The multi-tanh principle: a tutorial overview

This paper reviews a class of linear transconductance cells, having proven value in a variety of communications applications, characterized by the use of parallel- or series-connected sets of differential pairs of bipolar transistors whose inputs and outputs are connected in parallel. These cells invoke a well-developed concept, known as the "multi-tanh principle". The key idea is that the individually nonlinear (hyperbolic tangent, or tanh) transconductance functions may be separated along the input-voltage axis to achieve a much more linear overall function. The simplest of these is the so-called the "doublet"; the linearity criterion and noise behavior are discussed in detail. Some novel forms are presented. Higher order cells, including the "triplet", are then discussed, together with a novel method for achieving linear-in-dB gain control with an important modification for extending the dynamic range.