Perhaps an example will make it clear.

Suppose you have a coil which measures 1 uH at 1 MHz. It is known to
have a self-resonant (parallel) frequency of 100 MHz.

You measure its reactance at 1 MHz using the formula X=2*pi*F and find
it to be 6.28 ohms.
At 2 MHz you find it to be 12.56 ohms.
At 10 MHz you find it to be 62.8 ohms.
So far the reactance is changing linearly with respect to frequency.
(Actually it is not perfectly linear, but the difference at these
frequencies is small and probably would not be observed with run of the
mill test equipment.)

But, as you approach 100 MHz, you find the change is obviously no longer
linear.
At 95 MHz you would expect the reactance to be 6.28*95=596.6 ohms, but
much to your surprise, it measures 1000 ohms.
At 99 MHz, instead of the expected 6.28*99=621.72 ohms, it measures
50,000 ohms!!

All the above is perfectly normal and easily observable.

My point is that when a coil measures 50,000 ohms at 99 MHz, its
inductance HAS TO BE L=X/(2*pi*F), or 50,000/(6.28*99)=80.4 uH!

This is not an illusion. If you have an inductance meter which uses 99
MHz as a test frequency, it WILL MEASURE 80.4 uH.

And therefore, I maintain that inductance DOES vary with frequency.

How can it be otherwise?

--
Bill, W6WRT

The inductance is not changing. What you are measuring is not pure
inductance but the coil has a stray capacitance. That is what is making the
coil seof resonate.

YOu did not say what hapens at 110 mhz, 200 mhz, and 500 mhz, if you did ,
it would measuer capacitance reactance. How do you change a coil into a
capacitor ? You don't , but the effect of reactance has.

Look at it this from a totally differant angle. You stick the leads of a DV
voltmeter in the wall socket. It does not show any deflection other than
maybe the first jump when it is plugged in. Does that mean there is no
voltage or power in the circuit, I think not. Stick your fingers in it and
see what hapens :-)

Your method is flawed in the same way, you only measured inductance ( not
really that , but the inductive reactance at a given frequency, but did not
measuer capcitance. Where did the capacitance come from ? It is what makes
the coil selfresonante. If you measuer a circuit that has inductance,
capacitance and resistance, depending on if it is series or pareallel
resonate here is what will hapen. As the frequency is increaced the
inductance reactance will increace, it will measuer resistance at the
reosnant frequency , then a large capacitance reactance and then a small
capacitance reactance or else the reverse will hapen, capacitive reactance,
resisstance, inductive reactance. However none of the actual inductance,
capacitance or resistance values will change. YOu are confusing inductacne
and reactance.

YOu are only seeing one part of the big picture. YOu have to look at
several formulars to see what is going on in a circuit that has inductance
and capacitance.

In article , Bill Turner
writes:

The disagreement here seems to depend on how one defines what inductance
is. I maintain that inductance of a coil is nothing more than the
reactance divided by 2piF, as derived from the formula above. Do you
disagree with that? That formula has been taught for decades. Are you
saying it is wrong?

I'm saying that the student doesn't understand inductance.

Inductance does NOT vary over frequency for any coil of wire under
its self-resonance.

Reactance varies over frequency with inductance fixed...directly
proportional to frequency. Inductance doesn't vary.

Yes, you can FIND inductance in Henries if you measure its
reactance at a particular frequency. Inductance in Henries has NOT
changed by doing so. Inductance in Henries remains constant.

[feel free to quibble over the spelling of "Henries" v. "Henrys" :-) ]

If your reactance-measuring gizmo is not calibrated properly, then
its readings will show an APPARENT change in inductance. The
inductance still hasn't changed...only the calibration of the gizmo
is off.

Don't get all wound up and take a turn for the worse...

Len Anderson
retired (from regular hours) electronic engineer person

In article , Bill Turner
writes:

The disagreement here seems to depend on how one defines what inductance
is. I maintain that inductance of a coil is nothing more than the
reactance divided by 2piF, as derived from the formula above. Do you
disagree with that? That formula has been taught for decades. Are you
saying it is wrong?

