Winding coils

[Paul Keinanen]

Actually, one does come across such coils. All coils have a frequency
where they become a parallel resonant circuit, due to the capacitance
between windings. And oddly enough, *above* that parallel resonant
frequency, they become capacitive. Yes, you read that right, they
actually act like a capacitor, believe it or not.

This is only an artefact if you try to determine the inductance of an
inductor by measuring the reactance of that component at some
specified frequency. The inductive reactance (Xl=2*pi*f*L) will grow
in a linear way towards a positive value depending of the frequency.

Since the parasitic capacitances are present, the negative capacitive
reactance (Xc=-1/(2*pi*f*C) will complicate the situation. When
approaching resonance in a parallel resonant circuit, the reactance
goes to +infinity, switching rapidly to -infinity as the resonance
frequency has been passed and slowly approach the linear drop of the
negative capacitance at frequencies far above resonance.

One can still argue that the inductance and inductive reactance are as
well as the capacitance and the capacitive reactance are still there
as separate entities, but we can not measure them separately from
terminals of the coil. Thus, this is an artefact of the measurement
method.

Thus, the inductance should be measured at a low frequency to avoid
the capacitive reactance. On the other hand the capacitance should be
measured at a high frequency well above resonance to avoid the effects
of the inductance. Or just measure the inductance at a low frequency
and determine the capacitance from the resonance frequency and
inductance.

While inductance and capacitance are frequency independent, the
resistance of a coil will vary with frequency due to the skin effect,
since at higher frequencies, the conductivity of the inner part of the
conductor is not used.

Paul OH3LWR

 

[Winfield Hill]

Bill Turner wrote...

Yes, it really is true. If you graph the reactance vs frequency of any
coil, starting just above DC, it will rise in a near-linear fashion for
a while, but will begin to steepen and when approaching the
self-resonant frequency, will quickly rise to maximum, and at that point
will suddenly drop to the opposite (negative, or capacitive) extreme and
then diminish back to near zero as the frequency continues to increase.
At that self-resonant frequency, the coil is behaving like a parallel
resonant circuit, which of course it is, due to the parasitic
capacitance between each winding. This parasitic capacitance is
unavoidable and ALL coils exhibit this characteristic. The truly
strange thing is that above the self-resonant frequency, the coil
actually behaves exactly like a capacitor, believe it or not.

Bill, it's one thing to say a coil's reactance is non-linear, but it's
another to assert its inductance varies with frequency. As I responded
before, the inductance of air coils varies very little with frequency.
I know this having made many types of air coils to verify the standard
inductance formulas, and precisely measured them over a 60Hz to 50MHz
range. Earlier in the thread I pointed out the effects of SRF (self-
resonant frequency), due to the coil's parallel capacitance. It's not
useful to my thinking to characterize those two components as one part,
and it's little surprise one gets into trouble when attempting to do so.
A similar statement can be made at very low frequencies where the dc
resistance exceeds the reactance, and the coil is best considered as
two separate parts in series.

The capacitance and dc resistance are both simple and rather obvious
considerations, with straightforward solutions. In contrast, a subtle
and difficult issue in air coils is modeling Q or loss vs frequency.

The concept of ac resistance is often used for loss, and is expressed
as a ratio to the dc resistance, Rac/Rdc. Predicting that ratio is
the tough part, including not only the well-understood skin effect,
but also the relatively obscure and often larger proximity effect.
Further complications enter if one uses multiple wires, and how they
are wound, or if one uses any of the many types of litz wire.

Thanks,
- Win

whill_at_picovolt-dot-com

 

[Bill Turner]

One can still argue that the inductance and inductive reactance are as
well as the capacitance and the capacitive reactance are still there
as separate entities, but we can not measure them separately from
terminals of the coil. Thus, this is an artefact of the measurement
method.

Not only can you *not* measure them separately, they can not be
physically separated either, since the parasitic capacitance is always
present between adjacent windings. I would not call it an artifact of
the measurement method, but rather an artifact of the coil itself.

Thus, the inductance should be measured at a low frequency to avoid
the capacitive reactance.

