A power converter reduces output ripple without using an electrolytic primary-side capacitor that can reduce product lifetime. Primary-Side Regulation (PSR) using an auxiliary winding provides a regulated secondary voltage with some low-frequency ripple on a secondary winding of a transformer. A smaller secondary capacitor that is not an electrolytic capacitor filters the output of the secondary side. A bang-bang controller controls the secondary side current to reduce current ripple despite voltage ripple. The bang-bang controller has a series resistor and inductor in series with a load such as an LED. A voltage drop across the series resistor increases when a switch turns on. This increasing voltage drop toggles the switch off once an upper limit voltage is reached. The voltage drop then decreases as inductor current is shunted by a diode, until the voltage drop reaches a lower limit voltage and the switch toggles on again.