Methods and circuits related to power regulator start-up are disclosed. In one embodiment, a start-up circuit can include: (i) a delay circuit having a resistor and a capacitor, where the capacitor is coupled between ground and a common node; and (ii) a control chip that receives a reference voltage, and includes an input pin coupled to an input source, an output pin supplying power for a device, and a multiplexed pin coupled to the resistor at the common node to receive an enable signal. The start-up circuit outputs an electrical signal at the output pin based on a comparison of a voltage at the multiplexed pin against the reference voltage, and after a delay time determined by the capacitor and the reference voltage. The voltage at the multiplexed pin can increase continuously with a rising slope determined by input current flowing through the multiplexed pin during a start-up process.