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In this paper, a new method is proposed to eliminate electrolytic capacitors in a two-stage ac-dc light-emitting diode (LED) driver. DC-biased sinusoidal or square-wave LED driving-current can help to reduce the power imbalance between ac input and dc output. In doing so, film capacitors can be adopted to improve LED driver's lifetime. The relationship between the peak-to-average ratio of the pulsating current in LEDs and the storage capacitance according to given storage capacitance is derived. Using the proposed "zero-low-level square-wave driving current" scheme, the storage capacitance in the LED driver can be reduced to 52.7% comparing with that in the driver using constant dc driving current. The input power factor is almost unity, which complies with lighting equipment standards such as IEC-1000-3-2 for Class C equipments. The voltage across the storage capacitors is analyzed and verified during the whole pulse width modulation dimming range. For the ease of dimming and implementation, a 50 W LED driver with zero-low-level square-wave driving current is built and the experimental results are presented to verify the proposed methods.