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