Transformation qualities of warped multirate partial differential algebraic equations

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. © 2008 Springer-Verlag Berlin Heidelberg.