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The aim of this article is to study the phase center movement on a wide band antenna, and its effects on Doppler frequency measurements in FM-CW systems. In the first part, the FM-CW radar system is described. In the second part, the model used to compute the phase center position of a log-periodic dipole (LPD) antenna is presented and validated by measurements. In the final part, this method is applied to a HF-VHF LPD antenna and the Doppler effect of this antenna is computed in an FM-CW radar context.