 solutions to the manifold M, is much smaller than the time scale T/E over which the process p(t) is changing. The inequality (D.27) can, therefore, be seen as a kind of quasi-static approximation, expressing a slowly changing upper bound on the magnitude of Ax2(t). D.3 The behavior of 3(T) The second component of Ax(T) = Ax2(T) + Ax3(t) models the deviation from the manifold defined by the constraints implicit to the system of the DAEs (5.34) that model the core system. It is found by left multiplication of (D.3) with V3 (t,p) where V(t,p)C(t,p)= (D.28) (D.29) Hence, the rows of V(t,p) span the left null space of C(t,p). After a little algebra, it is then obtained that Ax3(T) = U3(t,p) (D.30) If we assume that C(t,p) and G(t,p) are continuous in their arguments, and, therefore, also V3 (t,p), and since we assumed the system to be T-periodic (and therefore also VT (t,p) and G(t,p)), all matrices and vectors in the right-hand side of (D.30) are bounded. Hence, SO is Ax3(T). D.4 Conclusions In this appendix, we presented expressions for the two components of the (normalized) deviation Ax(t) = Ax2(T)+AX3(T). The first component is directed along the space spanned by the stable modes of the attracting manifold. The second component models the deviation from the manifold defined by the constraints implicit to the system of the DAEs that model the core system. Both components were shown to remain bounded. Appendix Analysis of a harmonic oscillator This appendix deals with the analysis of the harmonic oscillator topology shown in Fig. E.1. Special interest is given to oscillator's operating-point phase behavior. This results in the expression for the impulse sensitivity function (ISF) corresponding to the source u(T). This ISF was, amongst others, used in the analysis of the injection locking problem treated in section 5.7.2 of chapter 5. Determining the oscillator's averaged dynamics The normalized circuit equations corresponding to the topology shown in Fig. E.1 are easily shown to equal1 (E.1) dyd - x a d d (E.2) IM,