A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits

Thong Nguyen, Xinying Wang, Xu Chen, Jose E Schutt-Aine

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Volterra kernels are well known to be the multidimensional extension of the impulse response of a linear time invariant (LTI) system. It can be used to accurately model weakly nonlinear, specifically, polynomial nonlinearity systems. It has been used in the past for white-box model order reduction (MOR) to model frequency-domain performance metric quantities such as distortion in power amplifiers (PA). In this paper, we train a neural network from time-domain response of high-speed link buffers to extract multiple high-order kernels at once. Once the kernels are extracted, they can fully characterize the dynamics of the buffers of interest. Using the kernels, we demonstrate that time-domain response is straight-forward to obtain using super-, or multi-dimensional convolution. Previous work has used a shallow feed-forward neural network to train the system by using Gaussian noise as the identification signal. This is not convenient for the method to be compatible with existing computer-aided design tools. In this work, we directly use a pseudo random bit sequence (PRBS) to train the network. The proposed technique is more challenging because the PRBS has flat regions which have highly rich frequency spectrum and requires longer memory length, but allows the method to be compatible with existing simulation programs. We investigate different topologies including feed-forward neural network and recurrent neural network. Comparisons between training phase, inference phase, convergence are presented using different neural network topologies. The paper presents a numerical example using a 28Gbps data rate PAM4 transceiver to validate the proposed method against traditional simulation methods such as IBIS or SPICE level simulation for comparison in speed and accuracy. Using Volterra kernels promises a novel way to perform accurate nonlinear circuit simulation in the LTI system framework which is already well known and well developed. It can be conveniently incorporated into existing EDA frameworks.

Original languageEnglish (US)
Title of host publicationProceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1889-1896
Number of pages8
ISBN (Electronic)9781728114989
DOIs
StatePublished - May 2019
Event69th IEEE Electronic Components and Technology Conference, ECTC 2019 - Las Vegas, United States
Duration: May 28 2019May 31 2019

Publication series

NameProceedings - Electronic Components and Technology Conference
Volume2019-May
ISSN (Print)0569-5503

Conference

Conference69th IEEE Electronic Components and Technology Conference, ECTC 2019
CountryUnited States
CityLas Vegas
Period5/28/195/31/19

Fingerprint

Feedforward neural networks
Networks (circuits)
Buffers
Topology
Neural networks
Recurrent neural networks
Circuit simulation
SPICE
Impulse response
Power amplifiers
Convolution
Transceivers
Computer aided design
Polynomials
Data storage equipment
Deep learning

Keywords

  • Behavioral modeling
  • High-speed channel
  • Neural network
  • PAM4
  • Signal integrity
  • Volterra kernels
  • Volterra series
  • Weakly nonlinear time-invariant

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering

Cite this

Nguyen, T., Wang, X., Chen, X., & Schutt-Aine, J. E. (2019). A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits. In Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019 (pp. 1889-1896). [8811319] (Proceedings - Electronic Components and Technology Conference; Vol. 2019-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECTC.2019.00291

A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits. / Nguyen, Thong; Wang, Xinying; Chen, Xu; Schutt-Aine, Jose E.

Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1889-1896 8811319 (Proceedings - Electronic Components and Technology Conference; Vol. 2019-May).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nguyen, T, Wang, X, Chen, X & Schutt-Aine, JE 2019, A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits. in Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019., 8811319, Proceedings - Electronic Components and Technology Conference, vol. 2019-May, Institute of Electrical and Electronics Engineers Inc., pp. 1889-1896, 69th IEEE Electronic Components and Technology Conference, ECTC 2019, Las Vegas, United States, 5/28/19. https://doi.org/10.1109/ECTC.2019.00291
Nguyen T, Wang X, Chen X, Schutt-Aine JE. A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits. In Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1889-1896. 8811319. (Proceedings - Electronic Components and Technology Conference). https://doi.org/10.1109/ECTC.2019.00291
Nguyen, Thong ; Wang, Xinying ; Chen, Xu ; Schutt-Aine, Jose E. / A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits. Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 1889-1896 (Proceedings - Electronic Components and Technology Conference).
@inproceedings{879c9f31760e4f66ab0c3aa7ae9e8810,
title = "A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits",
abstract = "Volterra kernels are well known to be the multidimensional extension of the impulse response of a linear time invariant (LTI) system. It can be used to accurately model weakly nonlinear, specifically, polynomial nonlinearity systems. It has been used in the past for white-box model order reduction (MOR) to model frequency-domain performance metric quantities such as distortion in power amplifiers (PA). In this paper, we train a neural network from time-domain response of high-speed link buffers to extract multiple high-order kernels at once. Once the kernels are extracted, they can fully characterize the dynamics of the buffers of interest. Using the kernels, we demonstrate that time-domain response is straight-forward to obtain using super-, or multi-dimensional convolution. Previous work has used a shallow feed-forward neural network to train the system by using Gaussian noise as the identification signal. This is not convenient for the method to be compatible with existing computer-aided design tools. In this work, we directly use a pseudo random bit sequence (PRBS) to train the network. The proposed technique is more challenging because the PRBS has flat regions which have highly rich frequency spectrum and requires longer memory length, but allows the method to be compatible with existing simulation programs. We investigate different topologies including feed-forward neural network and recurrent neural network. Comparisons between training phase, inference phase, convergence are presented using different neural network topologies. The paper presents a numerical example using a 28Gbps data rate PAM4 transceiver to validate the proposed method against traditional simulation methods such as IBIS or SPICE level simulation for comparison in speed and accuracy. Using Volterra kernels promises a novel way to perform accurate nonlinear circuit simulation in the LTI system framework which is already well known and well developed. It can be conveniently incorporated into existing EDA frameworks.",
keywords = "Behavioral modeling, High-speed channel, Neural network, PAM4, Signal integrity, Volterra kernels, Volterra series, Weakly nonlinear time-invariant",
author = "Thong Nguyen and Xinying Wang and Xu Chen and Schutt-Aine, {Jose E}",
year = "2019",
month = "5",
doi = "10.1109/ECTC.2019.00291",
language = "English (US)",
series = "Proceedings - Electronic Components and Technology Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1889--1896",
booktitle = "Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019",
address = "United States",

