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It looks like it could work. However, you'll need an output transformer that can handle all the power you intend to use. That manes you'll need a transformer that can handle the low frequency of 50Hz and 1200 watts or more. That's going to be a hefty transformer. And the turns ratio has to be such that you can get the required output peak (or the mid voltage if you want that instead) from 12v or a little less like 11v .
The more modern way of doing this is to create a DC to DC converter that converts 12vdc to 170vdc (if you want the peak, or 12v to 145v if you want the mid voltage). That 170vdc is then chopped up into 50Hz and that gives you the required AC output.
The reason this works better is because a smaller transformer can be used to convert 12v to 170v because it operates at a higher frequency and all that is left to do is chop it up which doesnt take a transformer to do, just an H bridge.
It seems like handling the power twice like this is a bad idea, but it keeps the size and cost way down and modern MOSFETs are pretty good.
The designer of that awful circuit forgot to read the datasheet of the CD4047:
1) The timing resistor value is much too low at 100 ohms. Texas Instruments recommends 10k to 1M. It could be 39k.
2) The timing capacitor value is much too high (because the resistor is much too low) and is probably a polarized electrolytic type of 4.7uF. It should be non-polarized and could be an accurate 0.1uF film type.
There should be plenty of that on the web. Maybe a push pull circuit with a step up transformer or something like that.
What im not sure of though is what kind of transformer or other magnetics you can get a hold of.
Also, these days they make cheaper DC to AC inverters probably much lower cost than making one yourself.
Honestly? Buy an inverter. They're 100x cheaper than what it would take to make a proper, reliable circuit.
There's a lot wrong here for a "1200W" solution. For one, high power levels like this are never done with line-freq transformers. I'm not saying 1200W transformers don't exist, but they'd be like 15lbs+, and very expensive. It's done with high-freq switchers instead which are much much smaller, lighter, and far cheaper.
And there's a whole book of things to do in controlling something like this, saturation protection, controlling MOSFET gates with good synchronization, etc.