Effects of gaps in inductors and transformers

at

This is not quite the right way to describe what is going on.

The maximum magnetic field you can build up in the magnetic path is independent of the gap - it is limited by the saturation flux for the core material. The number of ampere-turns of current through the winding required to generate that flux depends on the magnetic path length. The magnetic path length through the core itself is divided by the relative permeability of the core (about 1000 times air for ferrites, and 10,000 times air for iron) so even a small air-gap can dramatically increase the magnetic path length.

A ten-fold increase in magnetic path length allows a ten fold increase in current through the winding before you ht stuaration, and reduces the inductance of the assembly by a factor of ten, thus allowing a factor of ten increase in the energy stored in the inductance (LI^2) before saturation sets in.

A gap in a transformer core increases the leakage inductance, which is usually undesirable.

Moreoever, a transformer isn't usually used as an energy storage device, so increasing the energy storage capacity is rarely a design priority.

at

At 100kHz you probably need to worry more about inter-winding capacitance. The detailed structure of the windings can get to be very important at this sort of frequency. The pot core may well have a two or four section former with the windings built up as two or four successive sections, while the toriod is more likely to have its windings built up as successive layers, one on top of another, which gives a higher winding capacitance and a lower self-resonant frequency.

At even higher frequencies, you have to restrict yourself to single- layer windings to keep the interwinding capacitance within bounds, and eventually you have to go over to transmission line transformers.

-- Bill Sloman, Nijmegen

With the flyback converter being the counterexample for both. As more and more electronics are powered by switchers instead of linear supplies, and as most of those are flybacks, the day may come when transformers are indeed "usually" used for energy storage.

robert

Sloppy word usage. Flybacks don't use transformers. They use coupled inductors.

I guess you're right.

robert

OK. That is very helpful in understanding the principles involved. The gaps I saw in some large C-core inductors I have are about 0.1", and the laminated steel has a length of about 10". So if the magnetic path length is increased to 1000, that is a 100 fold decrease in inductance, allowing

Thank you for that information. I had posted on SEB that some small transformers may be made with a gap to make them impedance protected in case of an output overload or short. There are probably other ways to achieve this effect with looser coupling. As I had posted there, it comes at the price of low efficiency and poor regulation, but that's what is desired for self-protection.

The toroid has only about 10 turns of approx #16 wire on a core about 0.75" x 0.37". I don't know the internal construction of the pot core, but it is only about 0.5" square and 0.3" high. It most likely has several layers of windings.

Thanks,

Paul

Small, impractical nit: Won't the flux continue to increase with current, at a declining effective permeability, approaching u=1 at full saturation of the iron? Admittedly, this is a pretty low slope, but I don't think it goes to zero.

I know a guy who has a secret process for treating metglas, up to a permeability of about 1e6.

John

Sure, but you don't usually want your transformer or inductor to go into saturation. Currents go through the roof, the magnetic field extends outside the core material and so forth. Of course I once built a starter for a xenon lamp where the step-up transformer spent most of its time during start-up - probably a few microseconds - in saturation. I still eventually got my 20kV across the secondary, enough to get the electrodes to spark over, initiating the discharge - initially as a glow discharge, rapildy developing into an arc.

For many years Telcom metals have sold a bunch of funny alloys - mu- metal amongst others - offering permeabilities of the order of 1e5.

You've got to anneal them after you've deformed them into the shape you want to get these high permeabilities. National Standards labs use this sort of material as cores in precision ratio transformers. Hardly anybody else can afford it.

-- Bill Sloman, Nijmegen

Ha! I have a stack of Telcon HCR (square loop) and Mumetal toroids in stock, and even 1000:1 400Hz CT's wound on HCR. You can have some to play with..... cost you though. :)

There are many different reasons as to why magnetic circuits are gapped. For the switching power supply application, the main reason is to prevent core saturation under a DC bias and the gap is usually sized by volume so that the 1/2*mu*B^2 due to the DC is stored in the non-saturating gap. In an ac-transformer application, the load current has little to do with core flux density theoretically. The flux density is only determined by the primary voltage as this sets the dB/dt magnetization in the core, and the net flux due to the load current in primary and secondary is zero.

