Circuit simulation & numerical algorithms

Making the simulation of large, stiff, high-speed circuits fast enough to be useful.

My group develops the numerical machinery behind computer-aided design of electronic systems: high-order stable time-stepping, model order reduction for interconnects, and variability analysis for circuits whose behaviour is never quite what the nominal parameters say it is.

Circuit simulation Numerical algorithms Computational electromagnetics RF circuits

Research

Six active threads

Fast, stable transient simulation

High-order A-stable and L-stable integration methods for stiff differential equations, and Obreshkov-based simulators that keep accuracy without shrinking the time step.

Numerical inversion of the Laplace transform

Interpolation-supported and modified NILT schemes that give fast, stable time-domain responses with low-cost error estimation.

Model order reduction

Integrated congruence transform and moment-based interpolation projection for passive, compact macromodels of multiconductor and frequency-dependent interconnects.

Variability & statistical analysis

Decoupled and generalized Hermite polynomial chaos for propagating parameter uncertainty through nonlinear circuits and embedded macromodels.

Computational electromagnetics

Unconditionally stable high-order time-domain finite-element methods, and circuit-based analysis of field coupling with non-uniform transmission lines.

RF, microwave & power circuits

Envelope-following methods for highly oscillatory circuits, GPU-accelerated harmonic balance, and steady-state analysis of switching converters.

Prospective students

I supervise graduate students at the MASc, MCS and PhD levels in the School of Electrical Engineering and Computer Science. The work sits between numerical analysis and electronic design automation, so the students who do well here usually arrive with two of the following three and are willing to build the third.

  • A solid footing in linear algebra, differential equations and numerical methods.
  • Real programming ability — C/C++, Python or MATLAB, and comfort with the command line.
  • Background in circuits, electromagnetics or signal integrity.

If that sounds like you, email me with your CV, transcripts, and a short paragraph on which of the research threads above interests you and why. Please mention a specific paper — it tells me you have read something, and it makes for a much better first conversation. Admission is through the uOttawa graduate studies application; contacting me first is welcome but does not replace it.

Emad — this section is drafted from your publication record. Edit the wording, and add or remove a line about current funded openings before you publish.

Teaching

ELG 4137

Principles and Applications of VLSI Design I

Winter 2024

Update the term and add current courses here; course materials for enrolled students are on Brightspace.

