Sampled-data modeling applied to output impedance reveals missing term in state-space averaging model

The investigation of the stability of larger power systems requires knowledge about output impedances of switch mode power supplies (SMPSs). Methods for the prediction of this quantity of a SMPS comprise state-space averaging and sampled-data modeling. However, results obtained from both methods exhibit large differences. Furthermore, sampled-data modeling itself yields completely different results for different sampling points. Negative as well as positive incremental impedances may occur. Nevertheless, considerations of the steady-state in time domain prove the existence of these strongly different results, as discussed in this paper. In addition to that, it will be shown that only small additional effort is necessary to simulate the converter behavior with exact averaged quantities. This leads directly to an improvement of the state-space average model by means of adding an operating point dependent resistor.