Yeah it's 25v 470uF....Nichi or Panasonic, that's pretty much all I buy unless I need some weird value or package.
OK...I did some "what iffing" with PSU Designer (a great simulator IMO...at a great price...FREE!).
I attached the latest and greatest simulation. Not trying to over think this, but....using a 14VAC secondary, 470uF filter and 100 mA load.....
1. You can see the ripple waveform that will appear at the input of the LM340-12. It peaks at 18V and droops to around 16.5V. The regulator data sheet says dropout voltage is 2 Volts TYPICAL (which would be 14V) , so we have approx. 2.5V margin. The 18V peak is safely within the 25V rating of your filter cap.
2. I looked through the Triad and Hammond Mfg. catalogs to see what were standard secondary voltages in smallish current ratings and there were a number of options. I stuck with those brands rather that trusting potential fire hazards made by MyChowHung <g> as sold on Epay or Crapazon.
Triad and Hammond are reputable and available from multiple USA distributors.
3. Wildcards in the sim. The actual load current. Hopefully 100mA is good. I did a wild guess of the resistance of the xfmr secondary at 0.5 Ohms. That spec is never found in the spec sheets and I don't have anything similar lying around to do an actual measurement. Maybe someone on the forum has something similar to take an actual resistance reading?
4. AC mains voltage and Triad/Hammond primary specs. Interestingly, both companies use 115VAC, and if the spec sheet is accurate will result in a slightly higher secondary voltage.....a good thing in this situation
5. Allowance for low/high mains voltages from the power company. A big sag will cause the LM340 to drop out of regulation and a high will cause the voltage across the filter cap to exceed the 25V rating.
Probably other Partridges in this Pear Tree, but I'll stop now!
Next item on the agenda is the physical size and mounting of the replacement.
I attached sims with a 14VAC and 15V secondary.
Triad and Hammond xfmr links:
https://catalog.triadmagnetics.com/category/power-transformers/
https://www.hammfg.com/electronics/transformers/power
Bri