Transformer Diagram

Hi All,
I am having a difficult time finding a diagram on this so I can get some theory for it.

Any ideas?

It's a high frequency transformer of some kind, what is it out of? - most such devices are custom, and no specs or details available.

It's off of a circuit board used in a vacuum pump. These vacuum pumps are used in much larger systems for making semiconductors.

My entire problem is that a magnetic contactor is not being tripped by a relay. The relay has the required AC voltage sitting on the middle leg, but I'm not getting the 12VDC to the coil so it will close. I'm actually not reading any DC voltage at the coil, but rather, around 3VAC. It's been kicking my butt for a while now.

Have to ask;
What is this transformer’s relationship to the relay? What motivated you to suspect it enough to remove it?