Post #14 
 

Ferrite cores are gapped to reduce its high permeability and allow some energy to be stored in the air and not just all the energy in the core

I think that the most easy way to understand this is to apply constant volts/turns to the core, while measuring the current waveform in the coil, and when current gets too high let the coil freewheel and return to the supply all the energy it has stored [>10Mhz dual oscilloscope is mandatory and digital storage is a great thing to analyze curves without the circuit running]

Provided the vots / turns is keep constant, the sloppe of the current / time curve is nothing but the inverse of the inductance shown by the core for that current [all non-air-cored inductors have variable inductance depending on current]

As current increases, inductance suddenly changes from the high value given by the core permeability to the low value given by the coil itself as there were no core [leakage inductance]. 

This is called 'saturation'. It ocurrs when the core is 'full' of energy and its permeability suddenly decreases and can be easily seen as a knee in the current waveform [past this point, the core must be switched off quickly to prevent the current to rise without control]

The curves for ungapped cores show very high [magnetizing] inductances and very low saturation currents, so its main use are magnetic couplings where you expect the transformer to act as an ideal transformer capable of directly transferring long pulses of energy between windings, storing very little energy in the core itself

Examples of magnetic couplings are push-pull magnetically-coupled buck converter topologies used in AT & ATX PC power supplies and other medium or high applications [>200W]

As you progressively increase the gap, you can see how the [magnetizing] inductance decreases and the saturation current increases

If you try to calculate total stored energy for different gap lenghts [E = .5 * L * I^2] you can see how the value increases as gap increases, but the relationship appears to be very complex [not linear nor quadratic]

This means that cores are gapped to use them as inductors, whose energy storage capability, inductances and saturation currents can be adjusted with gap lenght and number of turns

Since the ferrite is still showing much higher permeability than if there were no core, gapped cores require much less turns to achieve the same inductance as an air cored inductor, and therefore, they provide lower leakage inductance between coils, allowing them to be used as thight coupled inductors

The most ussual application for coupled inductors are flyback converters, the standard topology for low power [<100W] supplies [VCR, DVD, TV, monitors, PlayStation, battery chargers, low power or standby section of AT & ATX, etc...]

The flyback topology is very demanding on leakage inductance since the energy is stored in the core through the primary and then it's released through the secondaries, so gapped coupled-inductors designed to have good coupling between winding are mandatory to reduce the energy dumped back to the primary while the leakage inductance of the secondaries is 'energized'

PC power supplies include :

- An ungapped ferrite core from common mode EMI filter [should have low losses up to several Mhz, not present in very crappy units]
- An iron powder core from differential mode EMI filter [dual inductor, not present in very crappy units]
- A gapped ferrite core for the standby flyback converter [not present in AT]
- An ungapped ferrite core for the magnetic coupling of the main buck converter
- An iron powder core as a coupled inductor for the main buck converter [some ATX use another core for 3.3V]
- An ungapped small core from the current transformer that drives switching transistors
- A saturable reactor from some ATX that employ pulse-delay techniques to get thight regulation on 3.3V output
- Ferrite bead inductors from pi filters on the output [crappy supplies doesn't include them]

In buck converters, the energy is stored and removed from the inductor through the same winding so they are forgiving on leakage inductance. The reason to use a coupled buck inductor in PC supplies is to provide some cross-regulation between 12V and 5V outputs since only 5V output has regulation

The reason to use iron-powder cores instead of gapped cores in the buck inductor of AT & ATX supplies is that low permeability iron-powder has really very progressive saturation, so you can reliably use a core smaller than required on its non-linear inductance zone to reduce size and costs at the expense of having a ripple current that increases with the load, instead of being constant like with an ideal inductor

PC power supplies are filled of cost-cutting tricks

Millwood : Don't expect much more than 400W output from a modified 200/250W AT/ATX PS [AT ones are easier to modify since there is no standby section to deal with]