Analysis of Resonance Problems of Arbitrarily Complicated Transmission Line Cavities by Using Complex Phase Angle Theory

A novel theory of complex phase angle is presented to deal with the resonance problems of an arbitrarily complicated transmission line cavity effectively, which merges various losses of transmission lines (including source and load losses) in the imaginary part of the complex phase angle. This letter shows that the real part of the complex phase angle $ theta ^prime $ determines the resonant frequency and the imaginary part $ theta ^prime prime $ relates to the quality factor $Q$ of the transmission line cavity physically. A loaded transmission line resonance cavity is given to illustrate the application and validation of the complex phase angle theory.