Trying to understand the working principle of a weird transformer driver / oscillator

Question

I'm trying to fix the high-voltage power supply of an old scope. The HV transformer is burnt, and I'm trying to replace it with a similar one (EPC19 core), but I'm failing.

I already know how to wind and drive this same transformer with a half-bridge, but the driving circuit in this particular scope is something I can't understand.

This is the scope's HV section schematics (I did the annotations in red, annotations in blue may be original from the schematics, or may have been made later by someone else):

The HV transformer is T1001. HV circuitry is inside the red line. T1001 has a feedback winding on the primary, and in the scope schematics, it seems to be changing TR1003 base constantly, making the thing oscillate at a given frequency.

In the original burnt transformer, 1-2 are 8 turns and 3-4 are 2 turns, both AWG 28, but they are strongly coupled: both windings are completely stacked on top of each other. There are no side turns. The bobbin has been made specially for that, the primary/feedback section is a deep slot for only one AWG 28 wire to fit. In my replacement bobbin, this is not possible without modifications. So, my first question: is this coupling critical to make this oscillator work?

I tried making a similar transformer using a core about the same size, (without the strong coupling between primary and feedback, with turns laying side by side) but the circuitry shows only marginal oscillation (2Vpp), with a DC level of 19V approximately. I was expecting something like the blue waveform, annotated on the schematics. Any ideas on what may be wrong?

Another question is: if I only make primary and feedback windings (1-2 and 3-4), should the circuit oscillate? Or oscillation depends on the secondary also? If only primary and feedback are needed, it's much easier to test (no need to wind hundreds of turns on secondary).

And the last, and most important question: How this circuit really works, and which features this transformer must have to properly work with this particular topology?

EDIT:

Adding some missing info:

• The transistor gets very hot in my tests. It's seems the oscillator is constantly on, making the transistor draw heavy current.

• The original core is formed by EI ferrites. Central part is circular. Replacement core (EPC19) has no gap, formed by two E parts. Central part is kind of oval, but with quite similar section area when compared to the original.

Answer 1

It appears you're dealing with a variant of the Armstrong Oscillator. The transformer, together with the transistor and C1005 create a self-oscillating circuit and the voltage created across the primary by the oscillation is stepped up according the the turns ratio.

A sample of the circuit's output voltage is fed back to the primary via R1015, forming a voltage divider with R1001. Once the desired output voltage is reached, the OpAmp will "steal" base drive from the transistor, and it will then create a smaller signal - that's the control loop.

Running the circuit without the secondary will not give you the desired results, because you need everything around the control loop, but you might still be able to observe some effects without closing the loop (E.g. Will it start up at all?).

Since the basic oscillating circuit relies heavily on the inductance and capacitance values around the transformer and the transistor, you might need to be very careful with the parasitics, too. Also, what about the air gap in the core? It has a great influence on both iductance and possible core saturation.