# Designing an air gap transformer Misunderstanding

Suppose my core is actually with a design which make it saturated and the voltage on the secondary is too high.

So I have to decrease the secondary voltage: For this I can increase the number of turn on the primary side N1. Nevertheless I will increase the magnetic excitation H which is equal with some appoximation to H = N1*I1/l. It will then saturated even "higher" my core. So I can't go this way.

I can lowering N2 : Unfortunately N2 is at its minimum.

Last solution to reduce the secondary voltage according to the Faraday's Law, reducing the variation of the magnetic flux over the time. (Consider that we cannot change the duty cycle).

How can I decrease the variation of the magnetic flux? Here is what I do not understand:

By decreasing N1, I decrease the excitation H1, so the magnetic flux. (cf B-H curves)

Nevertheless if I consider the Faraday's law, as the primary voltage is constant and the duty cycle fix, If I decrease N1, I increase the variation of the magnetic flux.

Where is my error?

• Normally, increasing N1 reduces I (by increasing L) instead of increasing H. Why is this not the case for you? Are you driving it from a current source rather than a voltage source?
– user16324
Jan 25, 2020 at 9:53

For this I can increase the number of turn on the primary side N1. Nevertheless I will increase the magnetic excitation H which is equal with some appoximation to H = N1*I1/l. It will then saturated even "higher" my core.

That would be entirely true if the magnetization current remained the same but, it doesn’t...

Increasing the number of primary turns increases the primary magnetization inductance. This, in turn naturally reduces the primary magnetization current because more inductance means a higher reactance at the excitation frequency (presumably 50 or 60 Hz or some other fixed value).

And, if you look at the formula for inductance, you’ll find it’s proportional to turns squared hence, if you were to double the number of turns, you would get 4 times the inductance and, for a given primary voltage and frequency, the magnetization current would reduce by four.

Another example - if turns increase by 10% then inductance increases by 21% and the current that causes saturation reduces by 21%.

Below is the formula for a solenoid but the same applies for a transformer winding (where $$\\mu_0\$$ is increased by the relative permeability of the core material and $$\\ell\$$ is the mean length around the core).

So, if you double the turns (for example), the overall effect on ampere turns (and H field) is that it halves. This is because current has quartered but turns have only doubled.

This means that the effects of saturation are reduced.

You can also introduce an air gap to reduce the effective magnetic permeability of the core. This also reduces inductance (by the amount the permeability is reduced) and, this is “corrected” by more turns but, remembering that inductance is proportional to turns squared, there is still a net benefit on reducing saturation.

Suppose my core is actually with a design which make it saturated and the voltage on the secondary is too high.

The only way you’ll get too high a secondary voltage is because the turns ratio is incorrect. Saturation does not make the secondary voltage increase.

By decreasing N1, I decrease the excitation H1, so the magnetic flux.

Decreasing the primary turns by (say) 2, lowers inductance by 4 and increases magnetization current four times hence ampere turns (and H field) increases by 2 and you get more saturation.

• Really nice explanation as always ! I said " Suppose my core is actually with a design which make it saturated and the voltage on the secondary is too high." If I m in the case the secondary voltage is too low and the core is saturated ? Why I cannot just reduce the turn number of N1 to reduce the magnetic excitation (core will not then be saturated) and increase the turn number of N2 for increasing the electromotive force and having the required secondary voltage ?
– Jess
Jan 25, 2020 at 20:51
• Core saturation doesn’t directly bring about a reduction in the secondary amplitude (if I understand what you are asking). Reducing N1 increases the level of saturation because inductance reduces as a square of the N1 reduction. This in turn increases current more than the number of turns reduces hence H increases. Jan 25, 2020 at 22:25
• The slope of the BH curve is permeability and, unless you introduce a gap that slope is fixed. Both B and H are incidental players and do not affect the voltage ratio dictated by the turns ratio. Jan 26, 2020 at 20:57
• Yes it does reduce. Jan 27, 2020 at 8:06
• @Jess I don't know why you need a flyback transformer at all. Your question never mentioned this and I answered the general case for all transformer types. You can gap the core for regular forward converters and you might not need to gap a core for some flyback converters. The same theory applies. Jan 27, 2020 at 9:16

Take transformer design one step at a time.

# Do you need an air gap or not?

It depends what type of transformer you want. Do you want a normal, forward, power transformer, with output voltage always a turns ratio of the input voltage? Or do you want a flyback transformer, which stores energy, only to release it into the load at a voltage defined by the load and the current?

A normal transformer uses no air-gap. A flyback uses an air-gap. The rest of this answer assumes you're making an ordinary power transformer with no air-gap.

# Avoid saturation with enough primary turns

The maximum volts per turn is defined by your core area, and your operating frequency. For a fixed input voltage, use enough turns so that your volts per turn is less than this maximum. More turns is fine.

# Now set the turns ratio to get the output voltage you need

You know the volts per turn, from the primary winding you're using. Put on enough secondary turns to give you the wanted output voltage.