John Devereux wrote:

Bill Turner writes:

On 6 Dec 2003 13:39:51 -0800, Winfield Hill
wrote:

We're talking a small air-coil here.

Doesn't matter what kind of coil; all coils have a non-linear plot of
either inductance vs frequency OR reactance vs frequency. ALL coils.

Well, just about anything is "non-linear" if you measure it accurately
enough! But is it really true that the *inductance* of a "small air
coil" is "dramatically" non-linear with frequency as you stated?

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.

--
Terry Pinnell
Hobbyist, West Sussex, UK

On Sat, 06 Dec 2003 17:32:58 -0800, Bill Turner
wrote:

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

On Sat, 06 Dec 2003 17:32:58 -0800, Bill Turner
wrote:

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

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 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

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

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

On Sat, 06 Dec 2003 17:32:58 -0800, Bill Turner
wrote:

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!

--

"I expect history will be kind to me, since I intend to write it."
- Winston Churchill

On Sat, 06 Dec 2003 17:32:58 -0800, Bill Turner
wrote:

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!

--

"I expect history will be kind to me, since I intend to write it."
- Winston Churchill

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.


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.