Error analysis for pseudo-logarithmic amplification

A logarithmic curve approximated by a series of line segments serves as the basis for a pseudo-logarithmic amplification scheme. The author studies the inherent deviation from a true logarithmic curve when approximated by such a piece-wise linear model. A commonly used logarithmic amplifier circuit is introduced and shown to coincide with the straight-line approximation in the limit of large stage gain. Practical implementations of the circuit often employ intermediate values of gain destroying the exact correspondence between the model and the circuit realization of the model. A discussion is included for the breakdown of the ability to the piece-wise linear approximation to describe the circuit in the limit of small stage gain.