I need help understanding how this DC to AC/DC converter works.
- How can I find the transformer data (number of windings?)
- How can I modify it to operate at 5V?
- Can I replace the transistors with MOSFETs to increase its efficiency?
How can I find the transformer data (number of windings?)
Transformers are often custom-made. If this one has any identifying markings on it, try searching for these on the web. Sometimes the manufacturer's "base" model or a similar model can be found. If nothing is found or there are no markings, then it was custom-made. Component manufacturers will not disclose any data about custom-made parts. The only place to get this info is from the company that bought them... i.e. cosbo. Sometimes these companies are willing to give out this information, but usually not. It wouldn't hurt to ask them.
People have disassembled transformers to copy or change them. Disassembly is the easy part; it is understanding how it is assembled and of exactly what materials, that makes a copy successful or not. It is a lot of work.
How can I modify it to operate at 5V?
Easiest would be to add a 5V to 12V "boost" power supply.
To allow it to run natively at 5V would almost certainly require a different primary winding at least. The details of this would need an entire book to explain, and much more to implement successfully.
Can I replace the transistors with MOSFETs to increase its efficiency?
Not easily, and efficiency improvement would be small if any.
T3 could likely be swapped with a suitably-rated N-channel enhancement-mode MOSFET and it would work, but the efficiency may not increase noticeably.
Bipolar junction transistors (BJTs) are current-controlled devices, which means the current fed into their base is what controls them. MOSFETs are voltage-controlled devices, so the voltage on their gate controls them. Sometimes these can be interchanged, if the application is a simple switch. But this is far more complex than that. Changing to all MOSFETs here means this whole schematic would need re-designed from scratch.
T2
will resist to reverse voltage like that (considering the 27 V Zener). \$\endgroup\$