The inductance should be measured at whatever frequency you plan to use
the inductor, whether a single frequency or a wide band of frequencies.
Otherwise you risk a nasty surprise. To measure a coil at low frequency
and then label it as a "one microhenry" coil, for example, is asking for
trouble when that "one microhenry" coil is used at a higher frequency.
To be accurate, when you specify inductance you must also specify the
frequency of measurement.

On the other hand the capacitance should be
measured at a high frequency well above resonance to avoid the effects
of the inductance. Or just measure the inductance at a low frequency
and determine the capacitance from the resonance frequency and
inductance.

I suppose you could do that, but in the end you will come up with a
value of reactance (and inductance) for a specific coil that is
dependant on a specific frequency. As long as that is kept in mind,
there are several avenues to success.

While inductance and capacitance are frequency independent, the
resistance of a coil will vary with frequency due to the skin effect,
since at higher frequencies, the conductivity of the inner part of the
conductor is not used.

Quite true and can be significant in some applications.

 

[Winfield Hill]

Paul Keinanen wrote...

While inductance and capacitance are frequency independent,
the resistance of a coil will vary with frequency due to the
skin effect, since at higher frequencies, the conductivity of
the inner part of the conductor is not used.

Skin effect applies equally around the periphery of each wire,
what you've described above is the more serious proximity effect.

Thanks,
- Win

whill_at_picovolt-dot-com

 

[Bill Turner]

Bill, it's one thing to say a coil's reactance is non-linear, but it's
another to assert its inductance varies with frequency.

Both statements are true and easily provable. A simple air core coil
which measures one microhenry at a low frequency may have an inductance
of several millihenries (or even henries) when near its self resonant
frequency. It's a simple law of physics; there is no way around it.
And *above* the self-resonant frequency, the choke actually behaves like
a capacitor, believe it or not.

As I responded
before, the inductance of air coils varies very little with frequency.

That statement is true only at relatively low frequencies. Get near the
self-resonant frequency of an air core coil and you'll find otherwise.
Designers using relatively large coils over a wide frequency range run
into this problem all the time. As I mentioned in another post, the
classic example for Amateur Radio is the plate choke in a tube type
amplifier. Designing such a choke that has enough inductance to work
over the entire HF spectrum without self-resonances is nearly
impossible. Many amplifier designers don't even try; they just switch
inductance in and out of the choke depending on frequency.

 

[Bill Turner]

Skin effect applies equally around the periphery of each wire,
what you've described above is the more serious proximity effect.

_________________________________________________________

Can you explain proximity effect a little more? What he is describing
sounds like skin effect to me.

 

[Paul Burridge]

Actually, one does come across such coils. All coils have a frequency
where they become a parallel resonant circuit, due to the capacitance
between windings. And oddly enough, *above* that parallel resonant
frequency, they become capacitive. Yes, you read that right, they
actually act like a capacitor, believe it or not.

Yes, I'm sure no one here disputes that coils behave like capacitors
above their SRF and capacitors behave like coils above the SRF. That's
not news. And it's to do with the *reactance* of the part, not its
inductance. AIUI, inductance is pretty much stable over the frequency
spectrum. You appear to be the only person here who claims otherwise.

Now, if you are always working with relatively small coils at relatively
low frequencies, you will probably never see this effect. But if you
ever have access to a $10,000 HP sweep impedance meter, hook up your
favorite coil and see just what I'm talking about. You will never look
at coils the same way again.

That's *reactance* giving rise to that effect, not inductance!

 

[Ralph Mowery]

Both statements are true and easily provable. A simple air core coil
which measures one microhenry at a low frequency may have an inductance
of several millihenries (or even henries) when near its self resonant
frequency. It's a simple law of physics; there is no way around it.
And *above* the self-resonant frequency, the choke actually behaves like
a capacitor, believe it or not.



That statement is true only at relatively low frequencies. Get near the
self-resonant frequency of an air core coil and you'll find otherwise.
Designers using relatively large coils over a wide frequency range run
into this problem all the time. As I mentioned in another post, the
classic example for Amateur Radio is the plate choke in a tube type
amplifier. Designing such a choke that has enough inductance to work
over the entire HF spectrum without self-resonances is nearly
impossible. Many amplifier designers don't even try; they just switch
inductance in and out of the choke depending on frequency.

