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A metamaterial-enabled approach is presented that allows one to engineer the dispersion of a log-periodic dipole array antenna (LPDA) to make it more suitable for wide bandwidth pulse transmission. By modifying the LPDA with electrically small transmission line metamaterial-based negative and positive phase shifters, the phase of each element of the LPDA are adjusted such that in the main beam direction, the phase shifts between each element approximates a linear phase variation. The performance characteristics of the resulting dispersion-engineered LPDA are obtained numerically with HFSS and MATLAB simulations. By measuring in the far field the fidelity between the actual transmitted pulse and the idealized output waveform, the required component values of the phase shifters are optimized. Significant improvements in the fidelity of the pulses transmitted are demonstrated with eight and ten element LPDAs.