"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante)
wrote:


Hmm. Pardon me if I am drifting off topic here, but I and a collegue
of mine recently noticed a quite noticeable deviance from the Z=wL in
the impedance of inductors in the HF range. These inductors were made
of standard ~0.3mm (I'll have to check this) wires and no iron core
(for loudspeaker crossovers). Any explanation to this, apart from
skin?
http://www.tolvan.com/coil.gif
Note that I don't claim big *audible* effects from this in most
applications, though.


In a series circuit containing resistance, inductance, and capacitance,
the impedance (Z) of the circuit will be equal to the square root of the
sums of the squares of the resistance and the square of the difference
between the inductive and capacitive reactance. That is,

Z = sqrt (R² + (Xl - Xc)²)

Of course, in a circuit containing only inductance, the inductive
reactance and impedance will be equal. However, such a scenario is
impossible and the effects of capacitance and resistance must always be
considered if accuracy is important.

Looking at just the inductor, since there is a voltage difference
between turns and the turns are dielectrically isolated from each other,
that gives rise to an inherent capacitance and since there is resistance
in the wire used to wind the inductor, that's also part of the inductor
and can't be separated from it. There are winding techniques used to
minimize the capacitance (which appears to be in _parallel_ with the
inductance) but in the case of coils wound for loudspeaker crossovers,
I'd seriously doubt whether the slightest consideration was given to
them.

Just to test the possibility of a parallel capacitance I entered it
into the program (it's another coil now, I could not find the first
one again). It turns out that I can get a pretty good match if I
parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a
resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of
this circuit will be just above 20 kHz (the limit of the soundcard)
and I get the feeling that the match will be very poor at higher
frequencies. Also, a stray capacitance of 0.22 uF appears very much,
so I don't beleive in it.

---
You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the
impedance curve to bend away from the model as the impedance changes.
To test the idea I took three resistors that happened to be on my
desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my
program showed 10.2 47.0 and 68.5 ohms respectively. That seems to
rule out this explanation since impedances in the range 10-68 ohms
seems to be measured accurately. Also the impedance curves of the
resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20
kHz, which would indicate a low stray capacitance in the equipment)
Resistor curves available at:
http://www.tolvan.com/10-47-68ohm.gif

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

Be that as it may, at resonance the reactances of the inductor and
capacitor will be equal, but opposite in sign, and in a series circuit
will cancel, leaving behind only the resistance of the circuit as the
impedance. If, then, you connect the resonant circuit in series with
your load:

Vin----[R]--[L]--[C]--+
|
[Rl]
|
Vret------------------+

And your load is totally resistive, the voltage across the load will
peak at the resonant frequency of the LC, whe

1
f = ------------
2pi(sqrt LC)

and will fall away from the peak value on either side of resonance, with
the result being that the LC will form a bandpass filter.


No problem with that.


With the circuit in parallel with the load:

Vin----+-----+
| |
[R] |
| |
[L] [Rl]
| |
[C] |
| |
Vret----+-----+

The voltage across the load will be at a minimum at the resonant
frequency of the LC and will rise on either side of resonance, making
the response that of a band-reject, or notch, filter.


Ok


In a parallel resonant circuit (a "tank"), however, the cancellation of
the reactances will give rise to circulating currents in the tank which
will only be limited by the series resistance of the elements comprising
the tank and the impedance will rise to a very high value.

Such being the case, a parallel resonant circuit connected in parallel
with a purely resistive load will be a bandpass filter, and connected in
series with the load will look like a notch at resonance; exactly the
opposite of the series tuned circuit.


I'm still with you.



Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).


Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close. My best
model fit was 0.22mH, and I think that the resonance in my simulation
was slightly above 20 kHz, so everything adds up fine. In the graph
http://www.tolvan.com/coil1.gif
we see the model impedance without the parallel cap being some 28
ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that
model (blue curve) seems OK too.


---

I suspect the resistance of the wire is what's causing the
deviation from "ideal" inductance, and I also suspect that skin effect
has _nothing_ to do with it since that's an effect which starts to
become significant at radio frequencies.

You say that you suspect the resistance to be responsible for the
increased impedance. Is there another effect than the skin effect that
could cause the resistance to increase with frequency?

---
There shouldn't be.
---


The new curve fittings can be seen at:
http://www.tolvan.com/coil1.gif
blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is
the same model paralleled with 0.22uF+33ohm, black is measured data.
Don't pay too much attention to the measured phase curve, I have a
delay between channels that ruins the HF phase response.

A photo of this particular coil is available at:
http://www.tolvan.com/coil1.jpg
wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm,
height 13 mm.

Could you or someone else verify that coils really do like this? I
have used different soundcards and differenct coils for the
measurements, but the same home-brewed program, so it would be nice
with a verification from someone else.
A 10 ohm resistor produces a straight line within 0.2 ohm using the
same equipment (phase is -130 degrees at 20kHz due to the delay I
mentioned :-( ).