Publications

41 items
Journal papers
  1. 38
    E. Gad, Y. Tao and M. Nakhla, “Fast and Stable Circuit Simulation via Interpolation-Supported Numerical Inversion of the Laplace Transform,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 12, no. 1, pp. 121–130, Jan. 2022.
    2022Best Paper Award — IEEE EPS, 2022
  2. 37
    Y. Tao, E. Gad and M. Nakhla, “Low-Cost Error Estimation for Fast and Stable Circuit Simulation Using Modified Inversion of the Laplace Transform,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 12, no. 7, pp. 1160–1170, July 2022.
    2022
  3. 36
    Y. Tao, E. Gad and M. Nakhla, “Fast and Stable Time-Domain Simulation Based on Modified Numerical Inversion of the Laplace Transform,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 11, no. 5, pp. 848–858, May 2021.
    2021
  4. 35
    Q.-J. Zhang, E. Gad, B. Nouri, W. Na and M. Nakhla, “Simulation and Automated Modeling of Microwave Circuits: State-of-the-Art and Emerging Trends,” IEEE Journal of Microwaves, vol. 1, no. 1, pp. 494–507, Winter 2021.
    2021
  5. 34
    B. Nouri, E. Gad, A. Nouri, M. Nakhla and Y. Tao, “DC-Centric Parameterized Reduced-Order Model via Moment-Based Interpolation Projection (MIP) Algorithm,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 10, no. 8, pp. 1348–1357, Aug. 2020.
    2020
  6. 33
    K. Taggar, E. Gad and D. McNamara, “High-Order Unconditionally Stable Time-Domain Finite-Element Method,” IEEE Antennas and Wireless Propagation Letters, vol. 18, no. 9, pp. 1775–1779, Sept. 2019.
    2019
  7. 32
    M. Plesnik, E. Gad and M. Nakhla, “Efficient Steady-State Simulation of Switching Power Converter Circuits,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 9, no. 7, pp. 1328–1336, July 2019.
    2019
  8. 31
    M. A. Farhan, M. S. Nakhla, E. Gad and R. Achar, “Parallel High-Order Envelope-Following Method for Fast Transient Analysis of Highly Oscillatory Circuits,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems.
    in press
  9. 30
    M. R. Rufui, E. Gad, M. Nakhla and R. Achar, “Fast Variability Analysis of General Nonlinear Circuits Using Decoupled Polynomial Chaos,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 5, no. 12, pp. 1860–1871, Dec. 2015.
    2015
  10. 29
    Y. Lin and E. Gad, “Formulation of the Obreshkov-Based Transient Circuit Simulator in the Presence of Nonlinear Memory Elements,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 34, no. 1, pp. 86–94, Jan. 2015.
    2015
  11. 28
    M. Farhan, E. Gad, M. Nakhla and R. Achar, “High-Order Envelope Following Method for Transient Simulation of Oscillator Circuits,” IEEE Transactions on Microwave Theory and Techniques, vol. 62, no. 12, pp. 3309–3317, Dec. 2014.
    2014
  12. 27
    M. R. Rufui, E. Gad, M. Nakhla and R. Achar, “Generalized Hermite Polynomial Chaos for Variability Analysis of Macromodels Embedded in Nonlinear Circuits,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 4, no. 4, pp. 673–684, Apr. 2014.
    2014
  13. 26
    T.-A. Pham, E. Gad, M. Nakhla and R. Achar, “Decoupled Polynomial Chaos and its Applications to Statistical Analysis of High-Speed Interconnects,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 4, no. 10, pp. 1635–1637, Oct. 2014.
    2014
  14. 25
    B. Bandali, E. Gad and M. Bolic, “Accelerated Harmonic-Balance Analysis using a Graphical Processing Unit Platform,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 33, no. 7, pp. 1017–1030, July 2014.
    2014
  15. 24
    M. Farhan, E. Gad, M. Nakhla and R. Achar, “Parallel Simulation of Large Linear Circuits With Nonlinear Terminations Using High-Order Stable Methods,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 4, no. 7, pp. 1201–1211, July 2014.
    2014
  16. 23
    M. Farhan, E. Gad, M. Nakhla and R. Achar, “A New Method for Fast Transient Simulation of Large Linear Circuits using High-Order Stable Methods,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 3, no. 4, pp. 661–669, Apr. 2013.
    2013
  17. 22
    M. Farhan, E. Gad, M. Nakhla and R. Achar, “Fast Simulation of Microwave Circuits with Non-Linear Terminations Using High-Order Stable Methods,” IEEE Transactions on Microwave Theory and Techniques, vol. 61, no. 1, pp. 360–371, Jan. 2013.
    2013
  18. 21
    Y. Zhou, E. Gad, M. Nakhla and R. Achar, “Structural Characterization and Efficient Implementation Techniques for A-Stable High-Order Methods,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 31, no. 1, pp. 101–108, Jan. 2012.
    2012
  19. 20
    J. C. G. Pimentel, E. Gad and S. Roy, “High-Order A-stable and L-stable State-Space Discrete Modelling of Continuous Systems,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 2, pp. 346–359, Feb. 2012.
    2012
  20. 19
    E. Gad, M. Nakhla, R. Achar and Y. Zhou, “A-stable and L-stable Methods for the Solution of Stiff Differential Equations,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 28, no. 9, pp. 1359–1372, Sept. 2009.
    2009
  21. 18
    C. Chen, D. Saraswat, R. Achar, E. Gad and M. Nakhla, “Passivity Compensation Algorithm for Method-of-Characteristics Based Multiconductor Transmission Line Interconnect Macromodels,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 17, no. 8, pp. 1061–1072, Aug. 2009.
    2009
  22. 17
    E. Gad, “High-Order Passive Delay-Based Macromodel for MTLs via Symplectic Integrators,” IEEE Microwave and Wireless Components Letters, vol. 18, no. 4, pp. 227–229, Apr. 2008.
    2008
  23. 16
