hi,
Fig #3.
D3 diode, is to allow only the positive half cycle of the mains supply [LINE] to pass current thru the LED.
D2 diode, is to ensure that a reverse voltage [>0.7v] cannot be applied to the LED.
D1 diode, conducts on the postive half cycle of the mains supply [LINE], when the EARTH connection is present.
This positive half cycle D1 conduction shorts out the D3 diode and LED, so the LED is NOT lit when the EARTH is present.
When the LINE voltage has a negative half cycle, [the EARTH/NEUTRAL will be positive with respect to the LINE],
then D1 diode blocks any current flow thru diode D3 and the LED.
In the event of a total loss of the EARTH connection, D1 will no longer conduct and the postive half cycle of the
mains voltage [LINE] will be drive current thru diode D3 and the LED.
To increase the apparent brightness of the LED a 16uF 16Vwkg capacitor could be connected in parallel with the LED.
As you have measured only a 2v to 3v differential between the EARTH and NEUTRAL this circuit will be OK.
For higher differential voltages I would add a suitable Zener diode in series with D3.
The circuit is designed to detect the total loss of the EARTH connection and is not designed for detecting EARTH/NEUTRAL connection reversals
The stated specification and value of the C1 capacitor are very important.
Capacitive reactance[ohms] = 1/(2 * pi * f * C)
So for a nominal 20mA half cycle, current thru C1 with a mains suppy of 250Vac at 50Hz, the formula reduces to....
C1= Ima/(V * 2 * pi * f ).............. = 0.02/( 250 * 6.28 * 50) = 0.25uF [ pref value 0.22uF] at 500Vac rating Polypropolyne.
For reference, a capacitor value of 0.47uF would give a nominal half cycle current of 40mA
Important:
this circuit is NOT mains isolated and should be enclosed in a non conductive enclosure which prevents
accidental contact with the circuit/wiring.
If you get a 'Wall wart' psu style plug assembly enclosure you could build the circuit within that enclosure.
Can you say why you are having/expecting problems with EARTH connections and possible EARTH/NEUTRAL reversals???