LEDs driven by AC without transformers or rectifiers

We explore the driving of LEDs by untransformed AC. An extreme case is driving 1.9 V threshold (red) LEDs with UK mains, peak voltage 325 V. Commonly, driving is by transformed, rectified (DC) supply with a series resistor (where a significant fraction of the power is wasted) to limit current in the LED. With AC, one can instead reactively limit to a maximum current safe for an LED by employing a series capacitive impedance. Cheaper and simpler supplies can thus be employed in some cases. We analyse such non-linear circuits, and also explore questions of duty cycle and power experimentally.