This back-to-basics radio really performs and sounds good too.
What happens if you use 12 volts as the high tension for a homebew valve receiver?
The answer is you lose the need for a mains power supply, eliminate AC hum problems and can prod around inside without getting bitten. Construction is also much quicker.
This video describes a 1 valve regenerative receiver using a 12AX7 mains valve. The filaments are wired in series and the whole lot is run from a 12 volt gel battery.
It tunes about 470 - 1900 kHz, allowing reception of signals on either side of the AM broadcast band. Eventually I'll add more coils for HF coverage.
The set was built in a day based on the refined Thames & Kosmos Radio Ace circuit available at:
http://members.iinet.net.au/~cool386/kits/ace.html I didn't need to change any component values as those given worked first time. An alternative link is http://www.vk6fh.com/vk6fh/12au7regen.htm
But I did (i) add an LM386 audio amplifier (22k plate resistor replaces the transformer primary) to provide speaker reception and (ii) wind the coil on a ferrite rod, complete with a winding for the antenna (about 70 turns with the tap at around 10 turns from ground).
If you don't want the LM386 stage, just wire some 2k impedance headphones instead of the transformer primary (satisfactory reception on local stations) or do like the original and use a power transformer to step down to low impedence phones.
As for valves, I agree that the 12AU7 provided the easiest regeneration. A 12AT7 was less active but could still be made to oscillate across the whole band. A 12AX7 also worked but only oscillated in the top half of the band with the coil tap used.
The performance achieved speaks for itself. But you won't need an external antenna unless planning to receive distant stations. The WIA's Amateur Radio magazine has full constructional details in its May 2012 issue.