Hi Chris,
No, I'm not about to raise my hands in horror

because I'd hate to discourage anyone from experimenting and learning. OK, it might seem to be an "unconventional" way to achieve the objective, and it might or might not end up being the final solution, but it's the journey that is important.
As you might already know, these charge-pumps can either be used as voltage "doublers", or to provide a voltage of "equal magnitude" but opposite polarity (the latter is the one you have, of course). The classic
MAX232 has a pair of charge pumps to produce plus and minus 10V from the incoming 5V rail so that it can generate reasonable RS-232 signals. They are built into most flash memory chips, and are often used to drive LEDs. Definitely a useful technology.
Things to watch for:
- First, the output voltages are approximate at best. So that's why I used quote marks above. There are losses in the diodes and switches.
- Also, they aren't terribly well regulated. That means the voltage "sags" as the load current is increases.
- And, any "switching" supply will have ripple on the output.
Whether any of these matter simply depend on your application. The TL084 is perhaps not bothered, but the 8038 might be, and as a result it might well be that you would need to provide some sort of regulation after the charge pumps. That's what I did with a 25V generator I made some years back.
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But before getting too involved with the charge pump, it might be worth thinking about the rectification stage.
If you feed 6V AC into a full-wave rectifier that is followed by a smoothing capacitor, you'd expect to get about 8.5V DC. This is because AC is generally quoted and measured in RMS terms (unless otherwise stated), but the rectifier will produce the peak voltage. For a sine wave, the magic number is 1.4 (which is the square-root of 2), so 6 times 1.4 is 8.5.
This is approximate because there are losses in the diodes (0.7V in each, and for a bridge rectifier, two are in series at once). But against that, the stated 6V from the transformer is at
full load - when at less than full load, the voltage rises. Perhaps by 20% for a small frame transformer like the one you're playing with. Easy enough to measure...
It's probably worth spending a few minutes experimenting with rectification strategies (if you wanted, you could try the ideas I've put on my article). From experience, it's a subject that trips people up, and there are one or two tricky concepts in there. When I run the power supply course at work, normally at least one person blows up a capacitor!
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If you wanted to use the charge-pump approach with your transformer, here's one option:
- Connect the two 6V AC windings in series to give 12V AC.
- Rectify and smooth that. You should have approximately 16-17V DC.
- Feed that into a doubling charge pump that makes approximately 30V DC
- Feed that into an inverting charge pump that makes approximately -30V DC
- Feed these two unregulated rails into a pair of voltage regulator ICs (such as the 7815 and 1915) which will make +/- 15V
The regulators will clean up the switching noise, and they will ensure that the generator has a rock-steady pair of 15V rails. It might seem that we are making very high voltages only to "waste" that in the ICs, but remember, these are optimistic voltages - they will be less in practice.
The main drawback with this approach is that you can't use a 555 to make the -30V rail. By the time you've worked out how best to tackle that, you might as well have brought the correct mains transformer! But then, you wouldn't have learnt anything
Another way:
- Take 6V AC from one of the secondary windings, rectify and smooth it to give approx 8V DC
- Feed this into a 555 voltage doubler to get approx 16V
- Feed this into a 7812 to make 12V (you need at least 3V more than the output for the regulator to do its job)
- Make an exact copy of all this, powered from the other 6V AC winding
- Join the two outputs together to make a split supply. This works because the two circuits are totally separate from each other.
This approach has the advantage of working with the 555 timer, so you've basically done the bulk of the work (you just need to reconfigure the diodes and capacitors in the output to make a doubler rather than an inverter). The only thing to check is that the function generator PCB will be happy at +/-12V
There is another, simpler way:
You can make voltage doublers that work on AC. These just require extra diodes and capacitors - no 555s required. Have a look:
http://en.wikipedia.org/wiki/Voltage_doubler- Connect the two 6V AC windings in series to give 12V AC.
- Feed this into a voltage doubler to get approximately 20-30V DC
- Feed that into an inverting charge pump to get approx -20V DC
- Feed these two unregulated rails into a pair of voltage regulator ICs to make +/- 15V
Again, the 555 won't work here, but a simple circuit using transistors could be devised if you want to explore further.
Or:
- Take 6V AC from one of the secondary windings, rectify and smooth it using a voltage doubler to get approx 16V DC
- Feed this into a 7812 to make 12V
- Make an exact copy of all this, powered from the other 6V AC winding
- Join the two outputs together to make a split supply, as before
Of all the options, I think this is probably the one I'd pick...
Of course, there is another, much more complex option:
A pair of switched-mode DC-DC converters could do this equally well. And you won't need the final step of regulation:
- Connect the transformer windings any way you like to give either 6 or 12V AC
- Rectify and smooth this
- Use a "Boost" converter to step this up to 15V DC
- Use a "Buck-Boost" converter to make -15V DC
Now these are quite different in operation to flying capacitor charge pumps - they store energy in an inductor rather than a capacitor. Luckily, the inductor is not critical - especially for low-power operation. There are many different chips out there that will do the necessary switching and regulation - try playing with the applet on this page to get some ideas:
http://www.ti.com/ww/en/simple_switcher/But ultimately, I'd regard all of this as a (valuable) learning experience first and foremost. Generally, a designer would only go to the complexity of a switching converter when some other constraint forces them to - obvious examples being battery operation, or a need for high efficiency. This is especially true for an analogue application, where noise might be an issue.
I hope these notes are of interest. Apologies for where I teach you to suck eggs, and equal apologies for when I've gone over your head (please tell me if I do either).
Oh, and when you've eventually had enough of all this, I did find another suitable PSU in the attic. It's an encapsulated lump that is intended to be soldered to a PCB, but I'm sure it could be clamped or secured with double-sided tape or similar. It takes in 240V and gives +/-15V regulated at 200mA IIRC. It's made by RS. If interested, I'll bring it downstairs, test it, and post all the details. It's probably better than the first one I suggested, and I'm sure I'll never need it.
All the best,
Mark