Authors V.N. Biryukov, A.M. Pilipenko
Month, Year 11, 2014 @en
Index UDC 621.373+519.622
Abstract The simulation features of harmonic and relaxation oscillators are considered when using the modern software packages for electronic circuits design. The advantages and disadvantages of the numerical methods for solving differential equations of stiff and oscillatory circuits are shown. Different types of generators (ideal oscillator, oscillator close to the harmonic and relaxation oscillator) were chosen as a test circuits. The choice of these devices for test is due to the fact that the modeling of self-excited oscillators represents the greatest difficulties for computer-aided circuit design. To estimate the accuracy of numerical methods the basic parameters of the simulated process (amplitude and period of the oscillations) error analysis was carried out. This approach, firstly satisfies the practical requirements, and secondly, allows estimating the simulation accuracy not only at the end of the observation interval, and over its entire length without any significant restrictions on the length of the interval. Properties presented in the paper are associated with periodic error of the solution in the analysis of harmonic oscillators. The disadvantage of numerical methods for the analysis of strongly nonlinear circuits, generating relaxation oscillations, is the appearance of large random errors.

Download PDF

Keywords Time-domain simulation; ordinary differential equations; oscillatory circuits; relaxation oscillator; error analysis.
References 1. Glebov A.L., Gourary M.M., Zharov M.M., Egorov Yu.B., Rusakov S.G., Stempkovsky. A.L., Ulyanov S.L., ed. By A.L. Stempkovsky. Aktual'nye problemy modelirovaniia v sistemakh avtomatizatsii skhemotekhnicheskogo proektirovaniia [Advanced circuit simulation methods in electronic design automation]. Moscow: Nauka, 2003, 430 p.
2. Biryukov V.N., Pilipenko A.M. An Approach to Estimate the Error of Oscillator Time-Domain Analysis, Proceedings of IEEE East-West Design and Test Symposium (EWDTS'2013). 2013, pp. 223-226.
3. Kalitkin N.N. Chislennye metody resheniia zhestkikh sistem [Numerical methods of solution of stiff systems], Matematicheskoe modelirovanie [Mathematical Models and Computer Simulations], 1995, Vol. 7, No. 5, pp. 8-11.
4. Biryukov V.N., Primenko K.L. K ocenke lokal'noj pogreshnosti raznostnyh shem [Estimation of the local error of difference schemes], Materialy Mezhdunarodnoy nauchnoy konferencii
«Informacionnoe obshhestvo: idei, tehnologii, sistemy» [Proceedings of International conference «The informational society: ideas, production engineering, systems»], Part 3, Taganrog: TTI YuFU, 2010, pp. 4-8.
5. Petzold L.R., Jay L.O., Yen J. Numerical solution of highly oscillatory ordinary differential equations, Acta Numerica. 1997, pp. 437-483.
6. Norenkov I.P., Evstifeev Yu.A., Manichev V.B. Adaptivnyi metod uskorennogo analiza mnogoperiodnykh elektronnykh skhem [Adaptive method for fast analysis of multiperiod electronic circuits], Izvestiya Vysshikh Uchebnykh Zavedenii Radioelektronika [Radioelectronics
and Communications Systems], 1987, Vol. 0, No. 6, pp. 47-51.
7. Zhuk D.M., Manichev V.B., Saharov M.K. SADEL – biblioteka «sverkhtochnykh» reshatelei dlia programmnogo kompleksa PA10 (SADEL-PA10) [SADEL – extra precision solvers library for program suite PA10 (SADEL-PA10)]. Vserossiiskaia nauchno-tekhnicheskaia
konferentsiia «Problemy razrabotki perspektivnykh mikro i nanoelektronnykh sistem» (MES – 2012): sbornik trudov [Problems of Perspective Micro- and Nanoelectronic Systems Development (MES – 2012). Proceedings]. Moscow, IPPM RAS, 2012, pp. 147-152.
8. Denisenko V.V. Tochnost' i dostovernost' modelirovaniya MOP-tranzistorov SBIS [The accuracy and validity of the simulation of VLSI MOS transistors], Mikroelektronika [Russian Microelectronics]. 2009, Vol. 38, No 4, pp. 302-308.
9. Biryukov V.N., Pilipenko A.M., Kovtun D.G. Otsenka tochnosti chislennogo analiza generatora garmonicheskikh kolebanii vo vremennoi oblasti [Estimation of the Numerical Methods' Accuracy of Oscillating Differential Equations Analysis in Time-Domain], Radiotekhnika [Radioengineering], 2011, No. 9, pp. 104-107.
10. Biryukov V.N., Gatko L.E. Tochnoe statsionarnoe reshenie uravneniia avtogeneratora [Exact stationary solution of the oscillator nonlinear differential equation], Nelineinyi mir [Nonlinear World], 2012, Vol. 10, No. 9, pp. 613-616.
11. Pilipenko A.M., Biryukov V.N. Issledovanie effektivnosti sovremennykh chislennykh metodov pri analize avtokolebatel'nykh tsepei [Research of efficiency of the modern numerical methods
for the analysis of self-oscillatory circuits], Zhurnal radioelektroniki [Journal of Radio Electronics], 2013, No. 8. Available at: (accessed 28 October 2014).
12. Zhuk D.M., Manichev V.B., Ilnitskij A.O. Metody i algoritmy resheniia differentsial'noalgebraicheskikh uravnenii dlia modelirovaniia dinamiki tekhnicheskikh sistem i ob"ektov
[Methods and algorithms of the decision of the differential-algebraic equations for modelling dynamics of technical systems and objects], Vserossiiskaia nauchno-tekhnicheskaia konferentsiia «Problemy razrabotki perspektivnykh mikro- i nanoelektronnykh sistem» (MES-2008): sbornik trudov [Problems of Perspective Micro- and Nanoelectronic Systems Development (MES-2008). Proceedings]. Moscow, IPPM RAS, 2008, pp. 108-113.
13. Pilipenko A.M., Biryukov V.N. Otsenka tochnosti chislennogo analiza relaksatsionnogo generatora [Accuracy estimation of the numerical methods of the analysis of the relaxation oscillator], Zhurnal radioelektroniki [Journal of Radio Electronics]. 2013, No. 11. Available at: (accessed 28 October 2014).
14. Hairer E., Wanner G. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer-Verlag, Heidelberg, 2010, 614 p.
15. Maffezzoni P. A Versatile Time-Domain Approach to Simulate Oscillators in RF Circuits, IEEE Transactions on Circuits and Systems, 2009, Vol. 56, No. 3, pp. 594-603.
16. Maffezzoni P., Codecasa L., D’Amore D. Time-domain simulation of nonlinear circuits through implicit Runge-Kutta methods, IEEE Transactions on Circuits and Systems, 2007,
Vol. 54, No. 2, pp. 391-400.

Comments are closed.