No and, sort-of-yes. (what? you were expecting a simple answer?)
The numbers you state give an estimated nearly 13v RMS output at no load, which is a bit too low for a "simple" directly-connected charger, and worse still for a series-pass type regulated charger. So in that case, no.
The yes bit comes from the fact that if you run a switchmode regulated system, you can step up, and in that case, the transformer *is* good enough. However, there is nothing off the shelf that does this, so it'll very much need to be an entirely custom job. Probably more worthwhile as a learning electronics project, rather than your first preference, a battery charger.
Are you in a hurry? Have a look around in your shed and find a 6V or so light bulb. Connect it in series to the battery and you got yourself a sort of constant current charger. Never short out them terminals though :)
I didn't mean you can't have both. My intention was to mean there are ramifications if you choose to use that particular transformer.
And that's where you're not quite making sense.
On one hand you're happy to turn this into a project, (which means complexity, time and money), on the other hand, you seem to insist on using that particular transformer, which would mean you save money on a transformer, but will make your life harder: I can suggest an SLA charger IC, but while they are usually configured in a buck configuration (in their appnotes), you could modify at least some of them for boost too. However, since your transformer will be either higher AND lower than what the battery needs depending on charge point and load, a full transformer will probably need to be used. This is technically doable, but no-one ever would do this because a suitably sourced power supply would mean a simple (and cheaper) buck configuration can be used.
At this point, if you need to ask for "a suitable step-up IC", then this project is either beyond your technical ability, or, near or within your technical ability but you're just a glutton for punishment.
What you're asking is available off the shelf right now at many shops, and that would be your cheapest, fastest, and least effort option.
Or, buy a suitable transformer as a new base. Heck, you might be even able to use a switcher that'll be lighter too. And with the way copper prices are going, maybe cheaper.
Unless you're a glutton for punishment, in which case, I'm unable to help you. :-)
Can you measure the DC resistance of the secondary (the 12 v side) and also the AC voltage output of transformer without anything attached (i.e. bridge rectifer and cap) ?
No. Only useful if the battery is very flat to put some charge into it or you can find a Dc-Dc battery charger that will use it.
Vin - voltage loss against internal battery resistance = final voltage on battery. Car batteries typically charge to ~13.5 volts, but sit around 12.? volts.
if using the transformer in the other thread you should use the 15 volt taps and change r4 to .1 ohm 5 watt. When adjusting the output voltage fit a small cap across the output (100uf or more). Also add a thermostat to the heat sink if you intend to allow charging of very flat batteries.
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