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Characteristic impedance of AWG 33 copper magnet wire 
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#1
Jul1114, 11:48 AM

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I am working on impedance measurements of closewound electromagnetic coils. I am using an Agilent LCR meter to measure the impedance of these coils over a frequency range of 20Hz2MHz. When I perform the measurements, I get impedance magnitude and phase angle in degrees. I would like to construct a Smith chart of these measurements, but I am unsure of how to measure the characteristic impedance of the coils. These are single strand, AWG 33 copper wires  diameter of approximately 180μm including the insulation. Thus, they are not traditional transmission lines, based on my understanding. What is the best method to measure the characteristic impedance of these coils? Is it simply the DC resistance? Thanks for your help.



#2
Jul1114, 03:03 PM

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A coil is not really a transmission line, it has an impedance, but not a characteristic impedance. AWG 33 copper magnet wire would only have a characteristic impedance when part of a transmission line such as when in conjunction with another parallel strand or above a ground plane.
The impedance of your coils at a particular frequency will be the inductive reactance in series with the wire resistance. The resistance will be slightly dependent on frequency due to skin effect. There will also be a slight parallel capacitive reactance, (negative), due to lead and terminal capacitance. Measure the inductance and series resistance with the meter. Compute reactance from inductance. Normalise the values to the chart reference impedance, then plot them on the Smith Chart. 


#3
Jul1114, 06:34 PM

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Thanks for your help. I'm a bit of a newbie to the whole transmission line theory. I'm hoping to perform some reflectometry measurements on the coil  do you think this is possible? Or do you have any literature that could point to the use of reflectometry on single wires (i.e. those that are not transmission lines)? I've also read that the reflection coefficient can be derived from the complex impedance. Again, it seems this requires the knowledge of some kind of characteristic impedance...
In performing these impedance measurements on the coils, I've come to some of the same realizations that you pointed out. In the lower frequency range, the coils are dominated by resistance in that the impedance Bode plot is essentially a flat line with no slope. However, as the frequency increases the slope changes to +20 dB/decade, indicating an inductive region. At some point in the response, the coil reaches antiresonance (maximum value of the impedance), but then begins to decrease at 20 dB/decade, indicating a capacitive region. I think this capacitive region is due to the effects of the turntoturn insulation capacitance of the coil. In order to compute the reactance and resistance could I not simply separate the real and imaginary portions of the complex impedance? If I do this, the resistance is highly frequency dependent. 


#4
Jul1114, 08:04 PM

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Characteristic impedance of AWG 33 copper magnet wire
You know the inductance from your lower frequency measurements. You know the parallel capacitance from your higher frequency measurements. You measured series resistance over the frequency range. For any frequency you can solve numerically for the complex Z = Parallel( XC, Series(R, XL) ) 


#5
Jul2214, 09:48 AM

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Sorry to reply so late; I was out of the country with limited internet access. If you have some time, I have some remaining questions.
I computed these values by splitting real and imaginary impedance measurements taken on an Agilent e4980A LCR meter. $$Z=\leftZ\righte^{j\theta} = R + jX$$ where, ##R = \Re\left\{\leftZ\righte^{j\theta}\right\}## and ##X = \Im\left\{\leftZ\righte^{j\theta}\right\}##. Your last response seemed to imply that if I removed the skin effect from the resistance measurements, the resistance would remain essentially constant over the frequency range. Based on my understanding of the skin effect, I would expect the resistance to increase as frequency increases, but that does not happen here. Do you have any thoughts as to the reason for this? Again, thanks for your help. 


#6
Jul2214, 05:37 PM

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It appears that up to 100 kHz things are well behaved.
Where the reactance changes sign there is a resonance. There are a couple of resonances, one at about 500 kHz and another at 1 MHz. The very high Q of the resonances shows the resistance is much lower than the reactance at resonance. It appears the instrument is being dominated by the reactance at resonance. A series resonant element in series with the DC resistance will look like resistance. It is being fooled about the resistive component. That could be because of the multiple turns and cross coupling. The instrument can only tell the difference between R and jX by the phase of the returned signal. I suggest that you read the resistance at 100 kHz, then replace the coil with an equivalent resistor. That will tell you if the resonance is in your instrument / leads. The resistance should steadily rise in proportion to the square root of the frequency. That is from the skin effect equation. All other changes to resistance estimates are measurement artefacts. 


#7
Jul2214, 09:49 PM

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I wouldn't say that the Q is "very high". The width of the resonance divided by its center freq looks from the plot to be of order 5well within expected values for a simple coil. BTW, the resonance is caused by capacitance between the turns in parallel with the inductance,



#8
Jul2214, 11:25 PM

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The coil is AWG33, close wound. We need to know; What is the coil length? What diameter? How many turns on the coil? How is the connection made to the meter? 


