A control circuit includes: a first switching element having a source, a gate, and a drain; a battery configured to supply a voltage to the gate through a second switching element; a PWM signal generator circuit configured to supply a PWM signal to the gate through a third switching element; and a gate control circuit configured to, under a power-off condition, turn on the second switching element to supply the voltage of the battery to the gate and turns off the third switching element, and configured to under a power-on condition, turn on the third switching element to supply the PWM signal voltage to the gate and turns off the second switching element.