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An approach for modeling antenna impedances and radiation fields in terms of fundamental eigenmodes is presented. Our method utilizes the simple frequency behavior of the characteristic modes to develop fundamental building blocks that superimpose to create the total response. In this paper, we study the modes of a dipole, but the method may be applied to more complicated structures as the modes retain many of their characteristics. We show that the eigenmode-based approach results in a more accurate model for the same complexity compared to a typical series RLC resonator model. Higher order modes can be more accurately modeled with added circuit complexity, but we show that this may not always be necessary. Because this method is based on the physical behavior of the fundamental modes, it also accurately connects circuit models to radiation patterns and other field behavior. To demonstrate this, we show that far field patterns, gain, and beam width of a dipole can be accurately extrapolated over a decade of bandwidth using data at two frequency points.