Log-domain filters, translinear circuits and the Bernoulli cell

In this paper a powerful analog circuit building block is identified, composed of a suitably biased npn bipolar junction transistor (BJT) with a grounded capacitor connected to the emitter. The collector current of the BJT is shown to have the form of Bernoulli's general non-linear differential equation and this configuration is termed a Bernoulli cell. By means of a suitable change of variables, Bernoulli's equation may be converted to a linear form and hence the Bernoulli cell can be exploited as a basic element for the synthesis of linear circuits.