}

TY - GEN

T1 - A deep learning approach for volterra kernel extraction for time domain simulation of weakly nonlinear circuits

AU - Nguyen, Thong

AU - Wang, Xinying

AU - Chen, Xu

AU - Schutt-Aine, Jose E

PY - 2019/5

Y1 - 2019/5

N2 - Volterra kernels are well known to be the multidimensional extension of the impulse response of a linear time invariant (LTI) system. It can be used to accurately model weakly nonlinear, specifically, polynomial nonlinearity systems. It has been used in the past for white-box model order reduction (MOR) to model frequency-domain performance metric quantities such as distortion in power amplifiers (PA). In this paper, we train a neural network from time-domain response of high-speed link buffers to extract multiple high-order kernels at once. Once the kernels are extracted, they can fully characterize the dynamics of the buffers of interest. Using the kernels, we demonstrate that time-domain response is straight-forward to obtain using super-, or multi-dimensional convolution. Previous work has used a shallow feed-forward neural network to train the system by using Gaussian noise as the identification signal. This is not convenient for the method to be compatible with existing computer-aided design tools. In this work, we directly use a pseudo random bit sequence (PRBS) to train the network. The proposed technique is more challenging because the PRBS has flat regions which have highly rich frequency spectrum and requires longer memory length, but allows the method to be compatible with existing simulation programs. We investigate different topologies including feed-forward neural network and recurrent neural network. Comparisons between training phase, inference phase, convergence are presented using different neural network topologies. The paper presents a numerical example using a 28Gbps data rate PAM4 transceiver to validate the proposed method against traditional simulation methods such as IBIS or SPICE level simulation for comparison in speed and accuracy. Using Volterra kernels promises a novel way to perform accurate nonlinear circuit simulation in the LTI system framework which is already well known and well developed. It can be conveniently incorporated into existing EDA frameworks.

AB - Volterra kernels are well known to be the multidimensional extension of the impulse response of a linear time invariant (LTI) system. It can be used to accurately model weakly nonlinear, specifically, polynomial nonlinearity systems. It has been used in the past for white-box model order reduction (MOR) to model frequency-domain performance metric quantities such as distortion in power amplifiers (PA). In this paper, we train a neural network from time-domain response of high-speed link buffers to extract multiple high-order kernels at once. Once the kernels are extracted, they can fully characterize the dynamics of the buffers of interest. Using the kernels, we demonstrate that time-domain response is straight-forward to obtain using super-, or multi-dimensional convolution. Previous work has used a shallow feed-forward neural network to train the system by using Gaussian noise as the identification signal. This is not convenient for the method to be compatible with existing computer-aided design tools. In this work, we directly use a pseudo random bit sequence (PRBS) to train the network. The proposed technique is more challenging because the PRBS has flat regions which have highly rich frequency spectrum and requires longer memory length, but allows the method to be compatible with existing simulation programs. We investigate different topologies including feed-forward neural network and recurrent neural network. Comparisons between training phase, inference phase, convergence are presented using different neural network topologies. The paper presents a numerical example using a 28Gbps data rate PAM4 transceiver to validate the proposed method against traditional simulation methods such as IBIS or SPICE level simulation for comparison in speed and accuracy. Using Volterra kernels promises a novel way to perform accurate nonlinear circuit simulation in the LTI system framework which is already well known and well developed. It can be conveniently incorporated into existing EDA frameworks.

KW - Behavioral modeling

KW - High-speed channel

KW - Neural network

KW - PAM4

KW - Signal integrity

KW - Volterra kernels

KW - Volterra series

KW - Weakly nonlinear time-invariant

UR - http://www.scopus.com/inward/record.url?scp=85072281385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072281385&partnerID=8YFLogxK

U2 - 10.1109/ECTC.2019.00291

DO - 10.1109/ECTC.2019.00291

M3 - Conference contribution

AN - SCOPUS:85072281385

T3 - Proceedings - Electronic Components and Technology Conference

SP - 1889

EP - 1896

BT - Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -