The figure illustrates a proposed analog amplifier circuit that would put out a voltage proportional to the logarithm of the ratio between two input signal currents, I1 and I2. In comparison with prior log-ratio amplifiers, this one would be relatively insensitive to variations of temperature over a wide range. An additional advantage of the proposed circuit is that the base of the logarithms could be varied.

This Log-Ratio Circuit would eliminate the effect of the temperature dependence in the outputs of the log-ratio amplifiers. It would also provide a convenient way to adjust the base of the logarithms.
In this circuit, as in other log-ratio amplifier circuits, the log function would be provided by transistors, the inputs and outputs of which are related in a highly temperature-dependent manner. In designing prior log-ratio amplifiers, attempts have been made to suppress the effects of temperature dependence by use of (a) thermostatically controlled heaters to maintain the transistors at constant temperatures or (b) adjusting the outputs by use of feedback from thermistors in close contact with the transistors. These attempts at temperature stabilization are subject to several limitations, one being that they are ineffective outside the temperature range of about 0 to 70 °C.

Unlike in prior log-ratio amplifier circuits, no attempt would be made to control temperature or compensate for changes in temperature in the proposed circuit. The proposed circuit would include two matched conventional log-ratio amplifiers, both mounted on the same die so that they could be assured of being at the same temperature. The input signal currents would be fed to one of the log-ratio amplifiers, which would respond by putting out a voltage (CkT/q)ln(I1/I2), where C is a constant that depends on the design, k is Boltzmann's constant, T is the absolute temperature, and q is the fundamental unit of electric charge.

Known control currents I3 and I4 would be fed as inputs to the other log-ratio amplifier, which would respond by putting out a voltage (CkT/q)ln(I3/I4). The outputs of the log-ratio amplifiers would be fed to a divider circuit: the temperature and the other equal terms in the numerator and denominator would cancel each other in the division, so that the output of the divider circuit would be proportional to ln(I1/I2)/ln(I3/I4 ), which is the same as log(I1/I2) to the base I3/I4. Thus the base of the logarithms could be selected by setting the control currents to obtain the desired value of I3/I4.

This work was done by Richard Steinke of Honeywell, Inc., for Johnson Space Center. For further information, access the Technical Support Package (TSP) free on-line at  under the Electronics & Computers category.