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A solution is presented for the time-domain voltage waveform which must be applied to the input terminals of a dipole antenna in order to maximize the amplitude of the radiated electric field at a specified time and far-field position. A constraint on the energy of the applied signal is used, and the applied signal is assumed to be bandlimited. The solution provides an upper bound on the maximum physically realizable electric field strength available from a dipole antenna, for fixed energy and bandwidth. Numerical examples are presented, and the effects of signal bandwidth, feed position, elevation angle, and dipole length are shown. The optimum solution is also compared with the response of a Gaussian input voltage pulse, and improvements of 6 dB or more are noted.