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There are many antenna designs capable of producing high quality circular polarization over very wide bandwidth. One of the beneficial attributes of circular polarization seen in narrowband applications is that one or both of the antennas in a link can be rotated around the boresight direction without significantly affecting the received signal. However, this does not apply to a broadband system, in which the received pulse shape will change under rotation. Calculations of maximum possible correlation between the rotated and unrotated pulse shapes as the antenna is rotated are presented, along with an experimental example. It is also shown that in general it is not possible to have the pulse shape and amplitude invariant under rotation for a broadband signal, even if completely general polarizations and antenna transfer functions are allowed.