  In this paper a new adaptive algorithm for multi-rate circuit simulation
encountered in the design of RF circuits based on spline wavelets is presented.
The circuit ordinary differential equations are first rewritten by a system of
(multi-rate) partial differential equations (MPDEs) in order to decouple the
different time scales. Second, a semi-discretization by Rothe's method of the
MPDEs results in a system of differential algebraic equations (DAEs) with
periodic boundary conditions. These boundary value problems are solved by a
Galerkin discretization using spline functions. An adaptive spline grid is
generated, using spline wavelets for non-uniform grids. Moreover the
instantaneous frequency is chosen adaptively to guarantee a smooth envelope
resulting in large time steps and therefore high run time efficiency. Numerical
tests on circuits exhibiting multi-rate behavior including mixers and PLL
conclude the paper.