#9
Y, 04:10 AM

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Debra, please stop posting totally irrelevant posts to what the OP is asking questions about Dave 


#10
Y, 06:50 AM

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#11
Y, 09:12 AM

P: 9

Thanks for all the input. I'll try to answer Baluncore's questions.
1) Wire is AWG 33, which implies a wire diameter of ~180μm. The diameter of the copper is ~173μm and there is ~3.5μm of insulation thickness surrounding the copper. The insulation is rated as Class F. 2) Coil length is unknown. However, the resistance of Coil 1 is approximately 11.4Ω and Coil 2 is 11.2Ω. Using the geometry and resistivity of copper (1.678e8), the approximate length can be determined. I've calculated the lengths as: ~63.9m and 62.8m for Coil 1 and Coil 2, respectively. 3) Inner diameter of the bobbin is 0.568in or 1.44cm 4) How many turns is unknown. There are approximately 2 layers of coil wrapped around the central bobbin. See pictures below. Coil1: Coil 2: 5) Connection to the LCR meter  see pictures below. This image only shows the connection with Coil 1, but both were connected in the same manner. The blue wires were soldered onto the ends of the magnet wire and the other ends are attached to the LCR meter via the connection box shown. All measurements were made while the coil was placed on the solenoid valve stem as shown. Thus, there is a (soft) magnetic core inside the solenoid. I've seen this resonance behavior before in much larger coils as well. For example, this coil (shown below) produces a similar impedance response. The impedance Bode plot is shown below. Sorry, the frequency resolution is not as good with this one, as I was first beginning to use the LCR meter. And the magnitude units should read as dBΩ and not just Ω... The LCR meter outputs ##\leftZ\right## measured in Ohms and ##\theta## measured in degrees. I've made measurements with the coil (only for Coil 1) attached directly to the LCR meter as shown below. The impedance measurements were taken with and without the (softly) magnetic core. Measurement setup: Impedance Bode plot with core: Impedance Bode plot without core: Thanks again for all the assistance. I really appreciate the input. 


#12
Y, 03:23 PM

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Hmmm. at 100khz 50 ohms with core, 55 ohms with no core ?
But at 100 hz, maybe 26 with core, 22 without. interesting. 


#13
Y, 07:35 PM

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In post #11, the "coil 2" picture shows a metal sleeve inside the bobbin. If that is stainless steel it will reduce the inductance very slightly. These coils have a ferromagnetic conductive core while being tested. Above about 10 kHz, skin effect will eliminate almost all of that ferromagnetic material from the inductance computation.
By length of the coil I meant the solenoid length, not the wire length. I was trying to compute the inductance from the solenoid dimensions. 


#14
Y, 08:13 PM

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And might it be worth twisting his test leads together to reduce enclosed area? 


#15
Y, 09:39 PM

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I expect twisting the leads will probably raise the external lead capacitance and so lower the resonant frequency. The reduction in area will not reduce inductance by much and so not increase the resonant frequency. It would be an interesting experiment to try. This circuit has a capacitance involved in the resonance that has not yet been positively identified. Where the leads come from the same end of the coil, the capacitance may be “coil end to coil end” capacitance due to the overlaying of the first layer of the coil by the second layer at the common terminal end. 


#16
T, 12:59 AM

P: 759

http://www.g3ynh.info/zdocs/refs/Medhurst/Med3543.pdf I wound an inductor similar to the OP's, but with 30 gauge wire rather than 33 gauge. There are a total of 210 turns, roughly in 2 layers: Then I generated a plot of the impedance and phase angle of the impedance over a frequency range of 20 Hz to 5 MHz. The vertical scale of the phase goes from 100° to 100° and is linear. The vertical scale for the impedance is logarithmic as shown. Phase is yellow and impedance is green: There are several self resonances as the sweep approaches 5 MHz; this is typical for a coil of this type. Here's another sweep, but showing AC resistance in green: A question for the OP. What is your purpose (goals?) in all this? 


#17
T, 03:55 AM

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We now see that the coils are scramble wound with no attempt made to keep the ends or layers of the coil apart. The ends of the coil can capacitively influence each other very strongly which will have a completely different self capacitance and resonance behaviour to an orderly close or space wind. It is the two layer wind that has brought the resonant frequency significantly down, by bringing the terminal ends together. If the coil is for an ironcored electromagnet, self resonance will matter little, especially when the magnetic circuit is closed. The forgotten art of winding coils with low selfcapacitance need not be revived. 


#18
T, 01:13 PM

P: 9

Also see post #11, picture 4. This coil was produced as a component of a Parker solenoid valve  not hand wound. The impedance response shows a similar behavior though the two ends of the coil do not see each other electrostatically. Below is the impedance response for this coil. 


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