---
Rather than trust a simulator, I'd actually _measure_ the self-resonant
frequency of the coil to determine what its distributed capacitance is
or, failing that, at the very least measure the resonant frequency at a
couple of places using known parallel and series capacitances in order
to determine what its true inductance is at different frequencies.

Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

So, I still only have the skin effect as a candidate. Hmmm...

Thanks,
Svante

John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante)
wrote:


Hmm. Pardon me if I am drifting off topic here, but I and a collegue
of mine recently noticed a quite noticeable deviance from the Z=wL in
the impedance of inductors in the HF range. These inductors were made
of standard ~0.3mm (I'll have to check this) wires and no iron core
(for loudspeaker crossovers). Any explanation to this, apart from
skin?
http://www.tolvan.com/coil.gif
Note that I don't claim big *audible* effects from this in most
applications, though.


In a series circuit containing resistance, inductance, and capacitance,
the impedance (Z) of the circuit will be equal to the square root of the
sums of the squares of the resistance and the square of the difference
between the inductive and capacitive reactance. That is,

Z = sqrt (R² + (Xl - Xc)²)

Of course, in a circuit containing only inductance, the inductive
reactance and impedance will be equal. However, such a scenario is
impossible and the effects of capacitance and resistance must always be
considered if accuracy is important.

Looking at just the inductor, since there is a voltage difference
between turns and the turns are dielectrically isolated from each other,
that gives rise to an inherent capacitance and since there is resistance
in the wire used to wind the inductor, that's also part of the inductor
and can't be separated from it. There are winding techniques used to
minimize the capacitance (which appears to be in _parallel_ with the
inductance) but in the case of coils wound for loudspeaker crossovers,
I'd seriously doubt whether the slightest consideration was given to
them.

Just to test the possibility of a parallel capacitance I entered it
into the program (it's another coil now, I could not find the first
one again). It turns out that I can get a pretty good match if I
parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a
resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of
this circuit will be just above 20 kHz (the limit of the soundcard)
and I get the feeling that the match will be very poor at higher
frequencies. Also, a stray capacitance of 0.22 uF appears very much,
so I don't beleive in it.

---
You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the
impedance curve to bend away from the model as the impedance changes.
To test the idea I took three resistors that happened to be on my
desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my
program showed 10.2 47.0 and 68.5 ohms respectively. That seems to
rule out this explanation since impedances in the range 10-68 ohms
seems to be measured accurately. Also the impedance curves of the
resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20
kHz, which would indicate a low stray capacitance in the equipment)
Resistor curves available at:
http://www.tolvan.com/10-47-68ohm.gif

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

Be that as it may, at resonance the reactances of the inductor and
capacitor will be equal, but opposite in sign, and in a series circuit
will cancel, leaving behind only the resistance of the circuit as the
impedance. If, then, you connect the resonant circuit in series with
your load:

Vin----[R]--[L]--[C]--+
|
[Rl]
|
Vret------------------+

And your load is totally resistive, the voltage across the load will
peak at the resonant frequency of the LC, whe

1
f = ------------
2pi(sqrt LC)

and will fall away from the peak value on either side of resonance, with
the result being that the LC will form a bandpass filter.


No problem with that.


With the circuit in parallel with the load:

Vin----+-----+
| |
[R] |
| |
[L] [Rl]
| |
[C] |
| |
Vret----+-----+

The voltage across the load will be at a minimum at the resonant
frequency of the LC and will rise on either side of resonance, making
the response that of a band-reject, or notch, filter.


Ok


In a parallel resonant circuit (a "tank"), however, the cancellation of
the reactances will give rise to circulating currents in the tank which
will only be limited by the series resistance of the elements comprising
the tank and the impedance will rise to a very high value.

Such being the case, a parallel resonant circuit connected in parallel
with a purely resistive load will be a bandpass filter, and connected in
series with the load will look like a notch at resonance; exactly the
opposite of the series tuned circuit.


I'm still with you.



Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).


Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close. My best
model fit was 0.22mH, and I think that the resonance in my simulation
was slightly above 20 kHz, so everything adds up fine. In the graph
http://www.tolvan.com/coil1.gif
we see the model impedance without the parallel cap being some 28
ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that
model (blue curve) seems OK too.


---

I suspect the resistance of the wire is what's causing the
deviation from "ideal" inductance, and I also suspect that skin effect
has _nothing_ to do with it since that's an effect which starts to
become significant at radio frequencies.

You say that you suspect the resistance to be responsible for the
increased impedance. Is there another effect than the skin effect that
could cause the resistance to increase with frequency?

---
There shouldn't be.
---


The new curve fittings can be seen at:
http://www.tolvan.com/coil1.gif
blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is
the same model paralleled with 0.22uF+33ohm, black is measured data.
Don't pay too much attention to the measured phase curve, I have a
delay between channels that ruins the HF phase response.

A photo of this particular coil is available at:
http://www.tolvan.com/coil1.jpg
wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm,
height 13 mm.

Could you or someone else verify that coils really do like this? I
have used different soundcards and differenct coils for the
measurements, but the same home-brewed program, so it would be nice
with a verification from someone else.
A 10 ohm resistor produces a straight line within 0.2 ohm using the
same equipment (phase is -130 degrees at 20kHz due to the delay I
mentioned :-( ).

---
Rather than trust a simulator, I'd actually _measure_ the self-resonant
frequency of the coil to determine what its distributed capacitance is
or, failing that, at the very least measure the resonant frequency at a
couple of places using known parallel and series capacitances in order
to determine what its true inductance is at different frequencies.

Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

So, I still only have the skin effect as a candidate. Hmmm...

Thanks,
Svante

John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante)
wrote:


Hmm. Pardon me if I am drifting off topic here, but I and a collegue
of mine recently noticed a quite noticeable deviance from the Z=wL in
the impedance of inductors in the HF range. These inductors were made
of standard ~0.3mm (I'll have to check this) wires and no iron core
(for loudspeaker crossovers). Any explanation to this, apart from
skin?
http://www.tolvan.com/coil.gif
Note that I don't claim big *audible* effects from this in most
applications, though.


In a series circuit containing resistance, inductance, and capacitance,
the impedance (Z) of the circuit will be equal to the square root of the
sums of the squares of the resistance and the square of the difference
between the inductive and capacitive reactance. That is,

Z = sqrt (R² + (Xl - Xc)²)

Of course, in a circuit containing only inductance, the inductive
reactance and impedance will be equal. However, such a scenario is
impossible and the effects of capacitance and resistance must always be
considered if accuracy is important.

Looking at just the inductor, since there is a voltage difference
between turns and the turns are dielectrically isolated from each other,
that gives rise to an inherent capacitance and since there is resistance
in the wire used to wind the inductor, that's also part of the inductor
and can't be separated from it. There are winding techniques used to
minimize the capacitance (which appears to be in _parallel_ with the
inductance) but in the case of coils wound for loudspeaker crossovers,
I'd seriously doubt whether the slightest consideration was given to
them.

Just to test the possibility of a parallel capacitance I entered it
into the program (it's another coil now, I could not find the first
one again). It turns out that I can get a pretty good match if I
parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a
resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of
this circuit will be just above 20 kHz (the limit of the soundcard)
and I get the feeling that the match will be very poor at higher
frequencies. Also, a stray capacitance of 0.22 uF appears very much,
so I don't beleive in it.

---
You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the
impedance curve to bend away from the model as the impedance changes.
To test the idea I took three resistors that happened to be on my
desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my
program showed 10.2 47.0 and 68.5 ohms respectively. That seems to
rule out this explanation since impedances in the range 10-68 ohms
seems to be measured accurately. Also the impedance curves of the
resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20
kHz, which would indicate a low stray capacitance in the equipment)
Resistor curves available at:
http://www.tolvan.com/10-47-68ohm.gif

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

Be that as it may, at resonance the reactances of the inductor and
capacitor will be equal, but opposite in sign, and in a series circuit
will cancel, leaving behind only the resistance of the circuit as the
impedance. If, then, you connect the resonant circuit in series with
your load:

Vin----[R]--[L]--[C]--+
|
[Rl]
|
Vret------------------+

And your load is totally resistive, the voltage across the load will
peak at the resonant frequency of the LC, whe

1
f = ------------
2pi(sqrt LC)

and will fall away from the peak value on either side of resonance, with
the result being that the LC will form a bandpass filter.


No problem with that.


With the circuit in parallel with the load:

Vin----+-----+
| |
[R] |
| |
[L] [Rl]
| |
[C] |
| |
Vret----+-----+

The voltage across the load will be at a minimum at the resonant
frequency of the LC and will rise on either side of resonance, making
the response that of a band-reject, or notch, filter.


Ok


In a parallel resonant circuit (a "tank"), however, the cancellation of
the reactances will give rise to circulating currents in the tank which
will only be limited by the series resistance of the elements comprising
the tank and the impedance will rise to a very high value.

Such being the case, a parallel resonant circuit connected in parallel
with a purely resistive load will be a bandpass filter, and connected in
series with the load will look like a notch at resonance; exactly the
opposite of the series tuned circuit.


I'm still with you.



Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).


Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close. My best
model fit was 0.22mH, and I think that the resonance in my simulation
was slightly above 20 kHz, so everything adds up fine. In the graph
http://www.tolvan.com/coil1.gif
we see the model impedance without the parallel cap being some 28
ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that
model (blue curve) seems OK too.


---

I suspect the resistance of the wire is what's causing the
deviation from "ideal" inductance, and I also suspect that skin effect
has _nothing_ to do with it since that's an effect which starts to
become significant at radio frequencies.

