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This would typically be a small ferrite core transformer. The numbers 4:50 are to indicate the primary to secondary ratio. In other words, for every 4 turns on the primary you would have 50 on the secondary but the article doesn't mention exactly how many turns that would actually be. It's just a guess but 4 turns sounds too low so try at least 8 with 100 on the secondary winding. The exact number would be decided by the core material, the oscillator frequency and how often it was triggered by the control signal.
First of all, thanks on fast answer, but I'm really don't know lot's about transformers, so the best option for me will be to buy the exact transformer on ebay. What do you think, is it possible to find it?
You can buy ferrite cores from several sources but the article doesn't tell you which one. I'm pretty sure the one in the schematic is home-made. It isn't difficult to do but you would have to contact the designer to find out the exact specification. It isn't an "off the shelf" component.
I don't know what you have in Croatia, but a start is that the inverter is rated at 10 Watts. I would start with a broken 230V - 12V "electronic" transformer as used for powering 12V miniature halogen filament bulbs as used under kitchen units. The "transformers" (actually inverters convert 230 V AC to 12 X 1.4 V, which means that as the rated DC being switched is 230V X 1.4 and the output is 12 X 1.4 the ratio is 230/12, not quite right for you. The inverters are always rated 30W + so the transformer should be adequately rated. I would look around municipal scrap heaps/dumps, They are units that look like this:= http://www.screwfix.com/c/electrical-lighting/lighting-transformers/cat840844
A transformer from one of these would be a good start. I would unwind the secondary and count the turns, then rewind with 20/50 X that number of thicker wire.