Estimating the Number of Turns of an Inductor

[Tim Williams]

Even then a
hefty treatise involving higher mathematics on how to calculate the
coefficient of coupling between two coils would be essential.

I bet I could dig up some Fraday's law stuff from my physics textbook. It'd
be a nasty integral to evaluate but would get you there.

Tim

 

[John Larkin]

** One you have got that far you have constructed a transformer. Drive some
AC current into the original inductor's winding ( from an audio generator or
similar) and measure the AC voltage on it and on the overwind you created.

The turns ratio and the (unloaded) voltage ratio you measure are in exact
proportion.

As long as the same flux traverses all the turns.


John

 

[Phil Allison]

"John Larkin"

On "Phil Allison"

As long as the same flux traverses all the turns.

** That is not a very helpful remark.

The suggestion was that the overwind be around the existing coil of the
inductor * PLUS * there is no load on the overwind so leakage inductance
is irrelevant.



................ Phil

 

[Phil Allison]

"Reg Edwards" <

But the primary-to-secondary coefficient of coupling, with the leakeage
reactances, is accurately KNOWN from the start of the design.

** Leakage reactance is irrelevant with a no load test.




............ Phil

 

[Tom Bruhns]

As has been pointed out in other postings to the thread, the
coefficient of coupling is important. Whatever flux from the primary
(driven winding) does not couple to the secondary will not induce
voltage in the secondary, and the measured turns ratio will be low as
a result. However, by measuring the inductance of the primary when
the secondary is open and again when it is shorted, and doing the same
with the secondary, you can find the leakage inductances and therefore
the coefficient of coupling, fairly accurately. (The second
measurement is really a check for consistency.) No need for xrays.
You could further improve the accuracy, I suppose, by including a
resistance value for each winding; ideally it would be the AC
resistance at the operating frequency. It will probably make for
easier calculations if you load the secondary very lightly for the
measurement.

But I'm still not seeing any need to know the number of turns, other
than for idle curosity. "I need to know because I want to"??

Cheers,
Tom

 

[Rich Grise]

pepepepepepepedantic

Well, it does make a difference.

I learned something today! Guess I can go back to bed.

Cheers!
Rich

 

[John Larkin]

** That is not a very helpful remark.

But it's true. There's not a lot of sense pretending you can measure
something if you can't.

The suggestion was that the overwind be around the existing coil of the
inductor * PLUS * there is no load on the overwind so leakage inductance
is irrelevant.

Leakage inductance means exactly that the same flux does *not* thread
all turns. So the unloaded voltage induced into the sense winding will
be less volts/turn than the main coil. This is the likely situation
for a drum core with a large air return path; some of the return flux
will sneak back *inside* the sense coil.

As the sense winding gets bigger in diameter, its signal level tends
to zero, loaded or not.

John

 

[Phil Allison]

"John Larkin"
"Phil Allison"

But it's true.

** It is *unhelpful* because it is so damn ambiguous.

There's not a lot of sense pretending you can measure
something if you can't.

** It makes less sense to scorn a perfectly practical test method.

Leakage inductance means exactly that the same flux does *not* thread
all turns. So the unloaded voltage induced into the sense winding will
be less volts/turn than the main coil. This is the likely situation
for a drum core with a large air return path; some of the return flux
will sneak back *inside* the sense coil.

** The overwind is to be around the existing coil, wound in parallel and on
top of it, touching it - is that hard to comprehend ?

A further ( rather obvious) condition is that the inductor coil current for
the test be low enough to not generate a significant voltage drop across the
coil's resistance - or you calculate that drop and take it into account.

As the sense winding gets bigger in diameter, its signal level tends
to zero, loaded or not.

** I just took a small mains toroidal ( 30VA) and with the primary
energised at 230 volts passed a one turn loop through the core and measured
0.102 volts rms across the ends. The loop could be made as open as you
liked or tight wrapped as you liked with NO change in the measured voltage.

The primary magnetising current was only 1.5 mA and the primary resistance
was 94 ohms - so a negligible primary drop of 140 mV.

So I make the primary turns to be 2255 ( +/- the AC voltmeter's 0.3 %
error, or about 7 turns)



............. Phil

 

[Tony Williams]

As has been pointed out in other postings to the thread, the
coefficient of coupling is important. Whatever flux from the
primary (driven winding) does not couple to the secondary will
not induce voltage in the secondary, and the measured turns ratio
will be low as a result. However, by measuring the inductance of
the primary when the secondary is open and again when it is
shorted, and doing the same with the secondary, you can find the
leakage inductances and therefore the coefficient of coupling,
fairly accurately.

That method of measuring the leakage inductance
(by shorting windings) gives a hint towards a
possible experimental method.... Short the sec
with an ammeter and treat the thing as a CT.