Youall seem to be hitting all around the 'problem'. A coil has 3
components, the resistance of the wire, the inductance, and the stray
capacitance. As the frequency is changed from DC to low AC to RF each
component has more or a less effect on how it acts in a circuit. The actual
value of each does not change, just the effect on an external circuit.

For small coils at DC the reisitance is the major item that will be seen by
an external circuit. At low to medium frequencies the inductance will be
the major factor. At very high frequencies the capacitance may be the major
factor. At self resonant frequencies , the tuned circuit effect takes
over.

 

[John Devereux]

_________________________________________________________

Yes, it really is true. If you graph the reactance vs frequency of any
coil, starting just above DC, it will rise in a near-linear fashion for
a while, but will begin to steepen and when approaching the
self-resonant frequency, will quickly rise to maximum, and at that point
will suddenly drop to the opposite (negative, or capacitive) extreme and
then diminish back to near zero as the frequency continues to increase.

No, you are talking about the *reactance* ("reactive impedance"). We
have been talking about the *inductance* ! They are not the same
thing.

If you model a real-world "coil" as a perfect capacitor in parallel
with a perfect, *fixed*, inductor, it will behave as you
describe. (Well you need a resistor too if you don't want infinite
"Q"!)

At that self-resonant frequency, the coil is behaving like a parallel
resonant circuit, which of course it is, due to the parasitic
capacitance between each winding. This parasitic capacitance is
unavoidable and ALL coils exhibit this characteristic. The truly
strange thing is that above the self-resonant frequency, the coil
actually behaves exactly like a capacitor, believe it or not.

Real "Inductors" do indeed have a self-capacitance too, which will
make the component deviate from that of an ideal inductor in the way
that you describe. But this in itself does not make the inductance
(i.e. the inductive part of the reactance), vary.

<SNIP>

 

[John Devereux]

Both statements are true and easily provable. A simple air core coil
which measures one microhenry at a low frequency may have an inductance
of several millihenries (or even henries) when near its self resonant
frequency.

No, it does not. I'm afraid you are using the word "inductance" in a
different way from everyone else

It's a simple law of physics; there is no way around it.
And *above* the self-resonant frequency, the choke actually behaves like
a capacitor, believe it or not.

Yes, because at high frequencies the current goes through the
capacitance of the coil rather than the *fixed* inductance.

(Uh, by the way, you do know who you are arguing with, right?)...

 

[John Popelish]

Both statements are true and easily provable. A simple air core coil
which measures one microhenry at a low frequency may have an inductance
of several millihenries (or even henries) when near its self resonant
frequency. It's a simple law of physics; there is no way around it.
And *above* the self-resonant frequency, the choke actually behaves like
a capacitor, believe it or not.

Now you have gone and said something that is simply not true. The
small inductor has a nearly fixed inductance with a parallel with a
nearly fixed capacitance. The combined impedance of these two fixed
reactances produces a nonlinear impedance, but there is nothing about
that impedance that implies a large change in either the inductance or
capacitance of the combination, at least not until you get to so high
a frequency that the winding is a significant fraction of a cycle
long. The rise in impedance near resonance does not exhibit the same
phase shift that between voltage and current that a large inductance
would have.

 

[John Popelish]

Not only can you *not* measure them separately, they can not be
physically separated either, since the parasitic capacitance is always
present between adjacent windings. I would not call it an artifact of
the measurement method, but rather an artifact of the coil itself.
Agreed.

The inductance should be measured at whatever frequency you plan to use
the inductor, whether a single frequency or a wide band of frequencies.
Otherwise you risk a nasty surprise. To measure a coil at low frequency
and then label it as a "one microhenry" coil, for example, is asking for
trouble when that "one microhenry" coil is used at a higher frequency.
To be accurate, when you specify inductance you must also specify the
frequency of measurement.

Agreed. One usually specifies an inductor that is measured at a
higher frequency than the one being used.

(snip)

 

[Bill Turner]

No, you are talking about the *reactance* ("reactive impedance"). We
have been talking about the *inductance* ! They are not the same
thing.

_________________________________________________________

No one ever said they were the same thing. They are related to each
other by the formula XsubL = 2 pi F L. That is a direct, linear
relationship.

Are you saying that formula is correct as some (low) frequency but
incorrect at another (high) frequency?

