Determination of Anisotropy Ratio κ/μ for Symmetric Three-Port Circulator Using Transmission Line Equivalent Model

In this article, the value of anisotropy ratio κ/ μ for ideal symmetric three-port circulator is derived by using the transmission line equivalent model. This value plays a vital role in the design of circulator. In order to obtain the value of κ/ μ, eigenvectors of the scattering matrix S for the circulator are given first. Then, one-port transmission line equivalent models for ideal circulator are presented. Finally, the value of κ/ μ is derived in terms of the relationships between reflection coefficients of three one-port transmission line equivalent models. Furthermore, a three-port waveguide circulator is designed in order to verify the theoretical value of κ/ μ. And the experimental value of κ/ μ is approximately equal to the theoretical result. Also, this value derived in this article is in good agreement with the one obtained by field method and circuit method in published literatures.