orst case) of the order N is the number of time- varying feedback loops, K is a measure for the number of tones taken into account (as defined above), T is the average number of terms necessary for modeling the open-loop 4.3 AUTOMATED SYMBOLIC LPTV SYSTEM ANALYSIS HTM elements and R - 1 is the order in up to which the contributions are computed. Note that N and T are mainly functions of the size of the block diagram being analyzed (as determined by the number of nodes of the corresponding signal flow graph). It is through these parameters that the block diagram size (or equivalently, the circuit size) influences the computational complexity. 4.3.6 SymbolicHTM: advantages and limitations The great advantage of the Symbolic HTM algorithm lies in the automated symbolic characterization of LPTV system behavior. HTM-based analysis is made accessible by partial elimination of tedious and error-prone pencil and paper computations. While being a strength, automation also implies a disadvantage. Automated analysis often relies on heuristics and is not necessarily as smart as a human may be. Results can, therefore, become more complicated than needed. SymbolicHTM, for example, relies on the assumption that all terms that are O (MR) are not important while all other terms are. If this assumption fails, it may either result in low-accuracy expressions or in expressions that are too complicated to handle. A further condition for SymbolicHTM to be applicable lies in the accuracy of (4.82) in computing the inverse of a HTM. Al- though it often works fine, this power-series approximation does not apply to all types of systems. For example, SymbolicHTM does not yield good results when applied to PLLs implemented using sampling-type PFDs14 Finally, care must be taken in order to avoid an explosion of the number of terms in the expressions that are generated. Computational complexity considerations in the previous section show that this number of terms grows exponentially with both the circuit size N and the order of the power-seri