After all, CT's have a current-ratio that is quite
close to the turns-ratio, even though the coupling
can be poor (as in a CT with a bar primary). This
is because the leakage inductance (and R-primary)
can be regarded as being in series with a constant
current stimulus source. The major source of error
is then the sideways current due to the shunt loss.

So perhaps do a short-circuit current-ratio test,
then measure the sideways shunt-current taken by
just the primary, at the same equivalent voltage.

 

[Rich Grise]

"John Larkin"

** I just took a small mains toroidal ( 30VA) and with the primary
energised at 230 volts passed a one turn loop through the core and measured
0.102 volts rms across the ends. The loop could be made as open as you
liked or tight wrapped as you liked with NO change in the measured

voltage.

The difference, of course, is that in a toroid, all the flux is constrained
to the core, so it'll work every time. As Mr. Larkin pointed out, since the
winding in question is on a bobbin, and would go in a cup core or pot core,
you would, in fact, lose leakage flux. So the problem does become kinda
non-trivial.

But I'm thinking some kind of temporary core, a la amprobe or some UI
core from the junk box, but then you're getting into Rube Golberg
stuff.

Cheers!
Rich

 

[Bill Jeffrey]

Okay, I have two identical adjustable core coils, one with the slug all
the way in and the other all the way out. The Out one measures 100 uH
and the In one measures 180 uh. I put both into a box, each with
terminals to the outside, so that the physical coil can't be seen. Then
I give them to you along with the inductance of each, and you tell me
that, by your formulas, the Out one has a different number of turns than
the In one????

No, I'm saying that you take the slug all the way out, and the bobbin
off the pot core/cup core, so you have an air core coil. Measure the
inductance and plug it into the formula. (You did say that it's wound
on a bobbin, which usually implies that you can get the bobbin off the
ferrite.)

There are many formulas for calculating inductance. All of them admit
to being approximations - but that's all you need. For example:

"For a coil of rectangular cross-section, of thickness t inches, length
l inches and mean diameter (average of inside and outside) d inches,
Hazletine's formula is L = 0.8d^2N^2 /(12d + 36l + 40t) uH"

Now if your entire coil, including the ferrite, is potted in epoxy, it
is a different situation. But I don't see that in any of your posts.

Bill

 

[Tom Bruhns]

"Reg Edwards" <




** Leakage reactance is irrelevant with a no load test.

You'll get a lot of disagreement with that; even experiments will
disagree with you. (One way to think about it is that the applied
primary voltage is split between the leakage inductance and the
perfectly-coupled inductance of the model. There's no drop across the
secondary's leakage inductance, but there for sure is across the
primary's leakage inductance.) But as Tony W. so kindly pointed out,
it's much less important if you use a short-circuit (current ratio)
test.

Cheers,
Tom

 

[John Larkin]

"John Larkin"
"Phil Allison"



** It is *unhelpful* because it is so damn ambiguous.



** It makes less sense to scorn a perfectly practical test method.




** The overwind is to be around the existing coil, wound in parallel and on
top of it, touching it - is that hard to comprehend ?

Not a bit. But the outer coil has - surprise! - a bigger diameter than
the inner, so more of the return flux is flowing *inside* the sense
coil, in the direction that reduces the induced voltage. Given a
typical drum/bobbin type inductor, I'd guess that the resulting error
might be in the 50% sort of turf; the actual error depends on the
geometry of the windings, and how close the sense winding can actually
get, given the insulation or epoxy or whatever cited.

A further ( rather obvious) condition is that the inductor coil current for
the test be low enough to not generate a significant voltage drop across the
coil's resistance - or you calculate that drop and take it into account.

Up to saturation - and an drum core will usually vaporize before it
saturates - the voltage ratio, whatever it is, will be independent of
drive level; the coupling is linear. A high drive *frequency* will
limimize the effects of copper loss, although it can be approximately
accounted for.

** I just took a small mains toroidal ( 30VA) and with the primary
energised at 230 volts passed a one turn loop through the core and measured
0.102 volts rms across the ends. The loop could be made as open as you
liked or tight wrapped as you liked with NO change in the measured voltage.

With a closed, high-permeability core, voltage ratios can track turns
ratios to a part per million, as in a precision AC ratio box. Since
virtually all the flux is concentrated in the steel, any loop of any
size pretty much slices the same amount of flux. A torroid is ideal
for close coupling. That's not the case with a system dominated by air
gap, because the flux is scattered all over in space.

The primary magnetising current was only 1.5 mA and the primary resistance
was 94 ohms - so a negligible primary drop of 140 mV.

So I make the primary turns to be 2255 ( +/- the AC voltmeter's 0.3 %
error, or about 7 turns)

Transformar manufacturers routinely use DVM-looking gadgets that
indicate turns ratio, and can easily and accurately resolve whole or
half turns. But only when leakage inductance is low, as for a closed,
high-mu core with tightly-coupled windings.

