  In radio frequency applications, electric circuits generate signals, which
are amplitude modulated and/or frequency modulated. A mathematical modelling
yields typically systems of differential algebraic equations (DAEs). A
multivariate signal model transforms the DAEs into multirate partial
differential algebraic equations (MPDAEs). In the case of frequency modulation,
an additional condition is required to identify an appropriate solution. We
consider a necessary condition for an optimal solution and a phase condition. A
method of lines, which discretises the MPDAEs as well as the additional
condition, generates a larger system of DAEs. We analyse the differential index
of this approximative DAE system, where the original DAEs are assumed to be
semi-explicit systems. The index depends on the inclusion of either
differential variables or algebraic variables in the additional condition. We
present results of numerical simulations for an illustrative example, where the
index is also verified by a numerical method.
