A critical study of linear arrays with equal side lobes

New and generalized expressions for the array factor of all physically realizable linear antenna arrays with progressive phase shifts are introduced. Based on these generalized expressions, a new way of synthesizing arrays with equal side lobes is available. It applies equally well to both broadside and endfire arrays, which may have either even or odd number of elements with unrestricted element spacing. No manipulations with transcendental functions are necessary, and the final expressions show a clear relationship between element excitations and null locations in the radiation pattern. Directive gain can be calculated directly from the array factor. Pattern optimization and sensitivity problems are discussed and typical examples are presented.