LEDs on 120v

Here is a very clever CONSTANT-CURRENT voltage-doubling design.
It produces up to 300v on a 120v supply and the current is 30mA. (see below for the reason why the current is 30mA for about 40 LEDs)

The amazing thing is, you can put any number of LEDs on the output, up to 80 white LEDs. When 80 LEDs are added, the current will reduce to only a few milliamps.

How does the circuit work?
We will explain how the circuit works in 3 steps. 

Step 1: The 1u charges to the peak voltage of 150v when the active line is 150v higher than the neutral: '

Step 2: When the active line is 150v LOWER than the neutral, the second capacitor charges as shown in the following diagram:

Step 3: The LEDs are connected to these capacitors and the resulting voltage is about 300v. 
The characteristic voltage of about 3.6v for a white LED will reduce the voltage and that's why the 300v is only a theoretical maximum.

On each half-cycle, the energy from a 1u is fed to the string of LEDs and it will deliver an average of about 70mA when only 1 LED is in the chain. 

This makes it a FULL WAVE capacitor-fed supply and because it is a capacitor-fed supply, it is a constant-current supply. The current will gradually decrease as the number of LEDs increase because the current though the capacitor depends on the voltage on each side of the capacitor. As the number of LEDs increase, the voltage on the LED-side of the capacitor increases, reducing the actual voltage across the capacitor. 

The current will decrease by about 1mA for each added LED.  

HOW TO VIEW THE "MAINS"

The mains is changing direction 50 or 60 times per second and this is called AC (Alternating Current). Instead of seeing the mains as "changing direction," it is more convenient to consider the Neutral as always at EARTH POTENTIAL and the Active is 150v higher than "earth" then 150v lower than earth. 

Now you can understand the diagrams above.