Analysis of pattern null-fill in linear arrays

The Schelkunoff polynomial method of array synthesis is extended to the design of arrays with null-fill at one or several positions. We show that identical amplitude patterns with null-fill can be achieved by moving a number of Schelkunoff roots inside or outside the unit circle. This is a special case of a general principle that any linear source will have an associated conjugate mirror source which yields the same amplitude pattern. We also present a circuit model for array element mismatch and use it to study the effect of mismatch on null-fill in a linear array.