A controller IC adjusts the on time and cycle time of current flowing through the primary inductor of a flyback converter to generate a constant output current and constant output voltage. A desired output current limit is achieved even with an inductor whose inductance varies from the stated magnitude. A transconductance current is generated from a voltage across an emitter resistor and is then integrated to generate an integrated-current voltage. An inductor switch is turned on by an oscillator signal and turned off at the earlier of when the integrated-current voltage reaches a charge limit voltage during constant current mode or when the emitter resistor voltage reaches an error voltage during constant voltage mode. Current is output independently of the primary inductance by varying the current limit voltage inversely proportionally to the input voltage and by adjusting the cycle time so that it varies inversely proportionally to the output voltage.