2. Time-Domain Parameters In case of broadband or pulse radiation antennas, an antenna should be matched to the feeding line, radiate a waveform similar to the excitation pulse, and most energy should be radiated in a direction where the pulse is of the desired shape. For the proper optimization in the time-domain, all this facts should be considered. An antenna is matched to the feeding line if no energy is reflected back from its feeding point. In the time- domain, energy propagating forward and backward along the feeding transmission line can hardly be distinguished. Moreover, an antenna is usually analyzed without the feeding transmission line. The time-domain condition that no energy is reflected from the feeding point of the antenna (in case the antenna is analyzed without the feeding line) can be accomplished if: 1. The shape of the excitation voltage pulse U(t) at the feeding point is the same as the current response I(t). Then, the antenna is able to accept all the energy of the excitation pulse. According to the systems theory [6], the transfer function of such kind of systems is a constant, at least for the most important part of the spectrum of the excitation signal. In the case of the antenna, the transfer function is equal to the input admittance of the antenna. Since the location of the excitation pulse and the response is the same, the admittance is then real. However, the input admittance of the antenna can be different from the admittance of the feeding line. 2. The input admittance of the antenna at its feeding point is the same as the admittance of the feeding line.