Pyramidal horn gain calculation with improved accuracy

Previously published methods for pyramidal horn gain calculation have used an approximate expression for the path length error that gives rise to aperture quadratic phase error. In this study pyramidal horn gain is calculated without approximating the path length error. These improved accuracy gain calculations give results equal to the previous approximate calculations for large apertures (A or B>50 λ) or small peak aperture phase error in wavelengths (S or T<0.2). For intermediate aperture size (5 λ⩽A⩽8 λ or 5 λ⩽B⩽8 λ) and intermediate peak aperture errors in wavelengths (0.2⩽S⩽0.6 or 0.2⩽T⩽0.6) the improved accuracy calculations will always yield higher gain than the previous approximate calculations by as much as a few tenths of a decibel, and by as much as 0.6 dB in the E plane. For large values of peak phase error in wavelengths (S or T>0.6) the improved accuracy method can yield lower gain than the previous calculations, especially for an E-plane flare