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

A method to assess the effect of component tolerances on the stability of closed loop switching regulators is given. Use of μ, 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 μ, 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 Δ-M structure. Subsequent determination of μ 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 Δ-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