Compact Expression for the Directivity of Binomial Array With No Restriction in Element Spacing

An attractive approach to design antenna arrays with minimum sidelobe level is based on the binomial expansion, and they are referred to as binomial arrays. In fact, binomial arrays with element spacing equal or less than λ/2 have no minor lobes. However, there are no compact expressions available to obtain the directivity of binomial arrays with no restriction in the element spacing, except when the element spacing is λ/2. This letter proposes a compact expression for the directivity of the binomial array with no restriction in the element spacing and number of elements. The procedure is based on the properties of the Pascal's triangle. Then, the array factor and directivity of the binomial array are calculated by using the properties of the Fourier transform.