You say that you suspect the resistance to be responsible for the
increased impedance. Is there another effect than the skin effect that
could cause the resistance to increase with frequency?

---
There shouldn't be.
---


The new curve fittings can be seen at:
http://www.tolvan.com/coil1.gif
blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is
the same model paralleled with 0.22uF+33ohm, black is measured data.
Don't pay too much attention to the measured phase curve, I have a
delay between channels that ruins the HF phase response.

A photo of this particular coil is available at:
http://www.tolvan.com/coil1.jpg
wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm,
height 13 mm.

Could you or someone else verify that coils really do like this? I
have used different soundcards and differenct coils for the
measurements, but the same home-brewed program, so it would be nice
with a verification from someone else.
A 10 ohm resistor produces a straight line within 0.2 ohm using the
same equipment (phase is -130 degrees at 20kHz due to the delay I
mentioned :-( ).

---
Rather than trust a simulator, I'd actually _measure_ the self-resonant
frequency of the coil to determine what its distributed capacitance is
or, failing that, at the very least measure the resonant frequency at a
couple of places using known parallel and series capacitances in order
to determine what its true inductance is at different frequencies.

Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

So, I still only have the skin effect as a candidate. Hmmm...

Thanks,
Svante

John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante)
wrote:


Hmm. Pardon me if I am drifting off topic here, but I and a collegue
of mine recently noticed a quite noticeable deviance from the Z=wL in
the impedance of inductors in the HF range. These inductors were made
of standard ~0.3mm (I'll have to check this) wires and no iron core
(for loudspeaker crossovers). Any explanation to this, apart from
skin?
http://www.tolvan.com/coil.gif
Note that I don't claim big *audible* effects from this in most
applications, though.


In a series circuit containing resistance, inductance, and capacitance,
the impedance (Z) of the circuit will be equal to the square root of the
sums of the squares of the resistance and the square of the difference
between the inductive and capacitive reactance. That is,

Z = sqrt (R² + (Xl - Xc)²)

Of course, in a circuit containing only inductance, the inductive
reactance and impedance will be equal. However, such a scenario is
impossible and the effects of capacitance and resistance must always be
considered if accuracy is important.

Looking at just the inductor, since there is a voltage difference
between turns and the turns are dielectrically isolated from each other,
that gives rise to an inherent capacitance and since there is resistance
in the wire used to wind the inductor, that's also part of the inductor
and can't be separated from it. There are winding techniques used to
minimize the capacitance (which appears to be in _parallel_ with the
inductance) but in the case of coils wound for loudspeaker crossovers,
I'd seriously doubt whether the slightest consideration was given to
them.

Just to test the possibility of a parallel capacitance I entered it
into the program (it's another coil now, I could not find the first
one again). It turns out that I can get a pretty good match if I
parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a
resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of
this circuit will be just above 20 kHz (the limit of the soundcard)
and I get the feeling that the match will be very poor at higher
frequencies. Also, a stray capacitance of 0.22 uF appears very much,
so I don't beleive in it.

---
You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the
impedance curve to bend away from the model as the impedance changes.
To test the idea I took three resistors that happened to be on my
desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my
program showed 10.2 47.0 and 68.5 ohms respectively. That seems to
rule out this explanation since impedances in the range 10-68 ohms
seems to be measured accurately. Also the impedance curves of the
resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20
kHz, which would indicate a low stray capacitance in the equipment)
Resistor curves available at:
http://www.tolvan.com/10-47-68ohm.gif

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

Be that as it may, at resonance the reactances of the inductor and
capacitor will be equal, but opposite in sign, and in a series circuit
will cancel, leaving behind only the resistance of the circuit as the
impedance. If, then, you connect the resonant circuit in series with
your load:

Vin----[R]--[L]--[C]--+
|
[Rl]
|
Vret------------------+

And your load is totally resistive, the voltage across the load will
peak at the resonant frequency of the LC, whe

1
f = ------------
2pi(sqrt LC)

and will fall away from the peak value on either side of resonance, with
the result being that the LC will form a bandpass filter.


No problem with that.


With the circuit in parallel with the load:

Vin----+-----+
| |
[R] |
| |
[L] [Rl]
| |
[C] |
| |
Vret----+-----+

The voltage across the load will be at a minimum at the resonant
frequency of the LC and will rise on either side of resonance, making
the response that of a band-reject, or notch, filter.


Ok


In a parallel resonant circuit (a "tank"), however, the cancellation of
the reactances will give rise to circulating currents in the tank which
will only be limited by the series resistance of the elements comprising
the tank and the impedance will rise to a very high value.

Such being the case, a parallel resonant circuit connected in parallel
with a purely resistive load will be a bandpass filter, and connected in
series with the load will look like a notch at resonance; exactly the
opposite of the series tuned circuit.


I'm still with you.



Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).


Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close. My best
model fit was 0.22mH, and I think that the resonance in my simulation
was slightly above 20 kHz, so everything adds up fine. In the graph
http://www.tolvan.com/coil1.gif
we see the model impedance without the parallel cap being some 28
ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that
model (blue curve) seems OK too.