I'll say it another way: Inductance and reactance are directly related
to each other by the (2 pi F) factor. Given one (inductance or
reactance) you can calculate the other. There is no other way.

 

[John Woodgate]

I read in sci.electronics.design that Terry Pinnell <terrypinDELETE@dial

Intuitively I'd have thought the answer was plainly No, but I'm
certainly not technically savvy enough to be confident about that. But
I strongly suspect that the thread is already ovedue an unambiguous
definition of 'inductance'. Where's John Woodgate when you really need
him...<g>.

I'm here today, but I was away all last week. I don't think I can add
much; small air-cored coils have inductance independent of frequency up
to about half the self-resonant frequency, when deviation begins to be
noticeable. Low-frequency iron-cored coils are quite another matter; the
inductance varies with frequency, voltage, temperature, previous history
and the state of the tide on Europa. Also, it comes in two varieties,
series equivalent and shunt equivalent, and you'd better get the right
one for your problem. As the inductor gets 'worse', at lower
frequencies, the shunt equivalent tends to infinity, which puzzles
students no end.

 

[John Woodgate]

I read in sci.electronics.design that Bill Turner <[email protected]>

Making a plate choke which covers all frequencies from 160
through 10 meters (including the WARC bands) with sufficient inductance
but without self-resonances in any ham band is difficult to the point of
being nearly impossible. Many amplifier designers give up trying to
design such a choke and simply switch part of the inductance in or out
of the circuit depending on which band is selected.

This is a 1920s problem. Just as you parallel capacitors of different
type, electrolytic, metallized foil and ceramic, to get a wideband
component, so you put inductors of different construction in series to
get a wide band component. You can wind them all on a bit of wax-
impregnated dowel if you like. (;-)

 

[John Woodgate]

I read in sci.electronics.design that John Devereux <[email protected]>

I'm afraid you are using the word "inductance" in a
different way from everyone else

It would be better to say 'equivalent inductance', being the value L -
1/(w^2C). L = true (series equivalent) inductance, C = self-capacitance
(treated as lumped in parallel with L) and w = 2[pi]f = angular
frequency.

Resistance ignored, as irrelevant at this level.

 

[John Woodgate]

I read in sci.electronics.design that Bill Turner <[email protected]>

Both statements are true and easily provable. A simple air core coil
which measures one microhenry at a low frequency may have an inductance
of several millihenries (or even henries) when near its self resonant
frequency.

This is what happens to the *parallel equivalent* inductance. The series
equivalent goes down as the frequency increases, and goes to zero at
resonance.

 

[Bill Turner]

This is a 1920s problem. Just as you parallel capacitors of different
type, electrolytic, metallized foil and ceramic, to get a wideband
component, so you put inductors of different construction in series to
get a wide band component. You can wind them all on a bit of wax-
impregnated dowel if you like. (;-)

_________________________________________________________

That will work, no doubt. My point was that it takes some serious
engineering and careful testing; you can't just wrap some wire on a form
and expect it to work correctly across a wide range of frequencies.

 

[Bill Turner]

small air-cored coils have inductance independent of frequency up
to about half the self-resonant frequency, when deviation begins to be
noticeable

_________________________________________________________

You are speaking in *practical* terms, which is fine. It's true that at
relatively low frequencies, well below the self-resonant point, coils
appear to have constant inductance. No argument there. The discussion
came about because someone asserted that inductance was a constant,
REGARDLESS of frequency, and that is just not true.

Perhaps our discussion is getting hung up over what is "practical" and
what is "theoretical". As long as we understand what is going on with
that little coil across a wide range of frequencies, all will be well.

 

[John Popelish]

You are speaking in *practical* terms, which is fine. It's true that at
relatively low frequencies, well below the self-resonant point, coils
appear to have constant inductance. No argument there. The discussion
came about because someone asserted that inductance was a constant,
REGARDLESS of frequency, and that is just not true.

I disagree. The inductive component of the impedance remains
essentially constant through resonance. What is non ideal about the
inductor is that it does not exhibit just inductance, but a parallel
combination if inductance and capacitance. Ignoring the capacitance
and calling the effect variable inductance is just not as accurate a
way to describe what is going on.