Abstract
Radio frequency (RF) applications exhibit oscillating signals, where the amplitude and the frequency change slowly in time. Numerical simulations can be performed by a multidimensional model involving systems of warped multirate partial differential algebraic equations (MPDAEs). Consequently, a frequency modulated signal demands a representation via a function in two variables as well as a univariate frequency function. The efficiency of this approach depends essentially on the determination of appropriate frequencies. However, the multidimensional representation is not specified uniquely by the corresponding RF signal. We prove that choices from a continuum of functions are feasible, which are interconnected by a specific transformation. Existence theorems for solutions of the MPDAE system demonstrate this degree of freedom. Furthermore, we perform numerical simulations to verify the transformation properties, where a voltage controlled oscillator is used.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brachtendorf, H. G.; Welsch, G.; Laur, R.; Bunse-Gerstner, A.: Numerical steady state analysis of electronic circuits driven by multi-tone signals. Electrical Engineering, 79, 103–112 (1996)
Chua, L. O.; Ushida, A.: Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies. IEEE CAS, 28(10), 953–971 (1981)
Günther, M.; Feldmann, U.: CAD based electric circuit modeling in industry I: mathematical structure and index of network equations. Surv. Math. Ind., 8, 97–129 (1999)
Ho, C.W.; Ruehli, A.E.; Brennan, P.A.: The modified nodal approach to network analysis. IEEE Trans. CAS, 22, 505–509 (1975)
Houben, S.H.M.J.: Simulating multi-tone free-running oscillators with optimal sweep following. In: Schilders, W.H.A., ter Maten, E.J.W., Houben, S.H.M.J. (eds.): Scientific Computing in Electrical Engineering, Mathematics in Industry, 4, 240–247, Springer, Berlin (2004)
Kampowsky, W.; Rentrop, P.; Schmitt, W.: Classification and numerical simulation of electric circuits. Surv. Math. Ind., 2, 23–65 (1992)
Narayan, O.; Roychowdhury, J.: Analyzing oscillators using multitime PDEs. IEEE Trans. CAS I, 50(7), 894–903 (2003)
Pulch, R.: Finite difference methods for multi time scale differential algebraic equations. Z. Angew. Math. Mech., 83(9), 571–583 (2003)
Pulch, R.: Multi time scale differential equations for simulating frequency modulated signals. Appl. Numer. Math., 53(2–4), 421–436 (2005)
Roychowdhury, J.: Analysing circuits with widely-separated time scales using numerical PDE methods. IEEE Trans. CAS I, 48(5), 578–594 (2001)
Stoer, J.; Bulirsch, R.: Introduction to Numerical Analysis. (3rd ed.) Springer, New York (2002)
Ushida, A.; Chua, L. O.: Frequency-domain analysis of nonlinear circuits driven by multi-tone signals. IEEE CAS, 31(9), 766–779 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pulch, R. (2008). Transformation Qualities of Warped Multirate Partial Differential Algebraic Equations. In: Breitner, M.H., Denk, G., Rentrop, P. (eds) From Nano to Space. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74238-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-74238-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74237-1
Online ISBN: 978-3-540-74238-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)