A control circuit for a power converter has a current source, a sampling circuit, a signal processing circuit, a driving circuit, and a shared pin. The shared pin is used for coupling with a resistor and a switch. The current source, coupled with the shared pin, provides a current through the shared pin to the resistor in a first period. The sampling circuit, coupled with the shared pin, samples signals on the shared pin for generating a first sampling value and a second sampling value. The signal processing circuit, coupled with the sampling circuit, compares the first sampling value and the second sampling value. The driving circuit generates driving signals for conducting the switch. When the difference of the first sampling value and the second sampling value is less than a predetermined value, the signal processing circuit configures the driving circuit to intermittently conduct the switch in a second period.