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The behavior of a two element segmented capped monopole antenna is described in terms of three natural resonances of the antenna structure. A numerical eigenmode solver is used to derive the resonant frequency and Q-factor of the natural resonances, as well as the impedance properties of these modes when excited individually. The impedance of the antenna is described as a lumped element network, where the component values of the network are determined from the impedance parameters of the resonant modes and the static properties of the antenna structure. The model is applied to predict the behavior of the antenna when a lumped element inductor is used to connect the two segments. The inductor tunes the properties of one of the three resonances, enabling the impedance bandwidth to be optimized. The analysis is then extended to predict the behavior of the antenna when the two vertical elements have different radii, a configuration that enables wide bandwidth operation without the use of an inductor. The modal analysis accurately predicts the impedance and far-field properties of the antennas. Analyzing the antenna in terms of its natural resonant modes provides physical insights into both its behavior and the fundamental limitations of its performance.