A Receptor Analog Having Logarithmic Response

In peripheral organs a logarithmic relationship between stimulus and response holds for a rather wide range of input magnitudes. This relationship is clearly demonstrated for Limulus between the frequency of discharge in the optic nerve, and the intensity of stimulating light. A simple relaxation oscillator is envisioned to model the generation of nerve impulses. The necessary transfer function of the charging circuit of the oscillator is computed so that the frequency of oscillation should be proportional to the logarithm of the magnitude of the input voltage. It is shown that the obtained transfer function can be realized by a tapered RC transmission line. The experimental verification of the derivation is given.