Transient plane wave magnetic field attenuation through an infinite plate using a simplified laplace transform function

Abstract

The Laplace transfer function for the magnetic field vector of a plane traveling wave impinging on a single semi-infinite metallic plate is found to have real poles, which permits restatement of the transfer function in the form of an infinite product. It is shown that the significant poles of the infinite product have periodicity of (n\pi)^{2}) to within a few hundredths of a percent for a wide range of physical constants. A further practical assumption permits using only the first 10 terms of the infinite product. The resultant simplified transfer function indicates that the single, semi-infinite plate shielding geometry is analogous to a finite number of cascaded low-pass filters with similar roll-off characteristics. Several curves of steady-state attenuation as a function of frequency are plotted using the original closed form transfer function and these curves correlate closely with those predicted by the simplified transfer function. In particular, the similar roll-off characteristics of the different samples of metal plates, the low-frequency asymptotic values of attenuation, and the relative 3-dB attenuation points are all accurately predicted by the simplified transfer function, which relates these points directly to the physical parameters of the metal plate and the dielectric on both sides. A sample calculation of the transient response shows that the peak magnetic intensity of an impulsive wave is attenuated approximately 260 dB for a \frac{1}{4} inch thick steel plate.