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Neuromorphic log-domain silicon synapse circuits obey Bernoulli dynamics: a unifying tutorial analysis

Neuromorphic log-domain silicon synapse circuits obey Bernoulli dynamics: a unifying tutorial analysis
Neuromorphic log-domain silicon synapse circuits obey Bernoulli dynamics: a unifying tutorial analysis
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
1662-4548
428
Papadimitriou, Konstantinos I.
c0535540-f862-41b1-9cf3-92b1f46a4145
Liu, Shih-Chii
724b1000-43ab-4934-bacf-cdb877b35472
Indiveri, Giacomo
2dcdb034-d331-48ad-80c3-23a7d69e1f4f
Drakakis, Emmanuel M.
e90f288a-ba96-4e6b-af0f-bb7ab850ce99
Papadimitriou, Konstantinos I.
c0535540-f862-41b1-9cf3-92b1f46a4145
Liu, Shih-Chii
724b1000-43ab-4934-bacf-cdb877b35472
Indiveri, Giacomo
2dcdb034-d331-48ad-80c3-23a7d69e1f4f
Drakakis, Emmanuel M.
e90f288a-ba96-4e6b-af0f-bb7ab850ce99

Papadimitriou, Konstantinos I., Liu, Shih-Chii, Indiveri, Giacomo and Drakakis, Emmanuel M. (2015) Neuromorphic log-domain silicon synapse circuits obey Bernoulli dynamics: a unifying tutorial analysis. Frontiers in Neuroscience, 8, 428. (doi:10.3389/fnins.2014.00428).

Record type: Article

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 (4th) order topology

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Accepted/In Press date: 6 December 2014
Published date: 20 January 2015
Organisations: Bioengineering Group

Identifiers

Local EPrints ID: 376754
URI: http://eprints.soton.ac.uk/id/eprint/376754
ISSN: 1662-4548
PURE UUID: 3949becd-bc5f-494d-ac96-d19c01778f7f

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Date deposited: 08 May 2015 10:59
Last modified: 14 Mar 2024 19:49

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Contributors

Author: Konstantinos I. Papadimitriou
Author: Shih-Chii Liu
Author: Giacomo Indiveri
Author: Emmanuel M. Drakakis

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