I would like know which is the maximum duty cycle of DC/DC inside the battery charger qb24780S.
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There is not a set design value for the maximum duty cycle. The converter's duty cycle can be affected by several factors, such as the input voltage, output voltage, switching frequency, and BTST refresh pulses. From a practical application perspective, the duty cycle is limited by the VCC series diode and the VCC_SRN sleep comparator, which requires a minimum voltage difference between the input voltage and the output voltage.
As a rule of thumb, we typically suggest that the minimum adapter voltage should be at least 1V higher than the battery's maximum charge voltage. This takes into account the VCC_SRN sleep comparator and the voltage drop between the adapter and VCC (in particular, the drop across the VCC diode), while also providing some extra margin just in case.
For more discussion of this topic, you may refer to the following E2E threads: