1. An apparatus for a power converter, the apparatus comprising:a drive signal generator configured to receive an input signal associated with a TRIAC dimmer and output a drive signal to a switch to affect a current that flows through a winding of a power converter;
the input signal includes a first pulse corresponding to a first input period, the first pulse being associated with a first pulse width; and
the first pulse width is larger than a first threshold under one or more conditions;
wherein the drive signal generator is further configured to:
in response to the first pulse width being smaller than a second threshold, even if the first pulse width is still larger than the first threshold, maintain the drive signal at a first logic level without modulation to keep the switch open during at least the first input period.