I'm saying that the student doesn't understand inductance.

Inductance does NOT vary over frequency for any coil of wire under
its self-resonance.

Reactance varies over frequency with inductance fixed...directly
proportional to frequency. Inductance doesn't vary.

Yes, you can FIND inductance in Henries if you measure its
reactance at a particular frequency. Inductance in Henries has NOT
changed by doing so. Inductance in Henries remains constant.

[feel free to quibble over the spelling of "Henries" v. "Henrys" :-) ]

If your reactance-measuring gizmo is not calibrated properly, then
its readings will show an APPARENT change in inductance. The
inductance still hasn't changed...only the calibration of the gizmo
is off.

Don't get all wound up and take a turn for the worse...

Len Anderson
retired (from regular hours) electronic engineer person

Bill Turner wrote:

On Tue, 09 Dec 2003 04:59:29 GMT, wrote:

I maintain it does. Otherwise the formula X=2piFL is invalid.

NO! In the above equation, X varies when F varies. The equation
does NOT mean that L varies as F varies.


__________________________________________________ _______

Perhaps an example will make it clear.

Suppose you have a coil which measures 1 uH at 1 MHz. It is known to
have a self-resonant (parallel) frequency of 100 MHz.

You measure its reactance at 1 MHz using the formula X=2*pi*F and find
it to be 6.28 ohms.
At 2 MHz you find it to be 12.56 ohms.
At 10 MHz you find it to be 62.8 ohms.
So far the reactance is changing linearly with respect to frequency.
(Actually it is not perfectly linear, but the difference at these
frequencies is small and probably would not be observed with run of the
mill test equipment.)

But, as you approach 100 MHz, you find the change is obviously no longer
linear.
At 95 MHz you would expect the reactance to be 6.28*95=596.6 ohms, but
much to your surprise, it measures 1000 ohms.
At 99 MHz, instead of the expected 6.28*99=621.72 ohms, it measures
50,000 ohms!!

All the above is perfectly normal and easily observable.

My point is that when a coil measures 50,000 ohms at 99 MHz, its
inductance HAS TO BE L=X/(2*pi*F), or 50,000/(6.28*99)=80.4 uH!

Here are your own words:
"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."

Your example ignores the capacitance, which you have stated
exists. There is nothing in your formula that addresses it.
You cannot use the formula or the math above (in your post) to
support your point of view, because it does not contain any
term for capacitance. The capacitance exists, and exhibits
a larger and larger affect on the circuit as the frequency
increases from 1 - 99 mHz.


This is not an illusion. If you have an inductance meter which uses 99
MHz as a test frequency, it WILL MEASURE 80.4 uH.

And therefore, I maintain that inductance DOES vary with frequency.

How can it be otherwise?

--
Bill, W6WRT

Bill Turner wrote:

On Tue, 09 Dec 2003 04:59:29 GMT, wrote:

I maintain it does. Otherwise the formula X=2piFL is invalid.

NO! In the above equation, X varies when F varies. The equation
does NOT mean that L varies as F varies.


__________________________________________________ _______

Perhaps an example will make it clear.

Suppose you have a coil which measures 1 uH at 1 MHz. It is known to
have a self-resonant (parallel) frequency of 100 MHz.

You measure its reactance at 1 MHz using the formula X=2*pi*F and find
it to be 6.28 ohms.
At 2 MHz you find it to be 12.56 ohms.
At 10 MHz you find it to be 62.8 ohms.
So far the reactance is changing linearly with respect to frequency.
(Actually it is not perfectly linear, but the difference at these
frequencies is small and probably would not be observed with run of the
mill test equipment.)

But, as you approach 100 MHz, you find the change is obviously no longer
linear.
At 95 MHz you would expect the reactance to be 6.28*95=596.6 ohms, but
much to your surprise, it measures 1000 ohms.
At 99 MHz, instead of the expected 6.28*99=621.72 ohms, it measures
50,000 ohms!!

