E.M. Drakakis

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.

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 Bernoullis general non-linear differential equation and this configuration is termed a Bernoulli cell. By means of a suitable change of variables, Bernoullis 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.

Multiple feedback log-domain filters

In this paper the design of a multiple feedback FLF log-domain filter is presented by means of the Bernoulli cell-based log-domain state space differential equations. Confirming HSPICE simulation results are presented.

Operational dc constraints for a class-A, third-order, observer canonical-form log-domain filter

This brief reveals certain nonevident though necessary dc constraints for the correct operation of a class-A log-domain third-order observer canonical-form frequency-shaping network. The impact of current-source mismatch upon these constraints is also examined. The brief sheds light on the issue of correct dc-biasing of class-A log-domain circuits.

Spectral impact of the modulation index upon internal log-domain currents

This brief investigates quantitatively the impact of the input-signal modulation index upon the spectral content of internal log-domain currents. A second-order log-domain topology is treated as an example circuit and the quantitative dependence of the harmonic contributions to the total harmonic content of current signals internal to the topology upon different levels of strength of applied input tones is illustrated. Subsequently, this frequency-domain information is correlated with the transition frequency of the active devices which carry the nonlinear currents providing a certain degree of quantitative design insight.