  An amplifier has been designed for optimal use of position sensitive thermal
neutron detectors using the principle of resistive charge division. The
important points in this optimization are: high counting rates and good spatial
resolution. This amplifier is built as a hybrid circuit and is now used on
several new instruments at the ILL. It consists of a fast low noise current
pre-amplifier, a gaussian shaping circuit based on a 4th order active filter
and an essentially noiseless baseline reconstruction. In this paper, we present
a rather complete theoretical analysis of the problem that lead us to the
choices made above, and allows for an optimal adaptation to other situations.
An analysis of unwanted, secondary effects is also worked out.