All the above is perfectly normal and easily observable.

My point is that when a coil measures 50,000 ohms at 99 MHz, its
inductance HAS TO BE L=X/(2*pi*F), or 50,000/(6.28*99)=80.4 uH!

Here are your own words:
"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."

Your example ignores the capacitance, which you have stated
exists. There is nothing in your formula that addresses it.
You cannot use the formula or the math above (in your post) to
support your point of view, because it does not contain any
term for capacitance. The capacitance exists, and exhibits
a larger and larger affect on the circuit as the frequency
increases from 1 - 99 mHz.


This is not an illusion. If you have an inductance meter which uses 99
MHz as a test frequency, it WILL MEASURE 80.4 uH.

And therefore, I maintain that inductance DOES vary with frequency.

How can it be otherwise?

--
Bill, W6WRT

In article ,
Paul Burridge wrote:

You measure its reactance at 1 MHz using the formula X=2*pi*F and find
it to be 6.28 ohms.
At 2 MHz you find it to be 12.56 ohms.
At 10 MHz you find it to be 62.8 ohms.
So far the reactance is changing linearly with respect to frequency.
(Actually it is not perfectly linear, but the difference at these
frequencies is small and probably would not be observed with run of the
mill test equipment.)

But, as you approach 100 MHz, you find the change is obviously no longer
linear.
At 95 MHz you would expect the reactance to be 6.28*95=596.6 ohms, but
much to your surprise, it measures 1000 ohms.
At 99 MHz, instead of the expected 6.28*99=621.72 ohms, it measures
50,000 ohms!!

All the above is perfectly normal and easily observable.

My point is that when a coil measures 50,000 ohms at 99 MHz, its
inductance HAS TO BE L=X/(2*pi*F), or 50,000/(6.28*99)=80.4 uH!

This is not an illusion. If you have an inductance meter which uses 99
MHz as a test frequency, it WILL MEASURE 80.4 uH.

And therefore, I maintain that inductance DOES vary with frequency.

How can it be otherwise?

As Spock said to Kirk, "You proceed from a false assumption." Or, to
put it another way, the scenario you've just laid out contains an
inherent contradiction.

The inductance meter that you are using (or assuming) is not actually
measuring inductance. It's measuring reactance, and back-calculating
to what the inductance would be *if* it were measuring a "pure"
inductance.

However, as you recognize, the component that you are measuring is
*not* a pure inductance. Its actual reactance is the result of
interaction between its inductance, its inter-winding and distributed
capacitance, and its winding resistance (at any given frequency).

So, what you're observing can best be interpreted as follows:

- At low frequencies (well below resonance), the component's
reactance is dominated by its inductive component. It's a decent
approximation of a "pure" inductance. The inductance meter gives
accurate estimate of the inductive component.

- At high frequencies (well above resonance), the component's
reactance is dominated by its capacitive component. It becomes a
decent approximation of a "pure" capacitance at some point, I
suspect.

At these frequencies, your simple inductance meter lies through its
teeth. It "tells" you that the part's inductance is such-and-
such, but it's not telling you the truth. It's hiding from you
the fact that the reactance it's seeing isn't inductive at all (the
reactance decreases as frequency goes up, and exhibits a capacitive
phase angle).

So, I think, what you're facing here is the problem which occurs when
you try to force simplifying assumptions ("the component being
measured is a pure inductance" and "an inductance meter actually
measures inductance") outside the range in which these assumptions are
valid.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

In article ,
Paul Burridge wrote:

You measure its reactance at 1 MHz using the formula X=2*pi*F and find
it to be 6.28 ohms.
At 2 MHz you find it to be 12.56 ohms.
At 10 MHz you find it to be 62.8 ohms.
So far the reactance is changing linearly with respect to frequency.
(Actually it is not perfectly linear, but the difference at these
frequencies is small and probably would not be observed with run of the
mill test equipment.)

