The Ducati 250 has does not have the correct regulator/rectifier fitted. The original probably gave up at some time over the last 50 years of its life and a previous owner fitted what looks like a British bike system that might even be older than the bike itself! The two parts are separate and are shown in the next picture by two green arrows.
The other thing that can be seen from the picture above is the amateur wiring using any old bits of car and household cable with Lucar connectors crimped onto them. That will all need to be changed to look more original. While this old system was fitted I checked the voltages, Battery was 12.83 volts without engine running, I have a feeling that my voltmeter is over reading by about 0.3 volts. With the engine running it went up to 15.4 volts, so it is charging the battery, but even if that is 15.1 after deducting the assumed voltmeter error, it is too high for my liking. with the puny 35 watt headlight on it dropped to 13.7 volts, indicating that the 40 watt alternator is getting near its limit.
I bought this regulator/rectifier from ebay for the grand sum of £17 from China. It claims to be a Mosfet RR, but I am not so sure for that sort of money. Mosfet is a new type of RR that is bang up to date, it generates less heat and is supposed to be more efficient. Read about it on Google if you are are an electronics buff. The fact that it has three alternator inputs (I have marked them in yellow) say that it can be used on a more modern 3 phase generator, but in this single phase application it is fine to use just two inputs as that is all that comes from the generator. The other two connectors are for battery positive and earth.
The voltages are a bit different, the battery was still around 12.8 volts, but the running was now at a much more controlled 14.4 to 14.5 volts. Switching the light on still dragged that down to 13.7, so the battery is still charging.
On an old bike with no electronics the original 15+ volts would probably do little harm. It might shorten the life of the battery a bit, but you may never notice. I intend to fit an electronic ignition system made by Elektronik Sachse in Germany, but having spoken to the company it seems that there have been a couple of failures of their electronic boxes (I understand that the rate is miniscule, about 2 to 3%), and that may be due to the users bikes charging system producing an over voltage. There website is CLICK HERE.
This regulator will also fit my wife’s Ducati ST2, a bike that is known for weak electrics and a bike that is also fitted as standard with a single phase generator.