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An efficient numerical implementation of the integral equation technique (IE) has been developed for the analysis of the electrical characteristics of finite microstrip structures. The technique formulates a volume version of the IE for the finite dielectric objects. The numerical implementation combines rooftop basis and testing functions for the conducting metallic areas, and two different choices for the dielectric objects. The first is based on a classical approach, combining pulse basis functions and deltas for testing. The second is a novel full Galerkin approach which employs rooftop functions defined on brick cells inside the dielectrics. The input impedances of two microstrip antennas have been computed with the new technique, showing good agreement with respect measurements. Also the radiation patterns of the antennas have been evaluated, showing again good agreement with respect to measurements. The practical value of the approach is that microstrip circuits can be designed minimizing the volume and size of the dielectric substrates. In addition, it is possible to accurately predict the backward radiation of practical microstrip radiators.