“Log-domain state-space”: a systematic transistor-levelapproach for log-domain filtering

摘要

In this paper the properties of a low-level nonlinearncontinuous-time circuit element-termed a Bernoulli Cell (ornOperator)-are described in a systematic way. This cell is composed of annn-p-n BJT and an emitter-connected grounded capacitor, and is governednby a differential equation of the Bernoulli form. Although this cell hasnthe potential for application in both linear and nonlinear analog signalnprocessing, this paper focuses on the field of input-output linearnlog-domain filtering. The Bernoulli Cell can be utilized in both thenanalysis and synthesis of log-domain circuits. The Bernoulli Cellnapproach leads to the creation of a system of linear differentialnequations with time dependent coefficients and state variablesnnonlinearly related to currents internal to the circuit; this set ofnequations is termed “log-domain state-space”, and can benused for the synthesis of linear log-domain filters. Four designnexamples-including a bandpass biquad-are presented