Transient response of a logarithmic amplifier

An analysis of the transient response of a logarithmic amplifier to a step function decrease in nuclear reactor period leads to a differential equation of the form exp
({\alpha}t) + a exp (bx) + cdx/dt = 0
. This equation is shown to be integrable and to relate the amplifier output voltage to reactor period and time. The result can be used to examine the suitability of a logarithmic amplifier for monitoring fast transient reactor excursions.