Multirate partial differential algebraic equations for simulating radio frequency signals

• Published in: European journal of applied mathematics Vol. 18; no. 6; pp. 709 - 743
• Main Authors: PULCH, ROLAND, GÜNTHER, MICHAEL, KNORR, STEPHANIE
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.12.2007
• Subjects: A Survey in Mathematics for Industry; Algebra; Applied mathematics; Mathematics; Radio frequency; Simulation
• ISSN: 0956-7925; 1469-4425
• DOI: 10.1017/S0956792507007188

In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and frequency may change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. We outline the theory of this multivariate approach with respect to the simulation of amplitude as well as frequency modulated signals. Furthermore, a survey of numerical methods for solving the arising problems of MPDAEs is given.