If you look at any hunky arc welder, even a small one is 200A rated secondary, you will notice that the current adjust dial is mechanically linked to a chunk of laminated iron that is moved in and out of a big gap in the core, directly adjusting the reluctance of the magnetic circuit and the magnitude of flux linked with the secondary.

usually when designing a flyback style transformer, the input & output voltages and max duty cycle set the turns ratio.

then choose a core, a switching frequency and the peak flux density (< Bsat at max Tcore).

then select the primary turns to give the desired Bmax,

Np = Vin*Ton/(Bmax*Ae)

then choose the air gap to give the correct inductance. If the air gap is -ve, you've picked the wrong core. And unless the gap is very small, just assume all of the energy is stored in the gap, and use

Lmag = mu_0*Np^2*Ae/l_gap so

l_gap = mu_0*Np^2*Ae/Lmag so

You need the following sums

L = uoueN^2Ae/Le

B = uoueNI/Le

H = NI/Le

dI = VinTon/L

You are not allowed to use one sum without thinking about how it might affect another one. You avoid that sort of sophistry by using all the sums to find your answer.

The B field don't depend on the core.

Choice 1) Do Sums. Choice 2) Use sophistry to prove it does.

Subsequently

Choice 1) Problem Solved. Choice 2) Invoke 'Ad Hominem' Attack strategy.

A gap affects ue. There is something about permeance and reluctance which is something like conductance and resistance. The gap appears in series with things so/but you get the answer by adding the reluctances.

Unfortunately designing magnetic components is hard because there are too many variables to play with.

N = LI/BAe

Works

But then you might need

AwAe = LIpkIrms/BpkJK

To get a first guess at what the size of your core should be. J and K are the guesses.... and then Bpk ignores the core loss so you might adjust something else for another guess. J ignores the winding losses so..... you might have to guess again.

Do you trust the software?

Leakage inductance has nothing to do with uncoupled flux. It's down to energy stored in the field(s) between the windings, series term.

If you want to control stuff then you might control the coupling of the flux and that is a parallel thing.

DNA

I don't think I need to go through all that calculation, especially when I am using off the shelf components (but I appreciate the information). The actual circuit performance and waveforms closely match what I see in LTspice. I was just surprised that the toroidal inductor rated at higher current did not produce as much output power. It may be that the smaller inductor (Sumida CDR127/LD100) may have more effective gap and thus allow higher current than the larger toroid (Miller 2101-H-RC). I have ordered 8 pieces of the board, and will soon be able to test them. They are designed so I can use either the on-board SMT inductor, or an external toroid, or both in parallel.

Basically, I can predict the maximum current in the inductor, and hence the energy stored, vs frequency. Using LTspice with a 61 ohm load, I found that at 200 kHz and 70% duty cycle the maximum inductor current with 12 VDC at

The maximum output will be generated when the inductor starts charging again after its energy has been discharged into the output capacitor, so there will be no "dead time". With 12 volts, the inductor charges to 8.4 A in 7 uSec, and it takes 3 uSec to charge the output capacitor, for 70% duty cycle. The output is about 48 VDC into 61 ohms, or 38 watts. I calculate the average input power to be about 70% of sqrt(8.4*8.4/2) * 12 V = 35.3 watts, plus the 780mA * 12V = 9.4W from the battery, or 44.7. I'm guessing at this, but the simulator measured input watts to be 43, so I'm close. This is 82% efficiency.

I'm running simulations in LTspice, and I think they are pretty much correct, but I am still a little puzzled. In the continuous mode operation at 200 kHz, I can see the DC component through the inductor as a 388 mA minimum current. I get input power of 28.77 W and output of 25.77 W or

BTW, a good reference for transformers, inductors, and other AC devices is:

The entire series is very good.

Paul

is:

I'm not impressed. I don't trust any article on transformers that doesn't include the transformer equations

V1= L1. dI1/dt + M. d I2/dt

V2= M. dI1/dt + L2. d I2/dt

Modelling a transformer as an "ideal" transformer plus leakage inductances doesn't give the same insight, and it certainly doesn't give you the right insight.

Incidentally, M above is less than the geometric mean of L1 and L2 - the ratio of M to the geometric mean of L1 and L2 is the coupling coefficient, and can be very close to one for good transformers with high permeability cores.

-- Bill Sloman, Nijmegen

Who's that?

Julian Bergoz.

John

John Larkin a écrit :

Well, I meant, is he, his company,... selling this. Is there a website?

His company is...

but if you ggogle his name, you'll get all sorts of interesting stuff. He's a very cool guy, and does some outrageous magnetics. He sponsors the "Farady Cup" awards, which is a pretty good English pun for a French-sponsored award.

John

John Larkin a écrit :

Interesting stuff. Thanks. And we are less than 1 and 1/2 hour drive away.