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In this paper the properties of a low-level nonlinear continuous-time circuit element-termed a Bernoulli Cell (or Operator)-are described in a systematic way. This cell is composed of an npn BJT and an emitter-connected grounded capacitor, and is governed by a differential equation of the Bernoulli form. Although this cell has the potential for application in both linear and nonlinear analog signal processing, this paper will focus on the field of input-output linear log-domain filtering. The Bernoulli Cell can be utilized in both the analysis and synthesis of log-domain circuits. The Bernoulli Cell approach leads to the creation of a system of linear differential equations with timedependent coefficients and state variables nonlinearly related to currents internal to the circuit; this set of equations is termed "log-domain state-space," and can be used for the synthesis of linear log-domain filters. Four design examples-including a bandpass biquad-are presented.

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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 timedomain 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.