Need advice on Power supply

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I posted this question in solid state amplifiers, here is a duplicate, just in case it was posted to wrong forum.

I have a small phono stage, that is a bit noisy.
I tried it direct with two 9V batteries, and it got better alot.
I am intending to power it up with five or six Li-Po rechargeable mobile phone batteries built into the the same enclosure.
The device has 24V DC wall charger type feeding into it, which goes into some smoothing and an LM317 regulator down to 20V.
The batteries (6 of them ) give (each) 4.1V on full charge to 3.7V nominal.

here is the question:
should I keep the LM317 in circuit to get my steady 20V or should I not ?

- Does the LM317 introduce any noise of its own?
- Are there any advantages keeping the LM317 in circuit (apart from steady 20V)?

Just a to avoid confusion:
- I can handle, charge and use the batteries safely.
- I charge the batteries first, then use the device off the batteries with no charger circuit connected.
 
If you leave the LM317 in the circuit, you need at least 22 Volt at the end of battery life. You will need >= 7 Li-Po cells.

Do you have a circuit diagram of your phono stage?

Greetings,
Udo
Clever of you to think that way! actually LM317 needs around 3V min. to give its best, since the batteries give 6X3.7=22.2 nominally ( down to their last 15% power), I was gonna adjust the LM317 for 19V output ( at full charge the voltage is 4.1V/cell). well spotted!
the majority of the noise is from the MC pre-pre.
to my eyes, this section is very sensitive to the quality of supply line.
 

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