In this paper, novel CMOS pseudo-exponential circuits operating in a class-AB mode are presented. The pseudo-exponential approximation employed is based on second order equations. Such terms are derived in a straightforward way from the inherent nonlinear currents of class-AB transconductors. The cells are appropriate to be integrated in portable equipment due to their compactness and very low power consumption. Measurement results from a fabricated prototype in a 0.5 ${mu}m$ technology reveal a range of 45 dB with errors lower than ${pm}0.5$ dB, a power consumption of 100 ${mu}W$, and an area of 0.01 $mm^2$.