title: Neuromorphic log-domain silicon synapse circuits obey bernoulli dynamics: a unifying tutorial analysis.
abstract: 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 (4(th)) order topology.
authors: Bioinspired VLSI Circuits and Systems Group, Department of Bioengineering, Imperial College London London, UK.
authors: Konstantinos I
authors: KI
authors: Papadimitriou
authors: Institute of Neuroinformatics, University of Zurich and ETH Zurich Zurich, Switzerland.
authors: Shih-Chii
authors: SC
authors: Liu
authors: Institute of Neuroinformatics, University of Zurich and ETH Zurich Zurich, Switzerland.
authors: Giacomo
authors: G
authors: Indiveri
authors: Bioinspired VLSI Circuits and Systems Group, Department of Bioengineering, Imperial College London London, UK.
authors: Emmanuel M
authors: EM
authors: Drakakis
keywords: analog VLSI (aVLSI); generalized bernoulli cell formalism; log-domain circuits; subthreshold MOSFETs; synaptic dynamics
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