Mathematical approximation of the hyperbolic tangent

This paper presents an assimilation of the transfer function of a differential pair of MOS transistors to a hyperbolic tangent function. Also it prove, that the characteristic of transfer function of a MOS differential pair is symmetrical and that is close to the one of the bipolar transistors differential pair (It represent the transfer function of this differential pair; it describe the output signal in the form of a hyperbolic tangent of the input signal) with minor differences in our application. For this comparison, we use a MOS model transistor (0.35 mum) resulting from the library of the AMS foundry and on other hand we use a perfect nonlinear model of the bipolar transistor resulting from the Agilent-ADS library.