Neuromorphic Log-Domain Silicon Synapse Circuits Obey Bernoulli Dynamics: A Unifying Tutorial Analysis (bibtex)

by K. Papadimitriou, S.-C. Liu, G. Indiveri, E.M. Drakakis

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 generalised 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.

Reference:

Neuromorphic Log-Domain Silicon Synapse Circuits Obey Bernoulli Dynamics: A Unifying Tutorial Analysis (K. Papadimitriou, S.-C. Liu, G. Indiveri, E.M. Drakakis), In Frontiers in Neuroscience, volume 8, 2014.

Bibtex Entry:

@Article{Papadimitriou_etal14, author = {Papadimitriou, K. and Liu, S.-C. and Indiveri, G. and Drakakis, E.M.}, title = {Neuromorphic Log-Domain Silicon Synapse Circuits Obey Bernoulli Dynamics: A Unifying Tutorial Analysis}, journal = {Frontiers in Neuroscience}, year = {2014}, volume = {8}, number = {428}, issn = {1662-453X}, doi = {10.3389/fnins.2014.00428}, url = {http://www.frontiersin.org/neuromorphic_engineering/10.3389/fnins.2014.00428/abstract}, 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 generalised 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.} }

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