Longitudinal coupling impedance of a hole in an infinite plane screen

An analytical formula for the longitudinal coupling impedance of a hole is developed using a variational method. We show that the coupling impedance can be expressed as a sum of functional series, whose argument is the dimensionless quantity kd alone, where k is the free-space wave number and d is the radius of the hole. When expanded in powers of kd, we recover the long wavelength result as a limiting case. The numerical evaluation reveals that the impedance can be well modeled by an RLC-resonator circuit. We also show the qualitatively good agreement between the theory and the MAFIA-T3 simulation for the geometry of a hole in a coupled waveguide with rectangular cross section