John

 

[John Larkin]

You'll get a lot of disagreement with that; even experiments will
disagree with you. (One way to think about it is that the applied
primary voltage is split between the leakage inductance and the
perfectly-coupled inductance of the model. There's no drop across the
secondary's leakage inductance, but there for sure is across the
primary's leakage inductance.) But as Tony W. so kindly pointed out,
it's much less important if you use a short-circuit (current ratio)
test.

Cheers,
Tom

Leakage inductance will diminish both voltage and current ratios. If
not, a 1" diameter 1-turn coil driven by 1 amp could induce an amp
into another 1" ring a mile away. Tesla would have liked that.

John

 

[Tim Williams]

Leakage inductance will diminish both voltage and current ratios. If
not, a 1" diameter 1-turn coil driven by 1 amp could induce an amp
into another 1" ring a mile away. Tesla would have liked that.

The other way to envision it is leakage inductance in series with secondary
inductance causing a voltage divider effect.

It's too bad I have PA killfiled 'cuz it'd be nice to see him squirm. >

Tim

 

[BFoelsch]

It's interesting, when I learned this stuff ( I won't tell you when, but my
then-new text was published in 1935!), albeit in the context of
utility/power engineering, about the LAST thing we learned was the tricks
and conventions about turns ratios, etc.

Just looking at a question in my book:

"Assuming a coil of thus & so dimensions surrounding a core of this &
that dimension & type of material, calculate: 1) The flux in the core, 2)
the flux in the air," etc.

Follow-up question:

"Assuming a second identical coil placed elsewhere on the core, calculate
induced voltage if only the flux in the iron passes through the second
coil," etc.

The whole text was written like that. The concept of a "perfect
transformer" was introduced much later, and only in certain contexts. For
utility purposes, perfect transformers are undesirable!

Kind of strange by today's standards; we were taught all the painful details
right up front, and later allowed to throw out the ones that didn't apply. I
think it's done the other way around today.

Oh, if anyone cares, book cited is "Alternating Current Machinery," Bryant &
Johnson, 1935.

 

[Ben Bradley]

In
sci.electronics.design,sci.electronics.repair,sci.electronics.components,alt.binaries.schematics.electronic,
"Watson A.Name - \"Watt Sun, the Dark Remover\""

If I don't know the number of turns to begin with, do you expect me to
UNwind the coil to find the number of turns?

You didn't answer the question. WHY do you want to find the number
of turns?

Okay, I'll answer for you. Reverse engineering. You want to make
one or more coils exactly like it. Of course, not only do you need the
number of turns (and the exact layout of the turns), you also need to
know exactly what the magnetic core material is - you can either ask
the manufacturer (of either the core or the coil), or measure its
physical size and test all its magnetic properties.

An inductor is one of the easier components to make in the "home
laboratory" and it's good to know you can look up formulas and stuff
(the ARRL handbook, at least older editions, has some useful coolbook
formulas for cylindrical coils) for those times when you need it ASAP
and can't wait for overnight delivery, but otherwise it's still
cheaper to buy than to build.

As I said, the coil is usually covered or potted in epoxy.

 

[BFoelsch]

OK, let's suggest something different.

1. Measure the diameter of the wire in the existing coil.

2. Measure the DC resistance of the existing coil, and calculate the length
of the wire needed to generate that resistance.

3. Figure out how many turns will use up that length of wire.

You did say ESTIMATE, did you not?

??!!??

 

[John Larkin]

It's interesting, when I learned this stuff ( I won't tell you when, but my
then-new text was published in 1935!), albeit in the context of
utility/power engineering, about the LAST thing we learned was the tricks
and conventions about turns ratios, etc.

Just looking at a question in my book:

"Assuming a coil of thus & so dimensions surrounding a core of this &
that dimension & type of material, calculate: 1) The flux in the core, 2)
the flux in the air," etc.

Follow-up question:

"Assuming a second identical coil placed elsewhere on the core, calculate
induced voltage if only the flux in the iron passes through the second
coil," etc.

I had to take a year of Electrical Machinery in college, including
labs with big transformers and motors and stuff. I learned a lot from
it.

The whole text was written like that. The concept of a "perfect
transformer" was introduced much later, and only in certain contexts. For
utility purposes, perfect transformers are undesirable!

Is that because they conduct short circuits too well?

John

 

[Jim Thompson]

On Sun, 06 Jun 2004 14:32:46 -0700, John Larkin

[snip]

I had to take a year of Electrical Machinery in college, including
labs with big transformers and motors and stuff. I learned a lot from
it.
[snip]
John

Same here. Now-a-days I think they just point at a motor and grunt,
judging from what little today's engineering graduates seem to know
:-(

...Jim Thompson