On the singularities in higher order resonant converters

In this correspondence, the singularities in higher order (n ≥ 3) LC resonant converters are examined based on circuit theory. It is shown that the system A-matrix for odd order LC resonant converters (neglecting all the parasitic resistances) is always singular. As a consequence, all the third order LC resonant converters in dc-dc power supply applications can be described and solved via a second order differential equation. A simple closed-form solution can then be obtained.