When measuring the radiation pattern in the E-plane and H-plane, it's common to rotate the measurement setup by 90° to capture the next plane.
Now, consider a rectangular waveguide antenna operating in the dominant TE₁₀ mode, which is linearly polarized. Let’s assume this waveguide antenna is used as a standard antenna (transmitting or receiving), with its electric field polarized along the y-axis(i.e., $\vec{E} = E_0 \hat{y}$)
If I measure the radiation pattern of a second antenna (the device under test) in the E-plane, and then rotate it by 90° to measure the H-plane, this seems to rotate its polarization from the y-axis to the x-axis — making it orthogonal to the standard antenna’s polarization.
In this case, the dot product $\hat{y} \cdot \hat{x} = 0$
meaning the polarization is cross-polarized, and theoretically, no signal should be received.
However, in practice, we do receive a signal in the H-plane. Why is that?
What is the correct interpretation of the 90° rotation during E- and H-plane measurements?
In an ideal world you would receive no signal for an H-polarized waveguide antenna in a field from a V-polarized antenna, in the two cardinal planes. However, at other positions there will be a signal, because the polarization of the transmitter is probably not exactly vertical except in those two planes. The same goes for the antenna you are measuring, it's polarization varies with direction. Look at different definitions of polarization, such as Ludwig I, II and III. Different antennas approximate these three polarization patterns, and others! Many antennas have peaks in cross-polarization in the 45 degree planes.
Reflections in your measurement chamber will also result in cross-polarized fields, as well as your measurement not quite being at the right angle to hit the null.
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