Electrostatic Physics Model

In the PAN system, the body is modeled as an equipotential, which has an induced charge caused by the potential on the transmitter electrode. This charge on the body is measurable by the receiver electrodes.

To effectively model this for arbitrary geometry, it is necessary to numerically solve Poisson's equation:

#equation65#

This is accomplished by successive over-relaxation (SOR) of the three-dimensional finite difference approximation of the diffusion equation, which Poisson's equation is a steady-state solution of. Doing this calculation gives the full values of the potential in the vicinity of the objects in question. Given #tex2html_wrap_inline1284# and the definition of electric field:

#equation71#

it is possible to calculate the charge on each of the objects

#equation74#

and from that, and the known potential between each pair of objects (#tex2html_wrap_inline1286#), the capacitance can be calculated:

#equation81#

More details of the electrostatic model used can be found in Chapter #chapepm#85>.