PAN Electric Field Modelling Project for Nature of Mathematical Modelling

Matthew Gray

October 16, 1996

The goal of this semester project will be to create a three dimensional electric field model of a PAN system. This model will essentially be solved by the solution of LaPlace’s equations using successive over-relaxation (SOR). There are some differences, described here.

In this version of the model, the human body will be modeled as an arbitrarily shaped equipotential containing net zero charge. This second condition produces a different sort of boundary condition which will be described below. The PAN device will be modeled as two plates of charge, with values to give the desired potential difference across the electrodes. The room will be modeled as flat walls a large distance (compared to the scale of the body) away. The walls will have a fixed potential of zero.

In order to satisfy all of these conditions, an arbitrary potential for the human body will be selected. Given, this new boundary condition, the field will be solved for all space by SOR. The surface integral of the field over the body will then be calculated and compared to zero. In all likelyhood, after the initial guess for the potential for the body, this value will not be zero. Based on the calculated charge, the guess for the potential for the body will be adjusted and SOR will be run again. This will be repeated until the charge contained in the body is considered to be sufficiently close to zero.

Once this is solved for the specific transmitter geometry, an arbitrary receiver geometry can be selected and field strengths, and hence receiver voltages can be calculated.

Issues: I’m not 100% sure if I’m likely to run into problems switching back and forth between using field strengths (needed to calculate the integral over the body), potentials (for ground and the body), and charges (for the transmitter plates).