Coupling to a probe in a metal can by an electric dipole

We describe a method to compute the coupling of a signal, caused by an elementary dipole, to a load impedance terminating a coaxial guide whose center conductor protrudes into a conducting can. The can is a right circular cylindrical shell with a flat bottom through which protrudes the coax center conductor. The coax axis is the same as the cylinder axis and its outer conductor terminates at, and is electrically connected to, the can bottom. The can wall and bottom are taken to be vanishingly thin and they are perfect conductors, as are the inner and outer walls of the coaxial waveguide. To perform this computation directly is very difficult so we resort to a method that allows us to realize significant computational savings with no loss in generality. In principle, the approach developed to solve this problem is exact and rigorous. Of course, approximations are made but only when the resulting error is very small. The indirect approach adopted takes advantage of the reciprocity theorem and allows one to determine the signal at the coax terminal load from knowledge of the field radiated by the monopole-can structure under the condition that the excitation results from a current generator impressed at the terminal end of the coax. This scheme depends upon the formulation and solution of a simple integral equation.