Superdirective spherical radiator

The condition for the maximum directivity from a spherical radiator is presented and it is shown that this directivity Index is 20 logN, where N is the number of consecutive modes excited. In this case, the relationship among the expansion coefficients is particularly simple and a closed‐form expression for the beam pattern function results. Using this method, a high directivity may be obtained no matter how small the sphere is, provided that the prescribed velocity distribution is maintained. Examples of the resulting beam patterns are given.