But, as you approach 100 MHz, you find the change is obviously no longer
linear.
At 95 MHz you would expect the reactance to be 6.28*95=596.6 ohms, but
much to your surprise, it measures 1000 ohms.
At 99 MHz, instead of the expected 6.28*99=621.72 ohms, it measures
50,000 ohms!!

All the above is perfectly normal and easily observable.

My point is that when a coil measures 50,000 ohms at 99 MHz, its
inductance HAS TO BE L=X/(2*pi*F), or 50,000/(6.28*99)=80.4 uH!

This is not an illusion. If you have an inductance meter which uses 99
MHz as a test frequency, it WILL MEASURE 80.4 uH.

And therefore, I maintain that inductance DOES vary with frequency.

How can it be otherwise?

As Spock said to Kirk, "You proceed from a false assumption." Or, to
put it another way, the scenario you've just laid out contains an
inherent contradiction.

The inductance meter that you are using (or assuming) is not actually
measuring inductance. It's measuring reactance, and back-calculating
to what the inductance would be *if* it were measuring a "pure"
inductance.

However, as you recognize, the component that you are measuring is
*not* a pure inductance. Its actual reactance is the result of
interaction between its inductance, its inter-winding and distributed
capacitance, and its winding resistance (at any given frequency).

So, what you're observing can best be interpreted as follows:

- At low frequencies (well below resonance), the component's
reactance is dominated by its inductive component. It's a decent
approximation of a "pure" inductance. The inductance meter gives
accurate estimate of the inductive component.

- At high frequencies (well above resonance), the component's
reactance is dominated by its capacitive component. It becomes a
decent approximation of a "pure" capacitance at some point, I
suspect.

At these frequencies, your simple inductance meter lies through its
teeth. It "tells" you that the part's inductance is such-and-
such, but it's not telling you the truth. It's hiding from you
the fact that the reactance it's seeing isn't inductive at all (the
reactance decreases as frequency goes up, and exhibits a capacitive
phase angle).

So, I think, what you're facing here is the problem which occurs when
you try to force simplifying assumptions ("the component being
measured is a pure inductance" and "an inductance meter actually
measures inductance") outside the range in which these assumptions are
valid.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

Bill Turner wrote:

On Tue, 9 Dec 2003 19:20:25 -0500, "Ralph Mowery"
wrote:

The inductance is not changing. What you are measuring is not pure
inductance but the coil has a stray capacitance. That is what is making the
coil seof resonate.

__________________________________________________ _______

I am well aware of that, but you are tap dancing around the relevance of
the formula X=2*pi*F*L.

Just answer this: If I have a coil of very high Q (no appreciable
resistance), and I apply 100 volts of 100 MHz AC to it, and measure a
current of 2 milliamps through it, then:

1. What is its reactance?
2. What is its inductance?

Its impedance has been measured to have a magnitude of 50,000 ohms.
If you have independent information that its Q is very high, you can
assume that this impedance is made up of some combination of inductive
reactance and capacitive reactance. With a single measurement such as
this, that is about all you can say.

It cannot be assumed to be all inductive reactance (or any particular
combination of inductive and capacitive reactances), just because
someone labeled the device as an inductor or because it looks like a
coil. Other measurements are needed to nail the details.

A parallel resonance with 50,000 ohms impedance (at some frequency) is
not the same thing as an inductance with 50,000 ohms of inductive
reactance (at the same frequency). They pass a similar magnitude of
current at that frequency for the same applied AC, but their current
phases do not match. And their reaction to nonsinusiodal waveforms is
very different.

--
John Popelish

Bill Turner wrote:

On Tue, 9 Dec 2003 19:20:25 -0500, "Ralph Mowery"
wrote:

The inductance is not changing. What you are measuring is not pure
inductance but the coil has a stray capacitance. That is what is making the
coil seof resonate.