---

I suspect the resistance of the wire is what's causing the
deviation from "ideal" inductance, and I also suspect that skin effect
has _nothing_ to do with it since that's an effect which starts to
become significant at radio frequencies.

You say that you suspect the resistance to be responsible for the
increased impedance. Is there another effect than the skin effect that
could cause the resistance to increase with frequency?

---
There shouldn't be.
---


The new curve fittings can be seen at:
http://www.tolvan.com/coil1.gif
blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is
the same model paralleled with 0.22uF+33ohm, black is measured data.
Don't pay too much attention to the measured phase curve, I have a
delay between channels that ruins the HF phase response.

A photo of this particular coil is available at:
http://www.tolvan.com/coil1.jpg
wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm,
height 13 mm.

Could you or someone else verify that coils really do like this? I
have used different soundcards and differenct coils for the
measurements, but the same home-brewed program, so it would be nice
with a verification from someone else.
A 10 ohm resistor produces a straight line within 0.2 ohm using the
same equipment (phase is -130 degrees at 20kHz due to the delay I
mentioned :-( ).

---
Rather than trust a simulator, I'd actually _measure_ the self-resonant
frequency of the coil to determine what its distributed capacitance is
or, failing that, at the very least measure the resonant frequency at a
couple of places using known parallel and series capacitances in order
to determine what its true inductance is at different frequencies.

Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

So, I still only have the skin effect as a candidate. Hmmm...

Thanks,
Svante

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

:-) Right, but I think I have tested the equipment in a post right
after yours, and I think it is OK. Measurning 10, 47 and 68 ohm
resistors give straight lines at 10 47 and 68 ohms,
http://www.tolvan.com/10-47-68ohm.gif

Adding a parallel cap of 0.47uF gives the "right" resonance frequency
of 15600Hz:
http://www.tolvan.com/coil1+047uF.gif
but the Q is wrong. I think the impedance curve is correct. I keep
being left with the skin effect here, which is the only effect I
cannot do the math for yet.

Ideas?
(original measurement at: http://www.tolvan.com/coil1.gif , black
curve )

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

:-) Right, but I think I have tested the equipment in a post right
after yours, and I think it is OK. Measurning 10, 47 and 68 ohm
resistors give straight lines at 10 47 and 68 ohms,
http://www.tolvan.com/10-47-68ohm.gif

Adding a parallel cap of 0.47uF gives the "right" resonance frequency
of 15600Hz:
http://www.tolvan.com/coil1+047uF.gif
but the Q is wrong. I think the impedance curve is correct. I keep
being left with the skin effect here, which is the only effect I
cannot do the math for yet.

Ideas?
(original measurement at: http://www.tolvan.com/coil1.gif , black
curve )

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

:-) Right, but I think I have tested the equipment in a post right
after yours, and I think it is OK. Measurning 10, 47 and 68 ohm
resistors give straight lines at 10 47 and 68 ohms,
http://www.tolvan.com/10-47-68ohm.gif

Adding a parallel cap of 0.47uF gives the "right" resonance frequency
of 15600Hz:
http://www.tolvan.com/coil1+047uF.gif
but the Q is wrong. I think the impedance curve is correct. I keep
being left with the skin effect here, which is the only effect I
cannot do the math for yet.

Ideas?
(original measurement at: http://www.tolvan.com/coil1.gif , black
curve )

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:

"Arny Krueger" wrote in message ...
"Svante" wrote in message
om

Do you think that a 0.22 uF stray capacitance is likely in this case?
That is what the red curve is (+ 33 ohm in series with the capacitance
for best fit, modeled).

How many feet of wire in that coil? There might be something like 30 pF of
stray capacitance per foot of wire in the coil.

Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which
would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26
feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF.
Is it possible that it is the skin effect anyway? So far it is the
only explanation that I have not been able to rule out. That or my
software. Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

John's dad say: "Never trust measurement that give wrong answer."

:-) Right, but I think I have tested the equipment in a post right
after yours, and I think it is OK. Measurning 10, 47 and 68 ohm
resistors give straight lines at 10 47 and 68 ohms,
http://www.tolvan.com/10-47-68ohm.gif

Adding a parallel cap of 0.47uF gives the "right" resonance frequency
of 15600Hz:
http://www.tolvan.com/coil1+047uF.gif
but the Q is wrong. I think the impedance curve is correct. I keep
being left with the skin effect here, which is the only effect I
cannot do the math for yet.

Ideas?
(original measurement at: http://www.tolvan.com/coil1.gif , black
curve )

Responding to myself...

(Svante) wrote in message

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the

Sorry, I didn't mean the precision of the 47 ohm resistor, this error
will propagate independent of the measured impedance, I mean the level
match between L and R channels. This error will be large for high
impedances, but as the tests showed 68 ohms are still OK.

