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In broadband phased arrays, the element spacing near the lowest frequency end can be much smaller than the wavelength. Besides this, in order to avoid sharp resonance related to the finite size of the elements, the antennas are often electrically connected to each other. Consequently, the couplings between elements can be extremely strong, and broadband behavior must be achieved by properly exploiting the effects of couplings, rather than tying to limit them. The arrays considered in this paper are composed of dielectric-free tapered-slot antennas. We show results obtained efficiently using frequency-domain and time-domain approaches for the analysis of arrays of tapered-slot antennas made of metallic plates. The frequency-domain approach consists of combining in a simple way results obtained with finite-by-infinite array simulations performed with a method of moments approach. The time-domain approach is an integral-equation technique; the marching-on-time procedure allows to omit matrix inversions. This method is particularly appropriate for the study of broadband devices. Key benefits of each approach are described, including computation of active and passive impedances needed for high-sensitivity arrays. The major features of the input impedances obtained by the two methods agree, providing a level of confidence in the results. However, small discrepancies between the results of the two methods remain to be resolved.