Customarily, logarithmic amplifiers exploit the V/I characteristic of a pn junction or approximate a log function in a piecewise-linear fashion. Both approaches suffer from inherent limitations. A pn junction's V/I characteristic has large temperature coefficients requiring ad hoc compensation circuitry. Piecewise-linear approximations exhibit discontinuities in their first derivatives

The circuit in Fig 1 is a true log amp having no junction-generated thermal terms for which to compensate and no discontinuities in its first derivative over its full useful range.

Commutating amp IC₁, voltage reference IC₅, capacitor C₁, and resistors R₁ through R₃ make an oscillator having a frequency (f) of

The voltage at point A in the circuit (also see Fig 2a) exhibits a true exponential form. The circuit then compares this voltage with the input voltage, V_IN, yielding a square wave whose duty cycle increases with V_IN (peak values are ±V_REF (see Fig 2b)). Lowpass filtering then produces the final output

which after numerical substitution yields

The constants in Eq 1 depend only on the values of R₁ and R₂. Because of symmetry, the circuit produces an output for both positive and negative values of V_IN such that V_OUT always obeys Eqs 2, 3, and 4.