Log-domain filtering and the Bernoulli cell

In this paper, the dynamic behavior of a nonlinear circuit element termed a Bernoulli cell is described, which is composed of a suitably biased bipolar junction transistor (BJT) and an emitter connected grounded capacitor. This cell has application in the synthesis of log-domain filters, since it facilitates the development of a low-level design approach in which a frequency-domain transfer function is decomposed into time-domain current product equalities that can be implemented by direct use of the translinear principle (TLP). Furthermore, the dynamic of a log-domain structure can be analyzed and its frequency response can be easily derived when the embedded Bernoulli cells are identified. An analysis and a synthesis example are presented.