On the multiplicity of solutions of Taylor linear sources generating symmetrical power patterns with filled nulls [antenna design applications]

As expressed in earlier works, if filled nulls are required in a power pattern generated by a Taylor line source, their corresponding roots must be complex. This leads to a multiplicity of solutions emerged from the fact that the power pattern keeps unaltered if the signs of the imaginary part of the roots are changed. In view of this attribute, the selection of the most favorable roots set, in terms of variability of amplitude excitation distribution, for example, is allowed. It is shown in this paper that, if the pattern is symmetric, a further consideration, never reported so far, can increase the number of available solutions.