Responding to myself...

(Svante) wrote in message

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the

Sorry, I didn't mean the precision of the 47 ohm resistor, this error
will propagate independent of the measured impedance, I mean the level
match between L and R channels. This error will be large for high
impedances, but as the tests showed 68 ohms are still OK.

Responding to myself...

(Svante) wrote in message

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the

Sorry, I didn't mean the precision of the 47 ohm resistor, this error
will propagate independent of the measured impedance, I mean the level
match between L and R channels. This error will be large for high
impedances, but as the tests showed 68 ohms are still OK.

Responding to myself...

(Svante) wrote in message

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.
I suddenly realise a possible error source here, but as I check it, it
does not appear to be the problem.
I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be
a measurement error, which will vary with the resistance. Error
percentages are likely to be smallest near 47 ohms, and increase as we
move away from this resistance. Such an error could cause the

Sorry, I didn't mean the precision of the 47 ohm resistor, this error
will propagate independent of the measured impedance, I mean the level
match between L and R channels. This error will be large for high
impedances, but as the tests showed 68 ohms are still OK.

On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote:


You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

---
I don't know what your equipment setup looks like, but offhand I'd say
your measurement technique may be flawed in that you seem to be treating
the LR combination as a simple voltage divider without taking phase into
consideration.
---

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

---
What has happened that has caused the peak to broaden is that the Q of
the circuit has been lowered. That can happen because of either series
resistance _in_ the tank or parallel resistance _across_ the tank. Take
a look at the impedance of what you're using to measure the voltage
across the tank with and you may find it there.
---


Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).

---
2.2E-5 actually, but yes, you're right. Good catch.
---

Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close.

---
Plugging in the 36 ohms for Xl gives us

L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH

which is a 70µH error. That comes out to about 32% referred to your
220µH, but when you consider the tolerance of the coil, the cap, and
whatever you used to measure the resonant frequency with, it's in the
ball park.
---


Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

---
Apparently. Another test you may want to run is to parallel the coil
with various capacitors while it's being excited with your cal square
wave and see what happens. You should certainly see the ringing with
0.2µF across the coil. You'll notice that as you decrease the
capacitance the ringing frequency will increase and the ringing envelope
will become shorter and shorter until you'll just see the LdI/Dt spikes
your photos show.

BTW, at that point there'll still be some ringing happening, but it'll
be so fast you won't be able to see it unless the bandwidth of your
scope's vertical amplifier(s) is wide enough.


So, I still only have the skin effect as a candidate. Hmmm...

---
No, you still have Q to consider, and I believe that if you look into
it, you'll find that's what's causing the broadening.

After all, the resonances are where they're supposed to be for the
values of the components, so as the impedance of the tank rises as it
gets nearer to resonance, any resistance in the circuit will tend to
swamp out the nice high impedance peak which would be there without the
extra R spoiling it.

Kind of like if you try to measure the voltage across a 10Mohm resistor
with a voltmeter having an input resistance of 10Mohms!

--
John Fields

On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote:


You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

---
I don't know what your equipment setup looks like, but offhand I'd say
your measurement technique may be flawed in that you seem to be treating
the LR combination as a simple voltage divider without taking phase into
consideration.
---

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

---
What has happened that has caused the peak to broaden is that the Q of
the circuit has been lowered. That can happen because of either series
resistance _in_ the tank or parallel resistance _across_ the tank. Take
a look at the impedance of what you're using to measure the voltage
across the tank with and you may find it there.
---


Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).

---
2.2E-5 actually, but yes, you're right. Good catch.
---

Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close.

---
Plugging in the 36 ohms for Xl gives us

L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH

which is a 70µH error. That comes out to about 32% referred to your
220µH, but when you consider the tolerance of the coil, the cap, and
whatever you used to measure the resonant frequency with, it's in the
ball park.
---


Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

---
Apparently. Another test you may want to run is to parallel the coil
with various capacitors while it's being excited with your cal square
wave and see what happens. You should certainly see the ringing with
0.2µF across the coil. You'll notice that as you decrease the
capacitance the ringing frequency will increase and the ringing envelope
will become shorter and shorter until you'll just see the LdI/Dt spikes
your photos show.

BTW, at that point there'll still be some ringing happening, but it'll
be so fast you won't be able to see it unless the bandwidth of your
scope's vertical amplifier(s) is wide enough.


So, I still only have the skin effect as a candidate. Hmmm...

---
No, you still have Q to consider, and I believe that if you look into
it, you'll find that's what's causing the broadening.

After all, the resonances are where they're supposed to be for the
values of the components, so as the impedance of the tank rises as it
gets nearer to resonance, any resistance in the circuit will tend to
swamp out the nice high impedance peak which would be there without the
extra R spoiling it.

Kind of like if you try to measure the voltage across a 10Mohm resistor
with a voltmeter having an input resistance of 10Mohms!

