# Synchronous Buck Converter Mathematics

Ive been trying to find a mathematical explanation on how a Synchronous Buck converter maintains continuous operation under ideal steady state conditions. I understand the underlying concept but i want to know how i can explain it mathematically (ideal case). • if you're looking for an ideal case and not concerned about switching losses / behavior then its exactly the same as a regular buck converter except your 1-Duty cycle is now your on time for the lower switch instead of the diode path. every single equation would still apply, again ideally. Oct 7 '20 at 3:59
• Could you please provide this explanation mathematically possibly ? Oct 7 '20 at 4:35
• You can have a look at the answer I gave here. There is nothing mysterious, it is just that the controlled low-side switch keeps conducting while the inductor current is zero (the diode would spontaneously block) and brings the inductor current negative until the high-switch turns back on again. In a no-load situation, the inductor average current is zero and it peaks above and below ground. Oct 7 '20 at 6:13