An Analysis of Broadband Circulators with External Tuning Elements

Equations are presented which show how the isolation-bandwidth characteristic of a given Y-circulator junction can be modified by external tuning elements. Results are given for tuning with one, two and, as a limiting case, an infinite number of resonant elements. The results suggest that there is only limited room for improvement in the best of the current state-of-the-art empirically designed circulators.