The flyback transformer, also called the line output transformer or LOPT ("LOPP-tee"), is driven with a pulsed waveform at the horizontal scan frequency by the line output transistor. (Or MOSFET, I guess). The line output transistor conducts during the visible horizontal scan, as the electron beam scans from left to right. During the scan, current builds steadily in the primary, as the magnetic flux in the core builds steadily.
The transformer has a ferrite core because of its relatively high operating frequency. Modern flyback transformers are encapsulated in a plastic housing (the ferrite core may be partly external).
At the end of the line, the line output transistor turns off and the current is interrupted. The magnetic energy that was stored in the core during the line scan cannot collapse instantly; the energy has to go somewhere, and the current "wants" to continue flowing in the same direction.
Because of how induction works (in other words, Kris doesn't know his physics very well), this causes the voltage across the primary to reverse direction and increase rapidly until something starts to conduct again, so the stored magnetic energy can dissipate.
This large reverse voltage spike at the primary is duplicated at the secondary, which is connected to a network of diodes and capacitors that used to be called a "tripler" (although its voltage multiplication factor isn't necessarily 3). Each positive voltage spike causes diodes to conduct, and charges capacitors.
Over a short time, these high positive pulses charge up the capacitors in the tripler and produce a very high DC voltage called the "EHT" (extra high tension) voltage, which is a positive DC voltage of around 20~30 kV for a medium-sized picture tube.
In modern flyback transformers, the diodes and capacitors are built into the unit, and the EHT emerges on the thickly insulated wire at the top, which runs off to the "ultor cap", a rubber-insulated metal clip that clips into a metal dome-like receptacle called the "ultor" that is manufactured into the glass bell of the picture tube. The ultor connection and connects internally to the metallic coating on the inside of the bell. Its function is to attract the electron beams towards the screen.
Other secondaries or taps on the main secondary of the flyback transformer are also used to generate other high voltages - normally the focus electrode voltage (around +8 kV) which focuses the electron beams, and the "A1" voltage (around +800V) which accelerates the electrons within the neck of the tube. These connections are made through two pins on the picture tube's base. The focus wire usually runs directly from the flyback transformer to an insulated direct connection on the tube base board.
Integrated flyback transformers include rotary controls to vary the focus and A1 voltages. The focus voltage obviously is set for best focus with a dim picture, and the A1 voltage is normally set so that the flyback lines just disappear with the screen at minimum brightness in a dark room.
Flyback transformers usually have several auxiliary secondaries that are used to generate supply rails for the vertical output circuitry, audio output circuitry and others. They also provide a line-synchronised pulse that feeds back to the small-signal circuitry where it can be used for AGC and/or colour burst gating.
In terms of safety, the focus and A1 voltages are not dangerous (unless the flyback is damaged) because they discharge through their adjustment potentiometers very quickly after the set is switched off, but the EHT voltage can remain dangerous for days or weeks, and potentially, years.
The main danger is the energy stored in the picture tube itself. There is a grey graphite coating called "aquadag" on the outside of the bell, often with tension springs and flat braided wire strapped onto it for electrical contact, which is connected to the set's earth - either directly, or through a current-detecting circuit called a beam limiter that is designed to protect the picture tube against excessive EHT current.
Because the inside of the bell and the outside of the bell are both coated with conductive material, the glass forms a dielectric between them and the capacitance between the two coatings is actually quite significant - a few nanofarads, I think. When that much capacitance is charged up to 25 kV it holds quite a lot of energy and will discharge with a big, loud spark.
If it discharges through you, it will hurt - a lot! It is also very dangerous if it flows through your heart - i.e. hand to hand, or left hand to feet. The best way to discharge it is to connect a wire directly to the strapping on the aquadag, and insert it under the ultor cap while it's still connected. There will be a big spark. Bring the wire closer to the ultor connection, until it touches.
Leave the connection for a few minutes. If you don't, the ultor may recharge itself because the capacitance is distributed and there is also distributed resistance.
You may want to make up a discharging cable, with an alligator clip at one end, and a piece of metal at the other for sliding under the ultor cap. Use good quality thick wire (e.g. monster cable, as used for loudspeakers), and make sure that the connections at both ends are visible while you're using the cable, and have good strain relief. If anything breaks, you want to know BEFORE you go poking around with it!
Also I wouldn't touch the metal directly; make up some kind of insulating barrier. Make sure the clip is firmly attached to the aquadag strapping, and will not pop off!
The capacitors in the flyback transformer can also store a charge on the EHT wire, but this will be discharged along with the picture tube, if the ultor cap is connected when you discharge the tube.
All of this information and advice is based on my experience with TV sets, which is mostly over 20 years old. I have no experience of very large CRT TVs and they may have some differences. Use your common sense when comparing my description to the set you have. If something I've said doesn't fit with what you see, ask someone!
You should not do any of this work if you have heart problems or a pacemaker.
