IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 5, MAY 2006 1433 Equivalent Circuit Model for a Waveguide Probe With Application to DRA Excitation Islam A. Eshrah, Student Member, IEEE, Ahmed A. Kishk, Fellow, IEEE, Alexander B. Yakovlev, Senior Member, IEEE, and Allen W. Glisson, Fellow, IEEE Abstract—A simple equivalent circuit is used to model an arbi- trarily loaded waveguide probe with emphasis on probe-excited di- electric resonator antennas. The values of the lumped inductance and capacitance are obtained via the method of moments analysis for the problem of a short-circuited probe acting as a waveguide scatterer. For problems involving the excitation of an external load, the aperture through which the probe extends to the load is mod- eled by a shunt capacitance, and an additional transformer is in- troduced to model the coupling to the load. Expressions for these circuit parameters are obtained using curve-fitting techniques and are employed to determine the lengths and positions of an array of waveguide probes used to feed external loads with feeding cur- rents of desired relative values. The procedure is applied to synthe- size waveguide-fed antenna arrays to achieve a specified radiation pattern. The scanning capabilities and the effect of the mutual cou- pling are studied by comparing radiation patterns obtained from the analysis of the whole array and from the pattern multiplication principle. Index Terms—Equivalent circuit, method of moments (MoM), rectangular waveguide, waveguide probe. I. INTRODUCTION A NALYSIS and design of large finite arrays using the full- wave numerical techniques become increasingly difficult problems as the array size increases, due to the prohibitively large solution domain that makes reaching an optimum design an infeasible process, especially as the number of optimization goals increases. Equivalent circuit modeling of the array and the feeding network is a powerful tool that can facilitate the design procedure [1]–[5], since an initial design of the feeding network may be rapidly reached; this is a basic step in the array design since it determines the input currents feeding the array elements. Waveguides are conventionally used as feeding structures for phased antenna arrays due to their low losses at high frequen- cies, which results in high radiation efficiency. Waveguide-fed arrays have been designed using traditional array synthesis methods [6] or improved design techniques for small and large arrays [7]–[9]. Recently, waveguide probes were used to excite dielectric resonator antennas (DRAs) [10], exhibiting a wide- band response with the proper choice of the design parameters, namely the probe length and position with respect to the wave- guide and the DRA. The wideband nature of DRAs and the low Manuscript received May 31, 2005; revised November 27, 2005. This work was supported in part by The Army Research Office under Grant DAAD19-02-1-0074. The authors are with the Department of Electrical Engineering, University of Mississippi, University, MS 38677 USA (e-mail: ieshrah@olemiss.edu; ahmed@olemiss.edu; yakovlev@olemiss.edu; aglisson@olemiss.edu). Digital Object Identifier 10.1109/TAP.2006.874334 Fig. 1. Waveguide probe exciting an arbitrary external load. losses of waveguides make the waveguide-probe-excited DRA a good candidate for array applications. This work attempts to achieve two goals: First, to develop an equivalent circuit model for an arbitrarily loaded waveguide probe such as shown in Fig. 1, to exploit the features of circuit simulators in optimizing the element parameters, and easily ex- tend the analysis to the array problem. The circuit parameters are determined by equating the reflection coefficient obtained through the method of moments (MoM) solution [10] to that obtained using the circuit analysis. Second, a design procedure for probe-fed DRA arrays is developed using the equivalent cir- cuit model for the feeding network. From the desired specifica- tions of the radiation pattern, the adopted synthesis technique is used to determine the relative feeding currents of the DRA array elements. Then using optimization, the equivalent circuit parameters are determined and are subsequently interpreted as physical dimensions and positions of the probes. In the section to follow, the procedure for extracting the equivalent circuit parameters is detailed. In Section III, the design procedure for the array is presented along with a brief description of the MoM solution of the whole array problem. Validation of the scattering parameters obtained from the circuit analysis compared to the full-wave solution is presented in Section IV, as well as expressions for the circuit parameters in terms of the physical dimensions of the probe and examples of array design problems. The results obtained assuming that the DRAs are isolated are compared to those obtained taking into consideration the external mutual coupling, showing that the radiation pattern and the scattering parameters are not signif- icantly affected by the external coupling. Finally, conclusions and future work are discussed in Section V. 0018-926X/$20.00 © 2006 IEEE