Impedance properties of complementary multiterminal planar structures

Booker has shown that Babinet\´s principle, properly extended to electromagnetic fields, leads to a simple relation between the impedances of two planar complementary structures. A relation, which generalizes this result, is found between the impedance matrices of two complementary -terminal structures. This relation is applied to the particular -terminal structures having -fold symmetry and to those that are also self-complementary. In the latter case the impedance matrix is real and entirely determined by the number of terminals. It is therefore independent of the exact shape of the elements composing the structure and of the frequency. By connecting in groups the terminals of such a structure various impedance levels, all frequency independent and real, may be achieved. Structures having their terminal pairs in different locations in the plane are also considered. A self-complementary two-port structure is found to be equivalent, from the impedance point of view, to a length of lossy transmission line having a characteristic impedance of ohms.