__________________________________________________ _______

I am well aware of that, but you are tap dancing around the relevance of
the formula X=2*pi*F*L.

Just answer this: If I have a coil of very high Q (no appreciable
resistance), and I apply 100 volts of 100 MHz AC to it, and measure a
current of 2 milliamps through it, then:

1. What is its reactance?
2. What is its inductance?

Its impedance has been measured to have a magnitude of 50,000 ohms.
If you have independent information that its Q is very high, you can
assume that this impedance is made up of some combination of inductive
reactance and capacitive reactance. With a single measurement such as
this, that is about all you can say.

It cannot be assumed to be all inductive reactance (or any particular
combination of inductive and capacitive reactances), just because
someone labeled the device as an inductor or because it looks like a
coil. Other measurements are needed to nail the details.

A parallel resonance with 50,000 ohms impedance (at some frequency) is
not the same thing as an inductance with 50,000 ohms of inductive
reactance (at the same frequency). They pass a similar magnitude of
current at that frequency for the same applied AC, but their current
phases do not match. And their reaction to nonsinusiodal waveforms is
very different.

--
John Popelish

In article , Bill Turner
writes:

On Tue, 09 Dec 2003 04:59:29 GMT, wrote:

I maintain it does. Otherwise the formula X=2piFL is invalid.

NO! In the above equation, X varies when F varies. The equation
does NOT mean that L varies as F varies.

_________________________________________________ ________

Perhaps an example will make it clear.

Suppose you have a coil which measures 1 uH at 1 MHz. It is known to
have a self-resonant (parallel) frequency of 100 MHz.

OK, it has a distributed capacity of 2.533 pFd.

The circuit being measured is composed of a pure inductance
of 1.000 uHy and pure capacitance of 2.533 pFd in parallel.

We can neglect the losses in each one of those components
for the sake of illustration.

You measure its reactance at 1 MHz using the formula X=2*pi*F and find
it to be 6.28 ohms.

The inductive reactance is 6.28319 Ohms at 1 MHz and the
capacitive reactance is 62.8326 KOhms at 1 MHz.

In terms of susceptance, the B_sub_L is 0.159153 and
15.9153x10^-6 mhos, respectively. Total susceptance is then
0.159137 mhos or 6.28389 Ohms. [reactance meter probably isn't
calibrated that close to show the slight change due to distributed
capacity]

At 2 MHz you find it to be 12.56 ohms.

At 2 MHz, the inductive reactance is 12.5664 Ohms or 0.0795775
mhos while the distributed capacitance has 31.8306 mhos. The
total susceptance is 0.0795456 mhos or 12.5714 Ohms. That is
within 0.0907% of 12.56 Ohms and darn few reactance measuring
gizmos are calibrated that close...

At 10 MHz you find it to be 62.8 ohms.

Okay, at 10 MHz, the inductive susceptance is 0.0159155 mhos
and the capacitive susceptance is 159.153 x 10^-6 mhos, the
total being 0.0157563 mhos or 63.4665 Ohms reactance. That's
an error of 1.061% from 62.8 and still fairly reasonable for the error
of a reactance meter or whatever.

So far the reactance is changing linearly with respect to frequency.
(Actually it is not perfectly linear, but the difference at these
frequencies is small and probably would not be observed with run of the
mill test equipment.)

Okay, that's progress. We are agreed that test equipment can have
errors...he said with a grin having worked in metrology and a
standards lab for over 2 years in the past... :-)

But, as you approach 100 MHz, you find the change is obviously no longer
linear.

Ah, but you are measuring TWO things at the same time, the
parallel of the true inductor and its distributed capacity. Once you
are into measuring multiple elements, you need a test setup to
try to get a handle on the individual components. That is why I
brought up the "true inductance" two-frequency test on a Q meter
that has a calibrated tuning capacitor. That WILL establish the
equivalent pure capacitor due to distributed winding capacity in the
coil (the physical inductor form).

