Analysis of complex cavities with abrupt transitions

We present a general analysis method to study the rf field of step cavities. First, based on the general theory of modal field expansion techniques, we got the general equations to the modal field expansion coefficients when a large waveguide step is illuminated by two sets of traveling-wave from both sides. Then we directly combined out the standing-wave amplitudes and their derivatives. Finally we solved the second order differential equations which the standing-wave amplitudes in complex cavities must obey, and calculated several examples. The method discussed here can be use for step cavity analysis and design.