Cross polarization caused by perturbed circular cross sections of waveguides and horn antennas

The cross polarization caused by a perturbed cross section of the conical hybrid-mode horn is analyzed. The perturbed cross section is assumed to be slightly elliptical. The theory previously presented for cross polarization in a smooth-walled waveguide supporting the
TE_{11}
- mode is referred and applied to the
HE_{11}
-mode as well. Simple analytical formulas which are sufficiently accurate for small ellipticites of the cross-section ellipse are presented. These show that the tolerances on the waveguide diameter are extremely strong, typically on the order of 2 to
4 \times 10^{-2}
mm in the horn throat for typical horn geometries at 12 GHz.