MAX8815A
Production
The MAX8815A DC-DC step-up converter is a high-efficiency, low quiescent current, synchronous step-up converter with True Shutdown™ and inrush-current...
Datasheet
MAX8815A on Analog.com
The datasheet graphs on page 6 INPUT CURRENT vs INPUT VOLTAGE are for two Vouts 3.3V and 5V respectively. We can notice that input current increases when the input voltage is very near to output voltage. This corresponds to a very low duty cycle and we know that for a Boost converter the average input current is equal to
Iin = Iout/(1 - D)
Thus for very low duty cycle the 1 - D term will be very close to 1, so Iin will be approximatively equal to Iout.
