Transient Excitation of Rectangular Resonators Through Electrically Small Circular Holes

In this paper, analytical solutions of response functions for rectangular resonators are investigated in time domain. Emphasis is placed on the study of electromagnetic field coupling to a 3-D cavity through a small circular aperture. The time-dependent parts of the resulting modal Green's functions exhibit typical behavior that is inherent in all resonating/oscillating linear physical systems: namely, they fulfill oscillating ordinary differential equations at any point of the considered resonator. Their solutions contain transient and steady-state parts. The transient parts of the response functions will become important for electromagnetic compatibility tests in particular of modern digital high-speed electronics.