A circuit, using a single tube, and having an output voltage which is proportional to the logarithm of a direct current input, is described. The input current range extends from less than 10−7ampere to 10−5ampere if a closely linear logarithmic relationship is desired; and from 10−8to 10−3ampere if only an approximately logarithmic characteristic is necessary. Because the circuit depends for its operation on a fundamental physical law (the Maxwellian distribution of velocities of the thermoelectrons emitted from a hot cathode), its characteristics are constant and predictable.