Worst case stability analysis of switching regulators using the structured singular value

Abstract

A method to assess the effect of component tolerances on the stability of closed loop switching regulators is given. Use of /spl mu/, the structured singular value, is made which obviates the need for time intensive Monte-Carlo simulation runs and also guarantees the assessment of the worst case condition of the system. Furthermore, through the use of newly developed software routines for /spl mu/, the effect of up to a hundred uncertainties may be taken into account. The analysis procedure entails isolating component value uncertainties from the nominal system and arranging into a standard /spl Delta/-M structure. Subsequent determination of /spl mu/ for this structure along with the small-gain theorem enables a robustness assessment to be made for the system under study. Two procedures are given which enable reduction of a switching regulator system to /spl Delta/-M form. The first considers uncertainties to exist only in inductor and capacitor values. The other extends the formulation to encompass resistance uncertainties as well. An example is given of a regulator design for which an assessment is made of the allowed component tolerances which guarantees a lower limit of the phase margin.