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I am measuring the inductance of a large coil using an LCR meter. I am using the series equivalent measurement mode at 100 Hz.

Why does the LCR meter show that the ESR is 656 Ohm and why does my multimeter show a DC resistance of 61.5 Ohm? I would assume the ESR is the real part of the inductor impedance which should be the same as the DCR.

In the figure below the voltage waveform is shown in blue. I am using a 50 Hz rectified voltage with an average voltage of 210 V (left side of scope y-axis), which gets chopped to around 110 V after some time (right side of scope y-axis).

enter image description here

Does the current waveform influence the AC impedance of the coil?

Rens
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3 Answers3

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DCR is the resistance at 0Hz = DC Resistance. ESR is the Equivalent Series Resistance, at the measuring frequency. Beside the DC resistance, also skin effect, eddy currents and core hysteresis contribute to the total resistance of the AC circuit, which are the real part of the impedance Re{Z}.

Marko Buršič
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An inductor has two sources of resistance (real part), DC and AC.
The ESR your LCR meter is measuring is DC + AC resistances.

DC resistance is what you measure using a DC ohmmeter (most DMMs use DC).

AC resistance is due to copper eddy losses due proximity effect (due to magnetic field induced by adjacent conductors) and skin effect (due to magnetic field around the conductor). There is also loss due to the core, but that usually will be low when when measuring with low level signals. Below 1 MHz, skin effect losses are generally insignificant and proximity effect losses will dominate. Proximity effect losses are proportional to \$ frequency^2\$ and \$wire\_diameter^4\$. An odd thing comes out of the equations which says that the AC resistance increases as the wire diameter increases. Experiments I have done show this to be true. If operating at a single frequency, there is an optimal wire diameter which minimizes AC+DC resistance. The equations and references for proximity effect can be found in this post.

[Edit] DC current through the inductor affects the inductance. When you get close to saturation of the core, the inductance will trend downwards. The inductance versus DC current is sometimes shown as a graph in data sheets.

qrk
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  • Do you think the proximity effect will be significant at 100Hz? – Rens Nov 11 '21 at 10:04
  • I am using a rectified AC 50Hz voltage to power the coil so i assume i need to use 100Hz for my calculations – Rens Nov 11 '21 at 10:05
  • @Rens You need to use the frequency at which your LCR meter measures it. Most good LCR meters can change their measurement frequency; if you want to know how it will perform at 100 Hz, set your LCR meter to measure at as close to 100 Hz as you can set it. If you have a particularly cheap LCR meter, you may not be able to change it, and you're just left with whatever frequency it measures at, which should be listed in the datasheet for the instrument. – Hearth Nov 11 '21 at 15:37
  • @Rens To be clear, the 100 Hz value is indeed the thing you would care about in a circuit that operates on rectified 50 Hz mains. The LCR meter is probably measuring at something more like 1 or 10 kHz, which means the value of ESR you get from that is not particularly relevant to what you're using the inductor for. – Hearth Nov 11 '21 at 15:40
  • @Rens A properly designed transformer will take in to consideration both DC and AC losses to minimize power loss in the windings. You should be measuring losses near the frequency of interest. – qrk Nov 11 '21 at 17:32
  • I don't think there will be much "copper eddy losses". The main loss mechanism at 100 Hz IMO can only be eddy losses in a conducting core. – tobalt Nov 11 '21 at 20:19
  • Thanx for the reply's. i'm able to select 100Hz frequency on my LCR meter (UNIT UT612). – Rens Nov 12 '21 at 07:50
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Both answers are good but I wanted to provide an even more condensed view: you tried to break down V/I as the sum of two things: DC resistance and inductance. But there are actually three things: DC resistance, frequency-dependent losses, and inductance. Inductance isn't inherently lossy (dissipative), but the other things like skin effect and eddy current losses are.

hobbs
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