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At the antenna connector you may receive (or transmit) only one wave polarization. (linaer or circular). The 90° far polarizzation is generally unwanted.
Cross-polarizzation (Xpol) is the 90° far, unwanted polarizzation.
Co-polar (Copol) is the wanted polarization.
I.e. if a standard antenna TX a vertical pol. , in far field region, when you RX a Vertical one, you RX the Copol, while if you try to receive Horrizontal, you'll receive the Xpol.
Many definitions exists for Xpol. For my knowledge, the most widely adopted is the Ludwing's one.
when an antenna transmit with a particular polarization (e.g. right handed circular, or horizontal) if the reciever has the same polorization it recieve all the available power from space but if it has xpol characteristic (e.g. left handed circular, or vertical respectivlly) theortically it recieve no power from space but in practice it recieve a little.
in datasheets for an antenna usually drawn to radation pattern, copol and xpol.
regards
Co and Cross polarizations exist only in the case of linearly polarized antennas.
Power received by an antenna is proportional to Cos(θ), where θ is the angle between the E-vectors of the received wave and that would induce in the Rxr antenna (depends on its geometry and orientation of feed ).Rxr antenna will receive maximum power only when θ=180• , which is co-polarization.When θ=90• minimum power is received, which is cross-polarization.
For a circularly polarized antenna, the same power is received irrespective of θ
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