I have a big coil I am working on (its radius is about 50 cm). It's a single layer coil built around a frame made of non conductive material, with some carbon fiber bars to hold everything together (their cross section is much smaller than the coil's radius). There are around 50 windings to the coil, and they are apart from each other.

The coil's length to width ratio is about 1. The wire should have a DC resistance of around 300 mohms, which is what I get when I measure it. The AC resistance (due to proximity and skin effects) at a few kHz, should be 0.5 to 1 ohms, according to my calculations (the frequency is low enough to have a low skin factor. The windings' pitch is greater than the wire's radius, so the proximity factor should be low as well).

In practice, the AC resistance is closer to 15 ohms, which is 20 times more than I expect.

I measured the AC resistance of the coil in two ways:
1) measuring the real part of its impedance
2) applying a known AC voltage and measuring the current, while the coil is in resonance by a low ESR serial capacitor.

The measured inductance is as expected, and there are no unwanted shorts between the windings.

My main concern is losses due to conductive materials close to the coil, but this value stays roughly the same even when I take the coil outside the lab to a place clear of metals which can interfere with the measurement.
I don't understand which physical phenomenon I am not taking into account.

 

I guess, something wrong with calculations. What frequency is?

 

The clue to the discrepancy is the "At Resonance" condition. The effective impedance of a resonant circuit is much greater than the impedance of either element. So at resonance you are measuring the effective impedance of the tuned circuit, which should be much greater, as you have discovered.
To measure the "AC resistance" (REACTANCE) of the coil, disconnect the capacitor and repeat the voltage and current measurements of the coil alone.

 

The clue to the discrepancy is the "At Resonance" condition. The effective impedance of a resonant circuit is much greater than the impedance of either element. So at resonance you are measuring the effective impedance of the tuned circuit, which should be much greater, as you have discovered.
To measure the "AC resistance" (REACTANCE) of the coil, disconnect the capacitor and repeat the voltage and current measurements of the coil alone.

I assumed that by "serial capacitor" he meant a series resonant circuit, which should read the ESR of the capacitor plus the AC resistance of the coil, plus core losses.

 

The frequency is around 40khz, the wire is AWG 18 (1mm in diameter), and the spacing between the windings is about 3mm.

Exactly at series resonance, the impedance should consist only the real part, and be lowest. since the inductor and capacitor cancel each other out

 

The frequency is around 40khz, the wire is AWG 18 (1mm in diameter), and the spacing between the windings is about 3mm.

Exactly at series resonance, the impedance should consist only the real part, and be lowest. since the inductor and capacitor cancel each other out

https://www.laushaus.com/tesla/primary_resistance.htm

 

The "real part" will include the ESR of the capacitor, which appears to not be zero. That is reasonable if the capacitor is not "perfect".

 

https://www.laushaus.com/tesla/primary_resistance.htm

Correction, the DC resistance I get is about 3.5 ohms. The AC resistance should be around 6 ohms, but I get around 15 ohms. From the link you sent, the AC resistance can be 4 times of the DC, but in the case there the wire is so thick that the skin effect is very sigificant, which is not my case. I still wonder what gives me more than twice the expected resistance.

 

Correction, the DC resistance I get is about 3.5 ohms. The AC resistance should be around 6 ohms, but I get around 15 ohms. From the link you sent, the AC resistance can be 4 times of the DC, but in the case there the wire is so thick that the skin effect is very sigificant, which is not my case. I still wonder what gives me more than twice the expected resistance.

As was early suspected, your calculations were wrong.
Calculate the skin effect (AC current depth on the wire) on copper at 40kHz. ~325um but the skin effect current distribution is not linear (actually, a negative exponential) into the conductor skin depth number we calculate.

This means you need to size the conductor to be multiple skin depths (5 or 6 with RF (40kHz can be RF) to keep the current in 'good' copper) as the EM energy surrounds the wire and the surface area of the 'first' metal matters most as the EM wave propagates.

 

The

As was early suspected, your calculations were wrong.
Calculate the skin effect (AC current depth on the wire) on copper at 40kHz. ~325um but the skin effect current distribution is not linear (actually, a negative exponential) into the conductor skin depth number we calculate.
View attachment 332212
This means you need to size the conductor to be multiple skin depths (5 or 6 with RF (40kHz can be RF) to keep the current in 'good' copper) as the EM energy surrounds the wire and the surface area of the 'first' metal matters most as the EM wave propagates.

View attachment 332209

The equation I use to calculate the skin factor is: r^2/(2r*delta-delta^2) which gives a skin factor of 1.14. For this spacing between the windinds and for this length to width ratio, the proximity factor should be around 1.3. So overall, Rac should be around 1.482*Rdc, and not 4 or higher

 

The equation I use to calculate the skin factor is: r^2/(2r*delta-delta^2) which gives a skin factor of 1.14. For this spacing between the windinds and for this length to width ratio, the proximity factor should be around 1.3. So overall, Rac should be around 1.482*Rdc, and not 4 or higher

Your valid measurement data is what's real and it's not really too far off now that the correct Rdc is used.

