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a regular transformer


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Ferrite core transformers sometimes do have a very small gap to prevent saturation and help in reset. In general, the idea with transformers is to NOT store any energy in the core. Leakage inductance, which all transformers have, will store energy in the core, so you want to minimize that with good inter-winding coupling and layer stack-up. Transformers also have copper & core losses. These relate to how big your winding window (how much copper of the best AWG can fit

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The gap is not fixed.... can vary. Look at some gapped core data sheets, you will find something called inductance factor (nH/1000turns), typical numbers you'll see are 100, 160 and 250. Each of these has a different gap. To really understand this, and get a feel for how diffeent parameters interact, read a few articles on couple inductor design. The energy is stored in the flux in the gap.

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