The circuit is a boost step-up regulator based around an LM2577-ADJ voltage regulator chip and a few other discrete components. Resistors R1 and R2 set the regulated output voltage. A switch inside the voltage regulator closes between pins 4 and 3, causing current to flow through the inductor to ground. When the switch is released a few microseconds later, a back-EMF 'kick' is produced by the inductor, resulting in a positive pulse with respect to the input voltage. This pulse charges the output capacitor via the schottky diode, which tends towards an equilibrium voltage.
The switch continues to oscillate, the diode preventing the switch from shorting the output capacitor during the 'on' phase. The output voltage is monitored via the voltage divider R1/R2, causing the duty cycle of the switch oscillator to be continuously regulated in order to maintain a constant output voltage under varying loads.
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