ACR Less Than DCR in Litz Wire

Check this out.

https://www.newenglandwire.com/traditional-litz-wire-theory/

These formulas and examples still show theoretically that ACR is higher than DCR.

Somewhere in your circuit, you must have some shunt capacitance.

I'm measuring the coil by itself. It's disconnected from the electronics. The LCR meter has been calibrated and is still certified.

You can never actually measure only a coil impedance. The wiring parasitics and stray magnetic fields also come into play. I suspect your coil is magnetically coupling with another magnetic field than just the one made by the coil windings.

Have you considered inter-winding capacitance? (just a guess.) That would depend on how the coil is wound. You might want to get a lot more data points, the complex impedance at a lot of different frequencies. You can find the resonant points where the impedance is purely resistive.

This might help:

https://link.springer.com/content/pdf/bbm%3A978-1-4020-9075-2%2F1.pdf

I agree.

Consider the situation where Xc is greater than Xl.

Even with Xc greater, even if either one was negative, the equation still shows the sum being squared, so it would be positive. Then it is added with the resistance, so theoretically, with that equation, there is no way that Z can be less than the DC resistance. No number can be plugged in to get Z less than DCR.

Your formula is for series impedances. If you have two impedances, Z₁ and Z₂, in parallel, the formula for Z_total is

1/Z_total = 1/Z₁ + 1/Z₂ .

As in your first comment,I agree there must be shunt capacitance in the circuit,and as with resistors in parallel,the total resistance of two or more in parallel will always be less than the smallest resistor or in this case,impedance,in the circuit.

Simply stated:

The 1/Z converts resistance to conductivity and then adds them together.

Higher conductivity is lower resistance or Impedance.

Fine Strand Anomalies

Rixter is right about shunt capacitance. Litz is particularly susceptible to having or developing such paths. Consider the following:

Litz wire is more difficult to electrically connect completely than
stranded wire with larger and fewer strands. If some litz strands
are connected at only one end then you get fewer strands involved at
DC than you have with AC. The single ended strands look like opens
at DC but look like parallel circuits with their capacitance to the
bundle in series with their individual strand impedance at AC. This
mechanism can result in a network with lower AC impedance than DC.
Even if good connection is initially achieved when manufactured,
corrosion or mechanical stresses can easily disconnect individual
tiny strands at one end and cause the AC network impedance to become
lower than the DC resistance.
Litz which has been mechanically stretched, crimped, or abraded can
develop strands which have become necked or broken somewhere beyond
the end connections. These can also present parallel AC paths with
lower impedance than their DC paths.
______________
thewildotter

Helpful response, thanks. So not all strands are connected at the end is what your saying?

Likely, since the ends are often where strands either start as or become DC opens. Strands open elsewhere are similar but the series capacitance to the bundle is lower than a strand broken at the end.

______________

thewildotter

Each Strand Insulated

Realize also that most Litz has individually insulated strands. In order to solder these strands one needs to first burn or abraid off the varnish. This potentially damages the fine strand of copper. Crimp connections are typically even worse since the crimper person may not understand the need to eliminate the varnish barrier to the connector.

___________

thewildotter

https://www.electronics-tutorials.ws/accircuits/ac-inductance.html

The chance of your measuring result being wrong is far higher than the chance of theory being wrong.

Make sure both meters are designed for DC, that they are both calibrated, that the measurement is within specs...

To my understanding, 58mR and 65mR are the same thing.

https://www.bkprecision.com/products/component-testers/891-300khz-bench-lcr-meter.html

The meter says the impedance is accurate to 0.05%. There is a 10.77% difference in my values. The meter has recently been calibrated, I have the certificate sitting under it.

OK, the accuracy claim hit my hot button . . .

Checking the datasheet, the claimed accuracy for DC, 20Hz-1kHz is 1% +/- 1 count. The unspecified part of that claim is that it typically applies to the range, not to the reading. If the measurement is taken on the 0.1 Ohm range, the error could be about 0.010 Ohms, while that same measurement was taken on the 1 Ohm range, the error could be about 0.1 Ohms.

To maximize your assurance of your measured values, connect the test leads together to see what the "zero" resistance/impedance readings are, and then connect to the device under test. Try to make this connection with the leads in the same position to minimize errors caused by lead inductance loop area changes.

Good idea. I’ll try that out, thanks.

When you get down below an Ohm with 4-terminal measurements, the contact methods become more important. At lower resistance, even the way you connect your Kelvin clips (or whatever connection method) for your "zero" connection makes a difference. Clipping them together in a stack-up of Lcur-Hcur-Hpot-Lpot (using front-panel names) will give you a different "zero) than a stack-up of Lcur-Lpot-Hcur-Hpot. Also, you can check the need for cable-routing precautions by moving the cables around (increasing inductive loop area) and watching what happens to the "zero" reading. Play with the connections enough to know what is important ans what is not.

Have fun!

Does anybody have some litz wire coils and an LCR meter that wouldn't mind trying this?

Experimental Procedure

Make a good electrical connection to both ends of your Litz. Measure ACR and DCR. Now at the midpoint of your length of Litz cut Litz strands until your ACR measures twice your original ACR. Now measure DCR. If it is more than twice your original DCR, smile. You have proven that dead end strands impact DCR more than ACR. The AC network still has some current flowing in the dead end strands via capacitive coupling between the dead end strands and the bundle. Hang the damaged Litz over your fireplace as a troubleshooting trophy.

____________

thewildotter

I said this earlier but I see it might be considered cryptic enough that people will not understand my suggestion.

With a purely serial network, the only way the resistance of a complete network can be less than the series resistor of the network is for a negative resistor to be in series. Passive negative resistors do not exist but active negative resistors do exist. The simplest active negative resistor is to add a dependent voltage source in the series network. I'm proposing the inductor might be producing such a dependent voltage through magnetic coupling. This is an unlikely scenario but certainly possible.

The likely scenario is the other method to reduce the impedance of a component. It is to have another impedance in parallel with that component. This is what many have accurately suggested with the stray, parasitic capacitance comments. The equation that is baffling the OP has the capacitance in series with the inductance and resistance not in parallel.

My vague recollection of 'resistance' meters was that they measured current and voltage, assumed to be simultaneously - and then calculated the resistance to display.

Thus your errors are not the litz, itself, but be traceable to something having an effect on the ability of the meter to measure currents, or the voltage measurements, or even the 'simultaneousness' of the measurement - singly, or in combination.

I know you say it's calibrated - so the error should be reliable.