--
John Fields

On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote:


You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

---
I don't know what your equipment setup looks like, but offhand I'd say
your measurement technique may be flawed in that you seem to be treating
the LR combination as a simple voltage divider without taking phase into
consideration.
---

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

---
What has happened that has caused the peak to broaden is that the Q of
the circuit has been lowered. That can happen because of either series
resistance _in_ the tank or parallel resistance _across_ the tank. Take
a look at the impedance of what you're using to measure the voltage
across the tank with and you may find it there.
---


Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).

---
2.2E-5 actually, but yes, you're right. Good catch.
---

Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close.

---
Plugging in the 36 ohms for Xl gives us

L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH

which is a 70µH error. That comes out to about 32% referred to your
220µH, but when you consider the tolerance of the coil, the cap, and
whatever you used to measure the resonant frequency with, it's in the
ball park.
---


Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

---
Apparently. Another test you may want to run is to parallel the coil
with various capacitors while it's being excited with your cal square
wave and see what happens. You should certainly see the ringing with
0.2µF across the coil. You'll notice that as you decrease the
capacitance the ringing frequency will increase and the ringing envelope
will become shorter and shorter until you'll just see the LdI/Dt spikes
your photos show.

BTW, at that point there'll still be some ringing happening, but it'll
be so fast you won't be able to see it unless the bandwidth of your
scope's vertical amplifier(s) is wide enough.


So, I still only have the skin effect as a candidate. Hmmm...

---
No, you still have Q to consider, and I believe that if you look into
it, you'll find that's what's causing the broadening.

After all, the resonances are where they're supposed to be for the
values of the components, so as the impedance of the tank rises as it
gets nearer to resonance, any resistance in the circuit will tend to
swamp out the nice high impedance peak which would be there without the
extra R spoiling it.

Kind of like if you try to measure the voltage across a 10Mohm resistor
with a voltmeter having an input resistance of 10Mohms!

--
John Fields

On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote:


You haven't described what you mean by a "match" or how the circuit is
implemented, so it's difficult to keep from guessing about what you're
trying to accomplish.

By "match" I mean tweaking the values of R1, R2, C and L (see graphs
below) by hand to make the curves fit the measured black curve as well
as possible. I tried to indicate the circuit I used with my way of
writing the parantheses, but anyway, here is a go with ASCII graphics
instead (view with courier):

--------------
|
L=0.22mH
Z = |
R1=0.7ohm
|
--------------

That was the blue curve in my simulation (
http://www.tolvan.com/coil1.gif ), and here is the red one:

----------*------------
| |
C=0.22uF L=0.22mH
Z = | |
R2=33ohm R1=0.7ohm
| |
----------*------------

My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

---
I don't know what your equipment setup looks like, but offhand I'd say
your measurement technique may be flawed in that you seem to be treating
the LR combination as a simple voltage divider without taking phase into
consideration.
---

OK, another experiment:
Paralleling the coil with a 0.47uF cap yields a resonance frequency of
15800 Hz, as seen from the location of the peak of the measured black
curve in:
http://www.tolvan.com/coil1+047uF.gif
The green curve is a model

----------*------------
| |
0.47uF 0.22mH
Z = | |
| 0.7ohm
| |
----------*------------


The resonance frequency is consistent with

1
f = ------------
2pi(sqrt LC)

which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This
pretty much rules out a stray capacitance of 0.22 uF, the resonance
frequency should then have been
1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz.
The broadening of the resonance peak, compared to the model, indicates
to me that something has happened to the resistance rather than with
the reactance at high frequencies.

---
What has happened that has caused the peak to broaden is that the Q of
the circuit has been lowered. That can happen because of either series
resistance _in_ the tank or parallel resistance _across_ the tank. Take
a look at the impedance of what you're using to measure the voltage
across the tank with and you may find it there.
---


Since the inductive and capacitive reactances will be equal at
resonance, for 0.22µF and 20kHz we have:

Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms

I get 36 ohms (typo here I think, should be 0.22E-6).

---
2.2E-5 actually, but yes, you're right. Good catch.
---

Then, for the inductance to have a reactance of 3.6 ohms, we have:

Xl = 2pifL

so, rearranging to solve for L,

L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH

Is that what the inductance of the coil at 20kHz is supposed to be?

Actually, 0.2 mH, but given the typo above you are close.

---
Plugging in the 36 ohms for Xl gives us

L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH

which is a 70µH error. That comes out to about 32% referred to your
220µH, but when you consider the tolerance of the coil, the cap, and
whatever you used to measure the resonant frequency with, it's in the
ball park.
---


Ok, lacking equipment to measure other than audio frequency at home, I
grabbed my old oscilloscope and connected this circuit to the probe
calibration square wave.


probe cal -----1 kohm------*-------ch2
|
coil
|
GND -----------------

http://www.tolvan.com/coilresonanceconnection.jpg

There is definitely no 20 kHz ringing
http://www.tolvan.com/coilresonancetrace1.jpg
and expanding the time scale
http://www.tolvan.com/coilresonancetrace2.jpg
reveals no resonances either.
Sorry about the poor focus. Obviously the scope does not deliver a
perfect square wave, but if there were (high Q) resonances they should
be seen here as ringings anyway. This tells me that the stray
capacitance of the coil is low, or at least not 0.22uF, which IMO
rules out the parallel capacitance theory as an explanation to the
increasing impedance of the coil in the upper audio band.

