This paper presents a thorough study of the time-domain theory of metal cavity resonators. The completeness of the vector modal functions of a perfectly conducting metal cavity is first proved by symmetric operator theory, and analytic solution for the field distribution inside the cavity excited by an arbitrary source is then obtained in terms of the vector modal functions. The main focus of the present paper is the time-domain theory of a waveguide cavity, for which the excitation problem may be reduced to the solution of a number of modified Klein-Gordon equations. These modified Klein- Gordon equation are then solved by the method of retarded Green's function in order that the causality condition is satisfied. Numerical examples are also presented to demonstrate the time-domain theory. The analysis indicates that the time-domain theory is capable of providing an exact picture for the physical process inside a closed cavity and can overcome some serious problems that may arise in traditional time-harmonic theory due to the lack of causality.
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