A Method for Calculating the Current Distribution of Tschebyscheff Arrays

Dolph has derived an optimum current distribution for equispaced broadside arrays based upon the properties of the Tschebyscheff polynomials. Design curves are given for arrays of 8, 12, 16, 20, and 24 elements. The equations to be computed are bulky, however, so that the numerical calculations become cumbersome for arrays of more than 24 elements. In this paper, the equations of Dolph's method are considerably simplified by algebraic means with no loss in exactness. The final current expressions are given in a closed, exact form. It is also shown that the expressions for the current elements may be easily tabulated. A table for a 24-element array is constructed as an example which may readily be extended to arrays of any number of elements.