In steady state operation the average capacitor current in a buck converter is zero, which means that the rippling part of the inductor current charges and discharges the capacitor, while the "DC" part of the inductor current is the load current. I am not sure how this "DC" component is equal to average inductor current.
How do I find the mathematical relationship between load current of a buck converter and average inductor current? How do I relate load current (which in itself does not depend on inductor/inductor current) to the average value of the inductor current?
I get that steady-state operation implies zero capacitor current (average). KCL at the output would yield Io = IL_AVG. But by evaluating the average value of the inductor current waveform, I couldn't find any way to equate the output current (Vo/Ro) to Average Inductor current (Ipeak/2). The output current does not depend on either the value of inductor or inductor current ripple. How then would you relate the average inductor current to load current?