Power management chip and operating method thereof

A power management chip includes a gate driver configured to output a first gate signal driving a first power switch and a second gate signal driving the second power switch, a multiplexer configured to receive an error detect signal from a first error amplifier and a first gate signal from the gate driver, and drive the first power switch with either of the error detect signal or the first gate signal in response to a mode select signal; an inductor detection logic configured to receive the inductor detect signal, output a comparison detect signal and a pulse signal for detecting an external inductor, and output the mode select signal corresponding to a result of the detecting, and a comparator comparing an internal output voltage of an output node and an output voltage of the feedback node in response to the comparison detect signal.