Hertzian Dipole Fields Through Pole - Zero Treatment

The equations for EM dipole near and far radiation fields are formulated for the complex frequency domain with a Laplace Transform analysis for Hertzian dipoles. An s-domain pulsed current source function from ordinary circuit analysis is used in the expressions, and is augmented as needed to refine the pulse. This formulation allows a lucid pole-zero treatment of the field transfer function, yielding any field at any distance through the inverse Laplace Transform. Zeros of these expressions always include the “radiation zeros”, essential properties of the dipole fields themselves. Methods for recovery of current pulse waveforms from Eand H-field measurements, using filter functions, are described. The inverse Laplace Transform of pole-zero expressions through Heaviside expansion is more accessible than ever through free web applets and commonly available software. Study of the small pulsed dipole has become important in semiconductor manufacturing, as engineers seek to monitor and control charged device model ESD events that could destroy components. Introduction Dipole radiation is treated in many physics and engineering textbooks on electromagnetism (EM), only a few of which are cited here [1–3]. The most familiar treatment results in