I have been following the math in Application Report SLVA458B in attempts to better understand buck regulators and I've met an impasse. In at least two places so far, the report has seemingly pulled numbers from thin air for use in the equations it details.
- Equation 9 calculates the output inductor's RMS current in terms of the duty cycle of the regulator's switch (among other things). Up to this point, the only duty-cycle related values that have been calculated are the maximum and minimum duty cycles, but using either of these values in equation 9 yields an inductor RMS current other than the 4.01A stated by the document. The only way I have found to make sense of the 4.01A figure is to use an average of Dmax and Dmin for D, and even then my calculation yields 4.01591997859092, rounding off to 4.02A. In my mind, the power supply should be designed to withstand the worst-case scenarios that it might be used in. By that logic, shouldn't we be using a maximum or a minimum duty cycle instead of some middling value?
- Equation 13 calculates the power dissipation that may occur in the regulator IC. This equation calls upon the duty cycle once again, bringing my first question back into the spotlight. It also calls upon high-side switch and low-side switch on resistance, which the TPS54620 lists in various terms not directly applicable to our use-case. The Application Report delivers a final value of 0.6613 with no hint as to the numbers used for duty cycle, Rhs, Rls, or the origins / reasoning behind these numbers.
Where do the values used for equations 9 and 13 come from, and why does equation 9 not use the calculated maximum/minimum duty cycle value?
