Non-minimum phase behavior due to fractional Hilbert transform in broadband circular polarization antennas

It is known that in a broadband antenna with ideal circular polarization, the antenna impulse responses of the linear components taken individually are related by a Hilbert transform. When considering port-to-port transmission s21(ω) between two such antennas in free space, it can be easily shown that rotating either antenna about the line-of-sight axis changes s21(ω) by a constant phase equal to the angle of rotation, which is equivalent to transforming the system impulse response according to a fractional Hilbert transform. In addition to change of pulse shape, a consequence of the rotation-induced transform is that neither s21(ω) nor the transfer function of an individual circularly-polarized antenna can be minimum phase, except possibly at particular angles of rotation. Experimental data is presented as an example of these effects.