Skip to main content
SpringerLink
Log in

Multirate Shooting Method with Frequency Sweep for Circuit Simulation

  • Conference paper
  • First Online:
Scientific Computing in Electrical Engineering

Part of the book series: Mathematics in Industry ((TECMI,volume 28))

  • 674 Accesses

Abstract

We introduce multirate shootings methods to compute the response of radio frequency (RF) circuits with frequency modulated stimuli. The multirate technique is based on reformulating the system of ordinary differential algebraic equations (DAE) by partial differential equations (PDE). The PDE is semi-discretized by Rothe’s method, i.e. by first discretizing the initial value problem. The resulting periodic boundary value problems are then solved by shooting techniques. Second, the instantaneous frequency is an additional unknown and concurrently estimated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We assume that a direct sparse solver is used to solve (11.2) and (11.6), which is reasonable in circuit simulation. For an iterative solver we have only to determine a preconditioner once for the multiple solves, i.e., similar considerations apply.

  2. 2.

    Other multistep method (e.g. trapezoidal rule) can be used, too.

References

  1. Brachtendorf, H.G.: Simulation des eingeschwungenen Verhaltens elektronischer Schaltungen. Shaker, Aachen (1994)

    Google Scholar 

  2. Brachtendorf, H.G., Welsch, G., Laur, R., Bunse-Gerstner, A.: Numerical steady state analysis of electronic circuits driven by multi-tone signals. Electr. Eng. 79(2), 103–112 (1996)

    Article  Google Scholar 

  3. Bittner, K., Brachtendorf, H.G.: Optimal frequency sweep method in multi-rate circuit simulation. COMPEL 33(4), 1189–1197 (2014)

    Article  MathSciNet  Google Scholar 

  4. Bittner, K., Brachtendorf, H.G.: Adaptive multi-rate wavelet method for circuit simulation. Radioengineering 23(1), 300–307 (2014)

    MATH  Google Scholar 

  5. Aprille, T.J., Trick, T.N.: Steady-state analysis of nonlinear circuits with periodic inputs. Proc. IEEE 60(1), 108–114 (1972)

    Article  MathSciNet  Google Scholar 

  6. Strohband, P.H., Laur, R., Engl, W.: TNPT - an efficient method to simulate forced RF networks in time domain. IEEE J. Solid-State circuits 12(3), 243–246 (1977)

    Article  Google Scholar 

  7. Skelboe, S.: Computation of the periodic steady-state response of nonlinear networks by extrapolation methods. IEEE Trans. Circuits Syst. CAS-27(3), 161–175 (1980)

    Article  MathSciNet  Google Scholar 

  8. Kakizaki, M., Sugawara, T.: A modified Newton method for the steady-state analysis. IEEE Trans. Comput. Aided Des. 4(4), 662–667 (1985)

    Article  Google Scholar 

  9. Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, 2nd edn. Springer, New York (1992)

    MATH  Google Scholar 

  10. Telichevesky, R., Kundert, K.S., White, J.K.: Efficient steady-state analysis based on matrix-free Krylov-subspace methods. In: Proceedings of the 32nd Design Automation Conference, DAC-95, pp. 480–484. ACM, New York (1995)

    Google Scholar 

  11. Baiz, A.: Effiziente Lösung periodischer differential-algebraischer Gleichungen in der Schaltungssimulation. Ph.D. thesis, TU Darmstadt (2003). Shaker Verlag, Aachen

    Google Scholar 

  12. Brachtendorf, H., Bittner, K.: Grid size adapted multistep methods for high Q oscillators. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 32(11), 1682–1693 (2013)

    Article  Google Scholar 

  13. Brachtendorf, H.G., Laur, R.: On consistent initial conditions for circuit’s DAEs with higher index. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(5), 606–612 (2001)

    Article  MathSciNet  Google Scholar 

  14. Saad, Y., Schultz, M.: GMRES a generalized minimal residual algorithm for solving nonsymmetric linear system. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)

    Article  MathSciNet  Google Scholar 

  15. Pulch, R.: Initial-boundary value problems of warped MPDAEs including minimisation criteria. Math. Comput. Simul. 79, 117–132 (2008)

    Article  MathSciNet  Google Scholar 

  16. Pulch, R.: Variational methods for solving warped multirate partial differential algebraic equations. SIAM J. Sci. Comput. 31(2), 1016–1034 (2008)

    Article  MathSciNet  Google Scholar 

  17. Houben, S.: Simulating multi-tone free-running oscillators with optimal sweep following. In: Schilders, W., ter Maten, E., Houben, S. (eds.): Scientific Computing in Electrical Engineering 2002. Mathematics in Industry, pp. 240–247. Springer, Berlin (2004)

    Google Scholar 

  18. Kugelmann, B., Pulch, R.: Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations. Appl. Numer. Math. 97, 69–87 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work has been partly supported by the fp7 project nanoCOPS under grant 619166 and the EFRE project Connected Vehicles under grant IWB2020.

Author information

Authors and Affiliations

  1. University of Applied Sciences of Upper Austria, Hagenberg, Austria

    Kai Bittner & Hans Georg Brachtendorf

Authors
  1. Kai Bittner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans Georg Brachtendorf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kai Bittner .

Editor information

Editors and Affiliations

  1. Institute of Computational Mathematics (NuMa), Johannes Kepler University (JKU), Linz, Austria

    Ulrich Langer

  2. Institute for Electric Drives and Power Electronics, Johannes Kepler University (JKU), Linz, Austria

    Wolfgang Amrhein

  3. Institute of Computational Mathematics (NuMa), Johannes Kepler University (JKU), Linz, Austria

    Walter Zulehner

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bittner, K., Brachtendorf, H.G. (2018). Multirate Shooting Method with Frequency Sweep for Circuit Simulation. In: Langer, U., Amrhein, W., Zulehner, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-75538-0_11

Download citation

Publish with us

Policies and ethics

Search

Navigation