Energiebasierte Normalisierung und Systemdekomposition mit dem Ziel der Sensitivitätsbetrachtung

Requirements of miniaturization of power supplies have been discussed, whereat suitable materials, technologies, components and related topologies have been considered, according to their control issues, within a power range of up to 100 Watts. Design methods were derived thereupon, which analyze related load resonant converters systematically based on normalized, unit-less parameters. The advantage of this methodology is a high grade on comparability between suitable topologies to be chosen, so that a top-down design method is immediately started with a theoretically proved selection of a thereby destined topology. Any further system properties can be handled afterwards in such a topology comparison, as well as a comprehensive system design is possible to retrieve correct time behavior and transfer ratios. This comprehends, under the condition that neglections have been done correctly regarding losses compared to the transferred power, that the tasks of statical or dynamical system comparison (topology comparison), the normalized parametric sensitivity analysis, the estimation of the regulation range, the stability, or the retrieving of statical, state variables in units, as well as transient time functions, can be met. From the system approach that has been worked out, and by the normalization proposed, a normalized energy expression was derived, which results from a simplified system decomposition, leading to system-cell based sensitivity analysis (energy evolution method EEM). Accordingly, the operational reliability will become possible to be estimated at sufficient accuracy against the theoretical predictions, in a meaning of tolerance analysis of components and functional parameters. The comparison of the proposed method (EEM) with the heuristic sensitivity analysis method (EHM) shows the tendency of general agreement between both methods. While the presented work provides also a precise definition and implementation of the switch operator of the EHM by an exact definition derived from the energy integral upon the switch state variable waveform, the improved agreement of the EHM with the EEM is worked out this way. At the same time, the results derived from the EHM as a predictive power transfer function within areas of low parameter sensitivity are to be considered as excellent estimations of the accurate power transfer functions which are partially off less than 10% only. Thus, this work proves that it is possible for „artificially learning“ physical systems, to inject an RMS value observed from the switch operator function depicted by the switch waveform, based on energy, into an extremely simplified equation system, to obtain a nearly precise energy transfer function of the system. This thereby fined heuristic method (EHM) provides new “igniting scientific stuff” for the requirement of research in the field of simplifying heuristic energy equations of complex resonant systems. Should there be a mathematical consideration that mathematical functions as Taylor or Volterra series are derivable, the nearly complete agreement is not explained yet within different cases of topologies. At this point, the improvement of the EHM provided in this work opens the urgent discussion, if not energy transferring systems, based on resonance or adiabatic switching, could not be approached in general by a simplified way. An exact analytical approach of such a theory is still missing, and may be searched in the area of analysis, as well as of stochastical or randomized mathematics.