Covariant and contravariant bilinear transformation of quadripole scattering matrix and matching strategy for a quadripole type domestic microwave oven

The author obtains two formulations for calculating the image scattering matrix of a quadripole through a linear octopole circuit, which become equivalent when the octopole circuit is reciprocal. Thus bilinear transformation can be used for quantifying that a magic tee can match perfectly any quadripole type applicator or any domestic microwave oven to two generators.