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    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

12AX7 preamp on 375V

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Given the voltage rating of the input cap, it's unlikely that the transformer is 300V. It's probably closer to 240V. The PS could be redesigned for a 375V transformer, but you'll have to spend quite a bit more for up-rated caps and the power resistors necessary to drop the voltage; the output from a 375V transformer after rectification and the first filter cap is going to be something like 520V. That means stacking 350V caps, putting equalizing resistors across them, and putting in higher value dropping resistors (which will need to be 5W or more units).

If I were building this and didn't know how to design power supplies, I'd email the original designer, ask what transformer he used, and bite the bullet. A 240V transformer capable of supplying that circuit is not expensive, under $20. It will cost you more for all the extra caps and resistors.
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You could change the power supply to use a choke input filter. If you use a tube rectifier like 5AR4 for example, your 375 V trafo will give something like 325 V on the output of the supply. You could drop it to 300 V with an RC filter.

Now, a capacitor input filter -- especially one with silicon rectifiers -- will yield more like 490~500 V. That's getting up there where capacitors become hard to source. 450 V caps are common and there is limited selection of 500 V caps, but to use your trafo I wouldn't go with less than 550~600V rated caps unless you're into exploding caps.

Unless there's a primary tap that you can use to get the right secondary voltage, a different option would be to remove some turns from the secondary of your transformer.

By far the easiest would be to get a transformer that provides the desired output voltage. Something like the Antek 1T250 would work just fine.

Even with a choke input supply (and that's tough since this circuit only draws ~4mA), you need the higher-rated caps in case the rectifier warms faster than the 12AX7s (likely) or in the event that a tube or other component fails and the current draw drops.

In any event, a new transformer is the path of least resistance.
Here's the full project:

I am going to connect the preamp to a tube power amp that I am modding:

An externally hosted image should be here but it was not working when we last tested it.

The pin #6 of the first tube (12AX7) is receiving 240V, right?
Can I use those 240V to feed my preamp, instead of installing a separate power supply? If so, is any moddification to the preamp necessary?

By the way, in case you missed it, the preamp diagram is:
Guitar Preamplifier Schematic - All Tube - KBapps.com

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