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Old 26th Mar 2014, 2:40 am   #1
kalee20
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Default Coil Design and Construction Manual (Babani) - Basic Error?

This little book I have had for many years, although I rarely refer to it. But recently, designing an inter-valve transformer and doing all the background reading I could, I dug it out and came across what seems to be a basic error.

See attached a couple of pages, dealing with the design of a choke (or transformer) carrying DC.

The table shows a set of designs, for particular inductance and current rating, using a stated laminated core. The resulting DC resistance, voltage drop, and required number of turns are given. The necessary air gap is not given in the table, basically it's adjust-on-test.

At the foot of the table are scaling factors, to enable other inductance or current requirements to be derived. But I don't understand the derivation of these and there seems to be a fundamental error.

If the current rating is to be multiplied by 10, keeping the same inductance, the table says the turns have to be multiplied by 3.2 (square root of 10?). I reckon this should be x10, not x3.2. Here's why.

Assume an original design is near optimal, ie the core is approaching saturation at the rated current (this means that the air gap is as small as possible, thus the number of turns is as low as possible to achieve required inductance, which allows the biggest wire gauge to fit the space, and so gives lowest DC resistance). Consider what happens if rated current is increased by x10, and turns by x3.2, while keeping inductance constant.

Increasing turns by x3.2 will increase inductance by x3.2² ie x10. So to bring inductance back down to original value, the air gap must be increased so that the overall reluctance is 10x original value.

Now, see the effect of increasing current by x10. This alone will increase flux by x10. And we have an increase in turns of x3.2, so the two together will give an increase of x32. But we had to increase the gap to change reluctance - throwing in the effect of this means we still end up with an increase in flux of x3.2.

If you continue increasing current rating, you will end up with an arbitrarily high flux density in the core - which is simply untenable, as all materials will saturate at some point. (The text makes it clear that the design table ignores effects such as temperature rise, power dissipation, etc. If any of these are excessive, there are scaling factors to allow use of larger or smaller core sets).

Conversely, increasing the gap a lot more, and increasing turns correspondingly, ending up with turns raised by x10 (rather than x3.2) ends up with a flux level equal to that as started, ie as high as possible without saturating the core.

The problem I have, is that I would have thought this would have been corrected by the 8th printing of the book. It came to light because I was trying to see what flux density other people worked their cores at, and I came up with a different figure for each line in the table.
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Old 26th Mar 2014, 9:13 pm   #2
Ed_Dinning
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Default Re: Coil Design and Construction Manual (Babani) - Basic Error?

Hi Peter, I've just checked my copies of Coil Design and Construction (1971 and 1984 versions) and they are similarly "vague". Radio Coil and Transformer Manual by Radiotrician, Bernards No44, the forerunners of the above is no better.

The Use of AF transformers (Crowhurst, 1953, Norman Price habdbook 3) has more detail on the design, with nomograns etc, but omits the case of DC in the windings and the effects of an airgap.

There were some good articles on this in Electronic Engineering in the early 40's and possibly WW at an earlier date.

Ed
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Old 26th Mar 2014, 10:02 pm   #3
cmjones01
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Default Re: Coil Design and Construction Manual (Babani) - Basic Error?

The numbers do seem strange - I don't see how it's possible to increase the current by a factor of 10 and keep the same inductance without increasing the core area.

On a related note, can anyone point me to a reference on how the inductance and saturation current of an inductor are affected by adding an air gap? I'm aware of the principle that an air gap is good for increasing saturation current, but it also has a big effect on the inductance. I did some experiments recently with the formulae in an Epcos ferrite core data sheet and it seemed to me that the overall energy storage possible in a gapped core was about the same as in a solid one - an air gap increase the saturation current but reduced the inductance so the effects pretty much cancelled out. I'd be delighted to be proven wrong, and it seems relevant to this discussion.

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Old 27th Mar 2014, 1:13 am   #4
kalee20
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Default Re: Coil Design and Construction Manual (Babani) - Basic Error?

Quote:
Originally Posted by cmjones01 View Post
On a related note, can anyone point me to a reference on how the inductance and saturation current of an inductor are affected by adding an air gap? I'm aware of the principle that an air gap is good for increasing saturation current, but it also has a big effect on the inductance.
I can't point you to a reference, but here's the idea...

Consider the core you have in your hand. Put some turns on it untilyou get the inductance you need.

Now pass a smidgen of DC through it. That will create a small, steady level of flux in the core. Ideally though the inductance won't change.

As you increase the current, however, the level of flux in the core will increase. Eventually, the core will saturate, and inductance will drop massively. Tough.

Suppose the curent we want to pass through our inductor is right at that threshold point. We need a way of shifting the operating point away from saturation.

We can add an air gap so that the flux in the core is halved (so we're only 50% towards saturation). Down side is that the inductance is also halved. BUT - and here's the clever bit - we can increase the turns by 1.41, which brings the flux in the core to 70% of saturation (flux is proportional to turns) yet the inductance will return to the original value (because inductance is proportional to turns²).

So now we have our inductor, with a good margin from saturation, yet giving us the inductance we want.

In principle, you can choose an air gap for any combination of current level and inductance requirement. In practice, there are other things to consider, such as temperature rise with lots of turns of the necessarily thinner wire to fit in the available space. But you'll get the idea.
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Old 27th Mar 2014, 12:10 pm   #5
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Default Re: Coil Design and Construction Manual (Babani) - Basic Error?

I don't have any expertise in this field, but there is a worked example of the design of a DC choke in my copy of the ITT Reference Data for Radio Engineers, 4th edition, which involves the use of "Hanna Curves" for determining air gaps.

The Square law relationship of current to inductance seem to be due to the magnetic energy stored being a function of the current squared.
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Old 27th Mar 2014, 5:29 pm   #6
kalee20
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Default Re: Coil Design and Construction Manual (Babani) - Basic Error?

Well, magnetic energy is proportional to current squared just as mechanical energy in a spring is proportional to extension squared, or in a flywheel it's proportional to speed squared.

But inductance is proportional to turns squared because doubling the turns doubles the flux. And then, when the flux changes, there are twice as many turns, so the same flux change doubles the terminal voltage. Put the two together and you get four times the voltage for the same current change, hence four times the inductance.

Imductance of course should be constant with current (excepting the case of non-linear inductors, just as there are non-linear resistors).
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