Degrees of freedom of the field and maximum directivity

Paper in proceeding, 2016

This contribution discusses the relationship between the number of degrees of freedom (DoF) and the maximum directivity for an arbitrary set of sources enclosed by a given spherical surface. In particular, it is shown that the number of DoF is equal to twice the maximum directivity. This provides a directivity limitation for arbitrarily sized antennas, thus, extending the validity of the known formulas for electrically large and electrically small antennas.