 

The

The equation I use to calculate the skin factor is: r^2/(2r*delta-delta^2) which gives a skin factor of 1.14. For this spacing between the windinds and for this length to width ratio, the proximity factor should be around 1.3. So overall, Rac should be around 1.482*Rdc, and not 4 or higher

Skin depth calculator shows skin depth 326 micrometers only . So, effective cross section of 1 mm wire is 0.001 sqmm only :

Skin Depth Calculator - Engineering Calculators & Tools (allaboutcircuits.com)

 

Is the TS able to do that same current and voltage measurement without a series resonance arrangement?? OR it should be correct if the voltage across the coil itself can be measured, since the current is the same thru the whole loop. That will allow an evaluation of the skin resistance effect.

 

The simplest and most accurate method is to pull the coil in resonance about that targeted frequency and measure in series voltage on capacitor, thus the Q-factor. There is elementary formula allowing to recalculate Q-factor toward R(ser). All other methods are plus minus three tram stops.

 

I have a big coil I am working on (its radius is about 50 cm). It's a single layer coil built around a frame made of non conductive material, with some carbon fiber bars to hold everything together (their cross section is much smaller than the coil's radius). There are around 50 windings to the coil, and they are apart from each other.

The coil's length to width ratio is about 1. The wire should have a DC resistance of around 300 mohms, which is what I get when I measure it. The AC resistance (due to proximity and skin effects) at a few kHz, should be 0.5 to 1 ohms, according to my calculations (the frequency is low enough to have a low skin factor. The windings' pitch is greater than the wire's radius, so the proximity factor should be low as well).

In practice, the AC resistance is closer to 15 ohms, which is 20 times more than I expect.

I measured the AC resistance of the coil in two ways:
1) measuring the real part of its impedance
2) applying a known AC voltage and measuring the current, while the coil is in resonance by a low ESR serial capacitor.

The measured inductance is as expected, and there are no unwanted shorts between the windings.

My main concern is losses due to conductive materials close to the coil, but this value stays roughly the same even when I take the coil outside the lab to a place clear of metals which can interfere with the measurement.
I don't understand which physical phenomenon I am not taking into account.

Hello,

If you can not think of anything else what you can do is measure at different frequencies and see if all the measurements correlate to your calculations. If they all do not, then you are not calculating something correctly.

I do not think that skin effect should be THAT significant at 40kHz with #18AWG wire.

I also have to ask what you are using to determine you are seeing true physical resonance.

 

Hello,

If you can not think of anything else what you can do is measure at different frequencies and see if all the measurements correlate to your calculations. If they all do not, then you are not calculating something correctly.

I do not think that skin effect should be THAT significant at 40kHz with #18AWG wire.

I also have to ask what you are using to determine you are seeing true physical resonance.

I know I am at resonance because I sweep over a band of frequencies and takes the one with the least resistance (highest current output). Also, I see the phase difference between voltage and current is zero. So far, I still not sure what makes my AC resistance more than twice than what it shoud, despite what all the previous good people suggested. The theories which were auggested above are possible, but they are not backed up with numbers.

 

I suggest adding a parallel capacitor and adjusting for a voltage peak, rather than a current peak.
I am also guessing that in your present measuring scheme there is a resistive material in the magnetic field that is causing additional losses to add to the measured effective reactance. This would also be indicated by the resonance peak being broad, instead of a sharp peak.

 

A paper.

 

One additional consideration is that with series resonance all of the loss in the capacitor is also influencing the results. Unless the capacitor is "perfect".

 

I know I am at resonance because I sweep over a band of frequencies and takes the one with the least resistance (highest current output). Also, I see the phase difference between voltage and current is zero. So far, I still not sure what makes my AC resistance more than twice than what it shoud, despite what all the previous good people suggested. The theories which were auggested above are possible, but they are not backed up with numbers.

There has got to be something unknown yet happening here.
One of the rules of thumb is that #26AWG wire is good up to 100kHz, but no thinner. If that was not true, some converters would have awful efficiency, way below what would normally be expected. Thus #18AWG at 40kHz shouldn't show 2x the AC resistance. There must be something else not accounted for.

For one thing, are you sure the wire is made of nearly pure copper? Some wire is made with aluminum and plated with copper.
I can't think of anything else offhand, but maybe you can try some other capacitors and test for resonance at other frequencies and see what you get. There should be some correlation that could be matched to some theory here. That might pinpoint the problem.

I just reread your first post and see you are saying it is 15 or more times higher than expected. That's just not possible unless something else is very wrong. Perhaps the generator impedance is affecting the measurements, or the measurement devices.
In cases like this you have to look at the entire setup in detail. Maybe you can post some real life pictures.