This Ible was written to answer the questions of fellow Ibler, Electorials. I hope it helps.

The flyback circuit is a classic method of generating moderately high voltages. It is not, by any means, the ONLY way, but it was once a very common circuit, and was employed in EVERY CRT based TV or monitor.

It is a VERY clever circuit, because it solves two design problems in the system with one circuit.

The scanning electron beam in a CRT needs to be a.) created and b.) scanned.

All pictures bar two are taken directly from Wikipedia.

Step 1: Creating an Electron Beam

The electron beam is created in an "electron gun". A wire filament is heated strongly in a vacuum, and in the presence of a high voltage. Electrons liberated by the heat and voltage are accelerated down the tube and attracted to the screen, where they stop suddenly and cause a phosphor to glow.

Wikipedia

SO, we need a high voltage.

Step 2: Scanning the Beam

How do we scan the beam ?

Well, an electron beam is a current, a current passing through a magnetic field experiences a force at right angles to the direction of both the field and the current.

So if we create a field, at right angles to the beam, we can cause the beam to bend, and scan.
If a current passes through a coil, it creates a field, if the current increases linearly, the field follows, if the field follows, the bending in the electron beam follows linearly too.

....we need a linearly ramping current

Oh, and at the END of the scan, it would be really nice if the trace flew back VERY quickly, so fast you can't see it happen. That's the "Flyback"

Wikipedia: Raster scanning

Step 3: How ? Charging the Primary

Well, we COULD do the two things we need with two completely independent circuits, but back in the dawn of television, a truly brilliant English engineer called Alan D. Blumlein invented a circuit that could do the job, whilst working in electronic television at EMI. It is the flyback circuit.

Here is the topology:

The flyback TRANSFORMER is something of a misnomer. In a classic transformer, changing currents in the primary induce changing currents in the secondary. In a flyback they specifically do NOT

WHY not ?

See the diode in the secondary ? Current can ONLY flow in the secondary....when none is flowing in the primary.....EH ?

So, lets start the circuit, and switch on the transistor under the primary - here its a switch, S, what will happen ?

Current will start to flow in the primary (Is). Since the secondary has a diode in series with it, NO CURRENT FLOWS IN THE SECONDARY....and current ramps.....linearly.....

Put the coils to deflect the electron beam in series with the primary, and that beautiful LINEAR ramping current (see step 7) will cause our beam to scan left to right smoothly.

Score +1 - we have a linear ramping current.

Oh, and STORED ENERGY IN THE MAGNETIC FIELD = 1/2 x L x I^2 Remember that bit.

Step 4: NOT Charging the Primary....

NOW turn OFF the current. What happens ?

WHERE DOES THE ENERGY GO !!

Step 5: MAGIC !

NOW, there is energy stored in the magnetic field in the core. It has to go SOMEWHERE, and it can't go into the primary, because we switched it off by opening S......

The great trick is the collapsing field will now induce a voltage in the secondary - moderated by the turns ratio - usually very high, and aided by the fact that because we are taking energy from the field, it collapses very quickly.......

.....so the current in the primary FALLS very quickly, and the electron beam jerks suddenly to the left.....

Score +2

Step 6: ZAPPED !

The rapidly collapsing field induces a current in the high turns of the secondary.....and the high voltage on the secondary pumps up C is used to drive the electron gun and the tube......

Step 7: Gotchas. Saturation.

MANY flyback circuits on Instructables, or questions asked of them are "why does my switching transistor melt" ? You need to know that a flyback transformer operates at line frequency - how fast does the beam scan ?

TYPICALLY, it would be ~64kHz in a 1024 x 768 monitor.

So, why not slower ?

SATURATION.

???

Just like an electric circuit, where we say that a voltage creates a current: I=V/R, there are magnetic circuits, where we say B=uxH. B is called FLUX DENSITY and its units are Teslas (T) or more likely mT or uT.

H is the field strength, and its related to current by N (number of turns of wire) x I (current)

UNLIKE the electric circuit, there is a maximum limit of H a material can withstand and still give you more B. This is called "Saturation flux density"

The RATE of ramping of the current is fixed by two things: the drive voltage and the INDUCTANCE of the primary.

The inductance is given by the formula L = A_lx n²

B supports the inductance of the device. So long as B can increase, I's growth is restriced by L.

V= L di/dt. - or the voltage ACROSS the coil is restricted by L and the rate of change of current IN the coil

We can also say that V= n d phi/dt - or the rate of change of FLUX in the coil is proportional to the voltage across it, but flux phi is related to B by phi = B x core area. B is a KEY property.

Flyback operation is VERY carefully adjusted to be in the NON-saturated part of the curve.

What happens if the core saturates ?

YOU HAVE NO INDUCTANCE !

What happens then ?

What limits the current ???

NOTHING LIMITS THE CURRENT, apart from the DC resistance of the switch and the coil !

So, apply a voltage for too long to the core and the flux rises PAST saturation.....and you say goodbye to your switching transistor.

Step 8: Gotchas. That Diode !!

The reverse biased diode on the output is VITAL. It makes the circuit work, and it MUST be connected so that energy ISN'T pumped into the secondary during the charging phase - omit it, and you have a normal transformer.