    E. Gad, “Circuit-Based Analysis of Electromagnetic Field Coupling with Nonuniform Transmission Lines,” IEEE Transactions on Electromagnetic Compatibility, vol. 50, no. 1, pp. 149–165, Feb. 2008.
    2008
  24. 15
    C. Chen, D. Saraswat, R. Achar, E. Gad, M. Nakhla and M. C. E. Yagoub, “A Robust Algorithm for Passive Reduced-Order Macromodeling of MTLs With FD-PUL Parameters Using Integrated Congruence Transform,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 3, pp. 574–578, Mar. 2008.
    2008
  25. 14
    W. Tseng, C. Chen, E. Gad, M. Nakhla and R. Achar, “Passive Order Reduction for RLC Circuits with Delay Elements,” IEEE Transactions on Advanced Packaging, vol. 30, no. 4, pp. 830–840, Nov. 2007.
    2007
  26. 13
    N. Soveiko, E. Gad and M. Nakhla, “A Wavelet-Based Approach for Steady-State Analysis of Nonlinear Circuits with Widely Separated Time Scales,” IEEE Microwave and Wireless Components Letters, vol. 17, no. 6, pp. 451–453, June 2007.
    2007
  27. 12
    C. Chen, E. Gad, M. Nakhla and R. Achar, “Analysis of Frequency-Dependent Interconnects Using Integrated Congruence Transform,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 26, no. 6, pp. 1139–1149, June 2007.
    2007
  28. 11
    C. Chen, E. Gad, M. Nakhla and R. Achar, “Passivity Verification in Delay-Based Macromodels of Multiconductor Electrical Interconnects,” IEEE Transactions on Advanced Packaging, vol. 30, no. 2, pp. 246–256, May 2007.
    2007
  29. 10
    P. Pai, E. Gad, R. Achar, M. Nakhla and R. Khazaka, “A Projection-Based Reduction Approach to Computing Sensitivity of Steady-State Response of Nonlinear Circuits,” INFORMS Journal on Computing, vol. 18, no. 2, pp. 173–185, Spring 2006.
    2006
  30. 9
    T. Ahmed, E. Gad and M. Yagoub, “An Adjoint-Based Approach to Computing Time-Domain Sensitivity of Multiport Systems Described by Reduced-Order Models,” IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 11, pp. 3538–3547, Nov. 2005.
    2005
  31. 8
    E. Gad, C. Chen, M. Nakhla and R. Achar, “Passivity Verification in Delay-Based Macromodels of Electrical Interconnects,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 10, pp. 2173–2187, Oct. 2005.
    2005
  32. 7
    E. Gad and M. Nakhla, “Efficient Model Reduction of Linear Periodically Time-Varying Systems via Compressed Transient System Function,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 6, pp. 1188–1204, June 2005.
    2005
  33. 6
    E. Gad and M. Nakhla, “Simulation and Sensitivity Analysis of Non-uniform Transmission Lines via Integrated Congruence Transform,” IEEE Transactions on Advanced Packaging, vol. 28, no. 1, pp. 32–44, Feb. 2005.
    2005
  34. 5
    E. Gad and M. Nakhla, “An Efficient Algorithm for Sensitivity Analysis of Non-uniform Transmission Lines,” IEEE Transactions on Advanced Packaging, vol. 28, no. 2, pp. 197–208, May 2005.
    2005
  35. 4
    E. Gad and M. Nakhla, “Efficient Simulation of Non-uniform Transmission Lines using Integrated Congruence Transform,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 12, no. 12, pp. 1307–1320, Dec. 2004.
    2004
  36. 3
    E. Gad, R. Khazaka, M. Nakhla and R. Griffith, “A Circuit Reduction Technique for Finding the Steady-State Solution of Nonlinear Circuits,” IEEE Transactions on Microwave Theory and Techniques, vol. 48, no. 12, pp. 2389–2396, Dec. 2000.
    2000Best Paper Award
  37. 2
    A. Dounavis, E. Gad, R. Achar and M. Nakhla, “Passive Model Reduction of Multiport Distributed Interconnects,” IEEE Transactions on Microwave Theory and Techniques, vol. 48, no. 12, pp. 2325–2334, Dec. 2000.
    2000
  38. 1
    E. Gad, A. Atiya, S. Shaheen and A. El-Dessouky, “A New Algorithm for Learning in Piecewise-Linear Neural Networks,” Neural Networks, vol. 13, no. 4–5, pp. 485–505, May/June 2000.
    2000
Book chapters
  1. 2
    B. Nouri, E. Gad, M. Nakhla and R. Achar, “Model Order Reduction in Microelectronics,” in Model Order Reduction, Volume 3: Applications (P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W. Schilders and L. Silveira, eds.), pp. 111–144. Berlin, Boston: De Gruyter, 2020.
    2020
  2. 1
    E. Gad, M. Nakhla and R. Achar, “Model-Order Reduction of High-Speed Interconnects Using Integrated Congruence Transform,” in Model Order Reduction: Theory, Research Aspects and Applications (W. H. A. Schilders, H. A. van der Vorst and J. Rommes, eds.), Mathematics in Industry, vol. 13. Berlin, Heidelberg: Springer, 2008.
    2008
Conference papers
  1. 1
    B. Bandali, E. Gad and M. Nakhla, “Fast and Stable Transient Simulation of Nonlinear Circuits using the Numerical Inversion of the Laplace Transform,” IEEE 25th Workshop on Signal and Power Integrity (SPI), Siegen, Germany, 2021, pp. 1–4.
    2021

No publications match that search.

Two entries need a quick check before publishing: the parallel envelope-following VLSI paper is still listed with early-access placeholders (vol. PP, no. 99), and I corrected the 2000 MTT volume number to 48 — confirm both against your records.

Alumni

  • Greg SomersSoftware Developer, IBM
  • Bardia BandaliSoftware / Hardware Engineer, Lotek
  • Yaoyao LinSoftware Developer

Education

  • 2003PhDCarleton University, Canada
  • 1997M.Eng.Cairo University, Egypt
  • 1991B.Eng.Alexandria University, Egypt

Contact

Emailegad [at] uottawa [dot] ca
OfficeCBY A-511
Telephone613-562-5800, ext. 6440
Fax613-562-5664
MailSchool of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Avenue, Ottawa, Ontario, Canada K1N 6N5