What does adjusting the core gap do?

[John123]

In a crt tv/monitor hv flyback transformer what is the effect of making the gap in the core bigger or smaller? Let's assume the drive topology is flyback, would making the gap bigger between the two core halves allow for more output voltage/power if everything else like primary voltage, number of turns, drive frequency and duty cycle stayed the same?

[SteveN87]

Yes - the power should increase.

Increasing the gap reduces the effective permeability, Ue, and hence reduces the primary inductance, Lp. For example, if Lp was 500uH with the original gap, increasing the gap so that Lp became 250uH (and keeping the voltage, frequency, duty cycle etc the same) would result in di/dt (the rate of increase of primary current, inversely proportional to inductance) doubling. So at the end of each cycle, the current in Lp would be twice its previous value. Because the energy stored is proportional to the inductance and to the square of the current, the net effect is to double the stored energy per cycle and hence double the power throughput. (Extra copper/core losses, flux fringing effects ignored.)

Even though we've doubled the MMF, due to the increased reluctance of the gap, those extra Ampere-turns give rise to less flux and hence less tendency to saturate.

Rgds,
Steve.

[klugesmith]

Yes, what Steve said.  (Welcome, Steve!)
Of course doubling the current quadruples the heat dissipated in windings.

Here's another view of same thing.
When the air gap is long enough to dominate the magnetic reluctance formula,
inductive energy storage is proportional to air gap volume and to B^2.

In fact you can work it out from fundamentals.   Energy in a magnetic field = 0.5 * B * H. 
For a given value of B, H in air is much higher than H in ferrite or steel.
1 tesla in air has energy density equivalent to 60 psi (4 bar).  400 kJ/m^2, maybe give or take a few powers of ten.
2 teslas, 240 psi (16 bar).
1/4 tesla (like gap in a ferrite core), 4 psi (1/4 bar).

[John123]

Yes - the power should increase.

Increasing the gap reduces the effective permeability, Ue, and hence reduces the primary inductance, Lp. For example, if Lp was 500uH with the original gap, increasing the gap so that Lp became 250uH (and keeping the voltage, frequency, duty cycle etc the same) would result in di/dt (the rate of increase of primary current, inversely proportional to inductance) doubling. So at the end of each cycle, the current in Lp would be twice its previous value. Because the energy stored is proportional to the inductance and to the square of the current, the net effect is to double the stored energy per cycle and hence double the power throughput. (Extra copper/core losses, flux fringing effects ignored.)

Even though we've doubled the MMF, due to the increased reluctance of the gap, those extra Ampere-turns give rise to less flux and hence less tendency to saturate.

Rgds,
Steve.

Yes, what Steve said.  (Welcome, Steve!)
Of course doubling the current quadruples the heat dissipated in windings.

Here's another view of same thing.
When the air gap is long enough to dominate the magnetic reluctance formula,
inductive energy storage is proportional to air gap volume and to B^2.

In fact you can work it out from fundamentals.   Energy in a magnetic field = 0.5 * B * H. 
For a given value of B, H in air is much higher than H in ferrite or steel.
1 tesla in air has energy density equivalent to 60 psi (4 bar).  400 kJ/m^2, maybe give or take a few powers of ten.
2 teslas, 240 psi (16 bar).
1/4 tesla (like gap in a ferrite core), 4 psi (1/4 bar).

Thanks Steve, Richard! So this could also mean there is a point where making the gap bigger makes performance worse? For an extreme example, two core halves on opposite ends of the desk is not going to make for a very good transformer/coupled choke. There has to be a certain point where the gap is too big to be of any practical use?

[davekni]

Even though we've doubled the MMF, due to the increased reluctance of the gap, those extra Ampere-turns give rise to less flux and hence less tendency to saturate.

Rgds,
Steve.

Presuming we are ignoring winding resistance (superconducting windings:), the above quote isn't quite accurate.  Since the voltage and time remain the same, the flux must remain the same too, as it's proportional to the integral of voltage over time.

Concerning the large-gap limit, it depends on the effect on coupling factor "k".  Most commercial flyback transformers have the primary winding inside the secondary.  Thus removing the core completely doesn't make k go to zero.  It might drop from say 0.96 with a normal gap to say 0.5 with no core.  Without winding resistance, that no-core case may be the highest-power case.

Many home-modified flyback transformers wind the primary on the opposite core leg.  Coupling factor drops rapidly with increased gap.  The per-cycle energy in the primary continues to go up as the inverse of inductance.  However, the fraction of that energy available in the secondary is k^2 times the primary energy, so is dropping.  The gap for maximum output power depends on geometry of the windings and core, so isn't trivial to predict.

[klugesmith]

Presuming we are ignoring winding resistance (superconducting windings:), the above quote isn't quite accurate.  Since the voltage and time remain the same, the flux must remain the same too, as it's proportional to the integral of voltage over time.

That's a good point of clarification.
Suppose longer air gap doubles the reluctance, thus halves the inductance, without much effect on coupling ratios.
We would reach the same flux (webers = volt-seconds/turn), and be equally close to core saturation, but now drawing twice the current.
As Steve said, that would double the energy storage.
As I said, same flux density in twice as much air volume.

As others have said, any increase in air gap length makes the core less effective in guiding magnetic flux.  That reduces the coupling between turns and between coils.  Not by much, when the air gap length is very small compared to the pole widths. 

Prev post gave wrong unit of measurement for energy density in air gap. 
For B = 1 T, it should be 400 kJ/m^3, not kJ/m^2.   
Can be expressed as a pressure, or lifting force per unit area: 400 kPa.
B^2 / 2*u0

[John123]

I feel I should explain my goals with this thread. Currently I'm having to turn the switching frequency down well into the audible range to get the required output voltage from the TV flyback transformer/LOPT when running from 12v (around 8khz I think to jump a 7cm gap). I know I should just increase the primary voltage, but this project is being designed to run off a 12v battery away from mains power sources. The primary is pretty low resistance.

So in essence I guess I'm trying to optimize the gap for 12v, I appear to be at a limit in terms of less primary turns as any lower and the drain pulse at turn off starts decreasing along with output voltage, what I've got now appears to be the sweet spot for turns. This is a simplified schematic.


Which is based on this except with a 600v low on resistance MOSFET and smaller primary capacitor, that snubber keeps the peak drain voltage from avalanching the fet.



If you notice at the bottom the designer states a bigger gap = higher power which is why I asked here for clarification 

[davekni]

When you reduce the turn-count, are you increasing the drive frequency proportionately?  At half the turn-count, the frequency needs to be twice (half the pulse width) to reach the same magnetic flux (same energy per pulse).  Current will double, so you'd need to make sure the FET is still maintaining low Vds while on.  This should produce twice the output power (same energy twice as often).

When reducing turns, it's best to still fill the winding length.  If 10 turns is 1 layer, split it into two 5-turn windings and connect them in parallel.  (Shorter windings reduce coupling factor.)

As frequency increases, the parasitic capacitance of the secondary winding will become more significant.  I don't know if it will be enough to cause issues for your case, as most flyback transformers are designed for at least 15kHz.  Higher frequency will also increase winding proximity-effect losses, but that's usually not too bad for single-layer coils.  Litz-wire is the normal solution if proximity-effect becomes problematic.