A new formulation for the design of Chebyshev arrays

A new formulation for the design of Chebyshev arrays is presented which makes no direct use of Chebyshev polynomials. The array factor is expressed in terms of cosine/cosine-hyperbolic functions based on which all analysis and design steps are carried out. Zeros of the array factor are used to obtain a system of equations for excitation currents. Solving this system of equations, current magnitudes are determined in terms of the current of one element chosen as the independent variable. A general formulation for an even or odd but otherwise arbitrary number of elements is presented. The minimum number of elements required to achieve the desired beamwidth and side lobe level is obtained in a single step without resorting to an iterative process. The optimum spacing between elements for broadside and end fire arrays is also addressed. Numerical results for example cases are provided