Theoretical Explanation and Prediction of Branches in Permittivity from S-parameter Values

In the field of electromagnetism, knowing the permittivity of a material can be useful. When using the scattering parameters to identify the permittivity of materials, branch discontinuities may be an issue. If they occur, branches of some systems could be neglected. This paper analyzes a theoretical solution for permittivity from the scattering parameters, particularly related to metamaterials, and shows that these branches are due to the use of the argument of an exponential function. Analyzing this exponential function can provide a unique and accurate prediction method of when branches will occur.