---
Apparently. Another test you may want to run is to parallel the coil
with various capacitors while it's being excited with your cal square
wave and see what happens. You should certainly see the ringing with
0.2µF across the coil. You'll notice that as you decrease the
capacitance the ringing frequency will increase and the ringing envelope
will become shorter and shorter until you'll just see the LdI/Dt spikes
your photos show.

BTW, at that point there'll still be some ringing happening, but it'll
be so fast you won't be able to see it unless the bandwidth of your
scope's vertical amplifier(s) is wide enough.


So, I still only have the skin effect as a candidate. Hmmm...

---
No, you still have Q to consider, and I believe that if you look into
it, you'll find that's what's causing the broadening.

After all, the resonances are where they're supposed to be for the
values of the components, so as the impedance of the tank rises as it
gets nearer to resonance, any resistance in the circuit will tend to
swamp out the nice high impedance peak which would be there without the
extra R spoiling it.

Kind of like if you try to measure the voltage across a 10Mohm resistor
with a voltmeter having an input resistance of 10Mohms!

--
John Fields

Svante wrote:


My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

If I understand you correctly, you are making an error here. You are
assuming that the voltage divider formula works like this:

mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs)

This is wrong.

I would give a counter example to show that you are wrong, and you can
work out the right equation.

Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would
be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to
your equation, you would have that being 0.5*mag(Lin).

Given that, I did not read the rest of your post.

Svante wrote:


My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

If I understand you correctly, you are making an error here. You are
assuming that the voltage divider formula works like this:

mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs)

This is wrong.

I would give a counter example to show that you are wrong, and you can
work out the right equation.

Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would
be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to
your equation, you would have that being 0.5*mag(Lin).

Given that, I did not read the rest of your post.

Svante wrote:


My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

If I understand you correctly, you are making an error here. You are
assuming that the voltage divider formula works like this:

mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs)

This is wrong.

I would give a counter example to show that you are wrong, and you can
work out the right equation.

Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would
be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to
your equation, you would have that being 0.5*mag(Lin).

Given that, I did not read the rest of your post.

Svante wrote:


My computer program measures Z by means of this circuit:

Lout ----------
|
Lin ----------*
|
Rs=47 ohm
|
Rin ----------*
|
Z
|
GND ----------

And calculates |Z| as

Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and
right inputs.

If I understand you correctly, you are making an error here. You are
assuming that the voltage divider formula works like this:

mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs)

This is wrong.

I would give a counter example to show that you are wrong, and you can
work out the right equation.

Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would
be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to
your equation, you would have that being 0.5*mag(Lin).

Given that, I did not read the rest of your post.

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

On 13 Feb 2004 11:35:52 -0800, (Svante)
wrote:

(Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

---
Google for "skin depth" and you'll get a lot of hits.

Basically, when the effect comes into play, you have to consider the
wire a tube with a wall thickness which goes inversely with frequency,
and the area of that annular ring now becomes the area through which
current flows.

--
John Fields

On 13 Feb 2004 11:35:52 -0800, (Svante)
wrote:

(Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

---
Google for "skin depth" and you'll get a lot of hits.

Basically, when the effect comes into play, you have to consider the
wire a tube with a wall thickness which goes inversely with frequency,
and the area of that annular ring now becomes the area through which
current flows.

--
John Fields

On 13 Feb 2004 11:35:52 -0800, (Svante)
wrote:

(Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante)
wrote:
Is there an equation somewhere describing the resistance of
a conductor as a function if frequency, including the skin effect?

http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html

Great, this page gives a hint, at 10 kHz the penetration depth into
copper would be 0.65 mm, which would make the current in the centre of
the conductor (my coil had a wire diameter of 0.9 mm) noticeably less
than for DC. I cannot find on the page how this would affect the
resistance of the circular wire though even if it gives a hint on the
order of magnitude of the effect. I wonder if the math for this is
terribly complex, I recall doing web searchs for this before and
ending up with penetration depths, but not that magic frequency
dependent factor for the circular conductor resistance.

Anyway, does it appear likely a penetration depth of 0.65 mm into a
0.9 mm wire would increase the resistance of 0.7 ohms to the
sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33
ohms I see at 20 kHz? Hmm...

---
Google for "skin depth" and you'll get a lot of hits.

Basically, when the effect comes into play, you have to consider the
wire a tube with a wall thickness which goes inversely with frequency,
and the area of that annular ring now becomes the area through which
current flows.

--
John Fields