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This paper introduces a new variation on the capacitive feed probe for patch antennas on thick substrates. It consists of a small circular probe-fed capacitor patch that is situated next to the resonant patch. This configuration can bring about significant savings in terms of manufacturing cost, but also lends itself to a very efficient full-wave analysis. As such, the main focus of this paper is a spectral-domain moment-method formulation, which was specifically developed for the analysis of large, but finite, arrays of these antenna elements. Entire-domain and subdomain basis functions are combined in an efficient way to minimize the computational requirements, most notably computer memory. It is shown that, for general antenna array configurations, memory savings of more than 1000 times can be achieved when compared with typical commercial software packages where only subdomain basis functions are used. A number of numerical and experimental results are also included in order to verify the spectral-domain moment-method formulation and to illustrate various applications of the new antenna element.