The LOG200 uses a differential amplifier to compare the voltage outputs of two logarithmic amplifiers. Logarithmic amplifiers rely on the feedback transistor relation of the base-emitter voltage (V_BE) to the collector current I_C, according to the principle:

where

• k = the Boltzmann constant, 1.381 × 10-23 J/K
• T = absolute temperature in kelvins (K)
• q = the elementary charge, 1.602 × 10-19 C
• I_S = the transistor reverse saturation current

For the basic logarithmic amplifier implementation shown in Figure 8-1, the following expression holds:

Figure 8-1 Basic Logarithmic Amplifier

When a difference amplifier with reference voltage V_REF is implemented to compare the outputs of two logarithmic amplifiers with input currents I₁ and I₂,

As I_S1 is approximately equivalent to I_S2 by design, this equation is equivalent to:

Figure 8-2 LOG200 Difference Amplifier

In the LOG200, the internal input resistors of the difference amplifier have a positive temperature coefficient to compensate for the temperature dependence of the above expression. The difference amplifier also gains up the nominal output, such that the output of the LOG200 is:

where K is the device scaling factor, nominally 250 mV/decade (252 mV/decade for preview material). Thus, for each 1-decade or order of magnitude shift in the difference of I₁ and I₂, the device output is correspondingly shifted by 250 mV (such as by 250 mV for I₁ = 10 µA and I₂ = 1 µA, or by –500 mV for I₁ = 10 nA and I₂ = 1 µA).