%A Papadimitriou,Konstantinos I. %A Liu,Shih-Chii %A Indiveri,Giacomo %A Drakakis,Emmanuel M. %D 2015 %J Frontiers in Neuroscience %C %F %G English %K analog VLSI (aVLSI),Generalised Bernoulli Cell Formalism,Log-Domain Circuits,Subthreshold MOSFETs,synaptic dynamics %Q %R 10.3389/fnins.2014.00428 %W %L %M %P %7 %8 2015-January-20 %9 Original Research %+ Emmanuel M. Drakakis,Bioinspired VLSI Circuits and Systems Group, Department of Bioengineering, Imperial College London,London, UK,e.drakakis@imperial.ac.uk %# %! Bernoulli Cell Based Neuromorphic Silicon Synapse Analysis %* %< %T Neuromorphic log-domain silicon synapse circuits obey bernoulli dynamics: a unifying tutorial analysis %U https://www.frontiersin.org/articles/10.3389/fnins.2014.00428 %V 8 %0 JOURNAL ARTICLE %@ 1662-453X %X The field of neuromorphic silicon synapse circuits is revisited and a parsimonious mathematical framework able to describe the dynamics of this class of log-domain circuits in the aggregate and in a systematic manner is proposed. Starting from the Bernoulli Cell Formalism (BCF), originally formulated for the modular synthesis and analysis of externally linear, time-invariant logarithmic filters, and by means of the identification of new types of Bernoulli Cell (BC) operators presented here, a generalized formalism (GBCF) is established. The expanded formalism covers two new possible and practical combinations of a MOS transistor (MOST) and a linear capacitor. The corresponding mathematical relations codifying each case are presented and discussed through the tutorial treatment of three well-known transistor-level examples of log-domain neuromorphic silicon synapses. The proposed mathematical tool unifies past analysis approaches of the same circuits under a common theoretical framework. The speed advantage of the proposed mathematical framework as an analysis tool is also demonstrated by a compelling comparative circuit analysis example of high order, where the GBCF and another well-known log-domain circuit analysis method are used for the determination of the input-output transfer function of the high (4th) order topology.