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Pulsed circular arrays are collecting growing interest in radar applications such as automotives and indoor navigations. This contribution presents the analytic derivation of the space-time and energy patterns of pulsed circular arrays in terms of geometrical and electrical parameters as well as of the signal distortion produced by the antennas' response. It is shown that the field emitted by circular arrays with many elements can be represented as a summation of a practically finite set of high-order Hermite-Rodriguez waveforms, while the energy pattern is a generalized hypergeometric function. The angular and temporal resolutions are finally related, through handy formulas, to the array size, the input signals and to the antenna types.