# Time function for an equivalent circuit

In the IEEE magazine 6. NO. 3. JULY 1991 A Novel Soft-Switching Full-Bridge DC/DC Converter: Analysis, Design Considerations, and Experimental Results at 1.5 kW, 1OOkHz the following converter has the active state when any of the pair of transistors S1-S4 and S2-S3 are on.

C1 and C2 represents the parasitic capacitance ( Snubber, Trafo, etc ).

The converter has the following equivalent circuit for the passive state, the state in which no power is transferred through the Transformer.

simulate this circuit – Schematic created using CircuitLab

All the energy needed to charge the capacitance must be accounted for and the the author came up with the following time function for voltage across C1. What was his approach to it?

\begin{aligned} V_{C1}(t) =& V'_O \frac{L_m}{L_m+L'_O}(1-\cos{\omega t}) \\ -& (I_m+I'_P)\sqrt{\frac{L_1+L_C+L_m||L'_O}{C_1}}\sin{\omega t} \\ +& V_{in}\cos{\omega t} \end{aligned}

EDIT: Franc enlightened me! Thank you!

• Who was the author? What was the paper? Commented Jan 7 at 20:59
• To make it a better question, please edit it and tell us which parts of the function are unclear. The function is a sum of three terms, so, hopefully, you understand at least some of them, or at least some of the factors (things on either side of multiplication signs). Commented Jan 8 at 4:01