Element spacing limitations of Dolph-Pritchard optimum endfire arrays

It is generally accepted that the Dolph-Pritchard technique for computing optimum or Chebyshev radiation patterns for single-lobe endfire arrays is valid for any array element spacing less than one-half wavelength. However, it can be shown that multiple-lobe radiation patterns will be obtained using this technique for element spacing less than one-half wavelength. A maximum element spacing for single-lobe radiation patterns can be derived, and this spacing is a function of the major-lobe-to-sidelobe amplitude ratio as well as the order of the Chebyshev polynomial. In general, for large amplitude ratios this maximum spacing approaches one-quarter wavelength.