• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

4100uF/450v *BIG* capacitors... any use?

I used to see them a lot in Delft, but never in Haarlem, 50 km or so north from Delft. Apparently taking nitrous oxide and throwing the little bottle (ampoule, vial?) it came in on the street is a very local habit (as well as a very bad one).
 
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bottles ... that appear at the side of the road?
Here, that would be $1 50ml bottles of FireBall.
https://en.wikipedia.org/wiki/Fireball_Cinnamon_Whisky
https://www.fireballwhisky.com/ {note this site's "Over 18?" question has the "right" answer circled}
https://www.fireballwhisky.com/swag/product-page.fireball-whisky-50ml-bottle.html

For a while we were picking bottles from our ditch almost every day. It even displaced the longtime Maine favorite, Allen's Coffee Brandy. (Ethanol to make you sleep and caffeine so you can't sleep.)

Whippet bottles, being steel, at least bring $20/ton at the scrapper's. The $0.95 (set so it is $1.00 with tax) tiny Fireball bottles are plastic, worthless or worse.
 
Back to school! You forget the 2 x diode dropout voltage AND ripple voltage

It won’t work except in rare cases. The exception confirms the rule.

A 6.3V transformer will even not work OK with some 5V LDO regulators 🙂
It will work perfectly with Schottky diodes and the right capacitor, I have done that, no problems whatsoever, other than needing a big cap.
 
Yeah don’t calculate but “just do something” 😀
BTW calculation also works 😎
1650980615761.png
 
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If the model for your source is accurate. Looks optimistic to me. Just a hundredth of an ohm, and no leakage L? Yeah, right. Let me know where you can buy that transformer, I want a few.
As I mentioned above, I have tried this in real life, more than once. I just modelled it quickly to see the values. I just checked the power transformer I use, Hammond 372JX, 0.027 ohms DC resistance on the 6.3V secondary. Maybe you should buy one 🙂
I just tried simulation using 0.1 ohm and 1000pf. Still works, a bit of ripple appeared, cured by increasing the cap to 16000uF.