[EricVanWyk]

Instead of a full wave rectifier, I think you could simply place another LED anti-parallel to your first one. That is to say, put it in the same place as LED1, but backwards.

You should check its reverse voltage rating. It is possible that you are exceeding it for the other half of your cycle. Remember, since the resistors are not conducting, they are not dropping voltage. Therefore, you see the full voltage in reverse. Adding the anti-parallel LED would fix this, as it would clamp the reverse voltage seen by LED1 to the forward voltage of LED2 (3.7Volts).

For reference, I've found a 3.7Volt LED with a reverse rating of 5Volts. If you were using this part, it would probably fail in a similar manner to what you are experiencing, as you hit it with 9.2ish volts reverse.

Please post the part number or the data sheet for the LED you are playing with.

Lastly, forgive my intrusion Al, but I'm not convinced on your second doubling of the voltage. I think our "disagreement" stems from semantics, and is highly dependent on what "Chief Pride" actually has in front of him. Since his multimeter says 6.5VRMS, I believe his Resistor/Diode circuit will only see 6.5V*sqrt(2) instantaneous peak voltage, so long as he is connecting at the same points the multimeter is. I do agree that the full range swing is 2x that, but I don't think it will ever "feel" it.

My reasoning goes as follows: If we pretend to ground one of the two outputs of the transformer, the other output will swing from +9.2ish Volts to -9.2ish Volts. The peak to peak is 18.4, but there is no single point in time that has that. However, I have been wrong at least twice in the past, so please correct me.