Once you KNOW the distributed capacity, its just a matter of some
button-pushing on a good scientific handheld calculator to derive
true inductance from the reactance readings of both inductance and
distributed capacity. [I recommend an HP 32 S II as an RPN fan]

The parallel capacitance will definitely exist as more picoFarads in
a circuit such as a FET gate which has a very high parallel resistance
(or very low conductance if you can think in terms of admittance).
That FET input capacitance will change the higher frequency resonance
even lower.

Offhand, I'd say that 2.533 pFd distributed capacity is rather high and
probably is around 1.0 pFd (solenoidal type, no core)...but a FET
gate input and its PCB traces to ground plane can be an additional
2.0 pFd. That's 3.0 pFd total and the self-resonance of that circuit is
now 91.888 MHz.

This is not an illusion. If you have an inductance meter which uses 99
MHz as a test frequency, it WILL MEASURE 80.4 uH.

That "inductance meter" is still measuring TWO THINGS AT THE
SAME TIME. The physical coil still has two components, the
pure inductance in parallel with a pure capacitance representing
the distributed capacity of the windings. Those are inseperable
unless you do something like the "true inductance" test at octave
separation frequencies or equivalent.

A Q Meter of any kind made today, last year, or back in the pre-
history before 1947, MEASURES THREE THINGS AT THE SAME
TIME! Yet the Q Meter is still accurate enough to derive the
equivalent parallel resistance, parallel inductance, and parallel
capacitance of the physical coil's windings. [it actually measures
conductance and susceptance as a total magnitude and relates
that to the Q or loss factor while the calibrated frequency setting
and calibrated variable capacitor allow separate "inductance"
measurement even though the Q Meter is "looking" at both L and
C_sub_d in parallel]

ANYONE using test equipment SHOULD be aware of what their
equipment does, how it works (in general), and what it really
measures. Since inductance does NOT change in a passive coil
(that isn't otherwise influenced by magnetic fields), what anyone
measures on a particular coil is THREE THINGS: The conductance
due to losses and the susceptance due to BOTH parallel inductance
and parallel capacitance. Conductance will change with frequency
depending on a lot of different factors (coil form, coil core, wire used,
shield used (if any), dielectric of the former material, core permittivity,
etc.). Susceptance will change with frequency because of the TWO
components...BUT THE INDUCTIVE COMPONENT DOES NOT
CHANGE.

And therefore, I maintain that inductance DOES vary with frequency.

How can it be otherwise?

The baseline taught in all textbooks (where I learned it first) and in
classes (where I learned it second) all agree that one MUST
separate the components into their "pure" form and THEN derive the
component parts by different tests. That is how it is perceived by
most other folks based on a lot of first-principle demonstration.

Inductance of a coil DOES NOT CHANGE WITH FREQUENCY.
Basic definition. First-principle stuff by definition.

You CAN say that APPARENT inductance changes if you are just
doing one kind of test. "Apparent" isn't going to work well when this
coil is dropped into a circuit thinking that "inductance changes with
frequency" and the circuit contains a lot of other sneaky little
components that can shoot the "apparent" reading way off. No one
successfully works with L-C and active-device networks using this
"apparent" reading. One separates the component parts first, then
combines them into manageable parallel-equivalent or series-equivalent
circuits.

The ILLUSION is from looking at an impedance- or admittance-measuring
instrument such as a Q Meter and thinking its calibrated inductance
dial "measures inductance." It doesn't...but it comes very close. That is
just the calibrated variable capacitor tuning to resonance at specific
frequencies...as a convenience to the user. The capacitance markings
will be accurate but any external coil that has significant parallel
capacitance from its windings will add to the calibrated capacity on the
dial. Some Q Meters allow variable frequency settings to do things
like the octave-separation-of-frequency measurement of the external
test parallel capacity.

An impedance or admittance bridge type of instrument can yield
different "errors" and "illusions" depending on their type/kind.

Len Anderson
retired (from regular hours) electronic engineer person