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OverUnity Research > Benches > Smudge (Moderator: Smudge) > A closer look at a simulated Negative resistance coil.
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Author Topic: A closer look at a simulated Negative resistance coil.  (Read 79934 times)
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Re: A closer look at a simulated Negative resistance coil. « Reply #75 on: 2015-02-17, 09:03:26 »

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Quote from: Peterae on 2015-02-16, 20:55:55
Ahah i am connecting a cap across the L and connecting scope probe and Sig gen in parallel.

I will try a series LC connection tomorrow and tune for max PK  O0

The output impedance of the sig gen is generally very low (like 50 ohms) and when shunted across a parallel LC circuit it lowers the Q so much that resonance is not easily detected.  A series LC across the sig gen could work where at resonance the LC impedance is lower than that of the sig gen, so there you look for a minimum signal across the sig gen.  But if you look across the L or C then the voltage there peaks at resonance.  But again the impedance of the sig gen lowers the Q so you get a very broad peak.  The parallel resonant LC circuit with some loose (1 turn) coupling from the sig gen will have a much greater Q so you get a very sharp peak easily found.  There are many techniques for coupling into both series and parallel circuits that work better but it would read like a text book if we went into them.

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Re: A closer look at a simulated Negative resistance coil. « Reply #76 on: 2015-02-17, 16:19:16 »

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Quote from: orthofield on 2015-02-16, 22:14:28
Hi Peterae,

This page basically reiterates what Smudge said about series measurements..

http://meettechniek.info/passive/magnetic-permeability.html

orthocoil

The method shown in that link does not use resonance, it measures the current through L and the voltage across L.  Then since Vmagnitude=imagnitude*omega*L you can get the inductance as L=Vmagnitude/(imagnitude*omega).  With the resonance method you don't need to measure any values, just tune for a peak, note the frequency then use the resonance formula.  A good cross check is to use both methods. O0

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Re: A closer look at a simulated Negative resistance coil. « Reply #77 on: 2015-02-17, 18:35:41 »

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OK i tried loose coupling the Sig Gen 1 loop through centre of toroid with a parallel Cap box across the Inductor and wow sharp peaks found, my problem now is even the 15pf of the scope probe limits the top frequency i can test at.

I measured my scope pf and my lcr reads 15.88pf

Just Probe 15.88pf 308khz 248v Calculated Inductance = 16.815mH
20pf + 16pf probe =36pf 263khz 248v pk-pk L=10.172mH
30pf + 16pf probe =46pf 242khz 248v pk-pk L = 9.4027mH
50pf + 16pf probe =66pf 208khz 225pk-pk L = 8.8709mH
150pf + 16pf probe = 166pf 155khz 221v pk-pk L=6.3514mH
250pf + 16pf probe =266pf 138khz 210v pk-pk L=5.0004mH
550pf + 16pf probe = 566pf 89khz 189 pk-pk L =5.6499mH
1nf 69.4khz 167v pk-pk L = 5.2592mH
2nf 48.1khz 139v pk-pk L =  5.4742mH
5nf 30.5khz 105v pk-pk L =  5.4459mH
10nf 21.6khz 82.8v pk-pk L = 5.4292mH
20nf 15.6khz 62v pk-pk L = 5.2043mH
50nf 9.77khz 39.5v pk-pk L = 5.3843mH

I see the inductance going up as the capacitance goes down, this surely is a sign there is stray capacitance acting on the circuit and giving false measurements, i could try using one of the primary low turn coils instead which should allow me to go higher in frequency?


EDIT OK just tried the low turn primary coil on top so can still only go up to 357khz with that coil.

just probe 357khz
50pf 352khz 45pk-pk
350pf 320khz 45.5pkpk
550pf 290khz 45pkpk
« Last Edit: 2015-02-17, 19:02:13 by Peterae »
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #78 on: 2015-02-17, 20:21:49 »

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The 3C90 mu does increase reaching a peak at about 400KHz and then it starts to decrease. However your results are showing a much larger increase there see chart.  This may be correct since other ferrites are known to have an increase due to a ferromagnetic resonance, see for instance the curve for TDK PE22 in the attached paper.  That paper attempts to show the possibility of using the permeability peak to get OU so you may get led down another avenue if you discover a large ferromagnetic resonance with this core. ;)

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Re: A closer look at a simulated Negative resistance coil. « Reply #79 on: 2015-02-17, 20:54:53 »

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And while we are on the subject of ferromagnetic (or ferrimagnetic) resonance here is another paper you may find interesting.  Enjoy :)

Smudge
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #80 on: 2015-02-17, 21:13:14 »
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Hi Smudge,

I haven't looked at your 'precession' paper yet... 
Still examining the paper on using the permeability peak, which I find quite interesting.
 
I can imagine a circuit where the core is in a tank circuit along with a varactor or other frequency changing element. A pulse is introduced at the peak mu frequency, adjusted by the biased varactor. As soon as the decaying oscillation starts, the varactor bias is shut off, and the frequency drops. With the drop in frequency, the increase in mu causes an increase in current in the coil which can be tapped for power.
I also wonder, if a weak signal is introduced at this high frequency permeability peak, will the presence of this signal control the low frequency mu? It's pretty well known that mu can be increased, and hys. losses decreased by superimposing a small HF signal on a core. The superimposed signal can be smaller magnitude than the LF signal. This was patented in the 1920s.
Also, I'm still trying to find a patent in my files that shows a method for changing mu of a 'dielectric' ferrite by superimposing an electric field on it. 

orthocoil
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #81 on: 2015-02-17, 21:18:33 »

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OK thanks Smudge so whats my next move i need help working through this stuff  O0

If you point me i will do my best to do the bench work  ;)

I almost have the digital monostable fully working now, just one more problem to sort in code and i will be flying with nS pulses, still not yet sure how low it goes, but i do get a pulse when it's set above 6nS but the pulse is wider, more tests are needed when the code is sorted to see how well the 6amp fet driver performs.

I could also go back to my first toroid and run the tests on that one using the loose coupling.

« Last Edit: 2015-02-18, 06:25:05 by Peterae »
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #82 on: 2015-02-18, 10:17:36 »

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Quote from: Peterae on 2015-02-17, 21:18:33
OK thanks Smudge so whats my next move i need help working through this stuff  O0

If you point me i will do my best to do the bench work  ;)

I almost have the digital monostable fully working now, just one more problem to sort in code and i will be flying with nS pulses, still not yet sure how low it goes, but i do get a pulse when it's set above 6nS but the pulse is wider, more tests are needed when the code is sorted to see how well the 6amp fet driver performs.

I could also go back to my first toroid and run the tests on that one using the loose coupling.

Well you could extend the measurements to higher frequencies by putting a 1K resistor between your sig gen and the 1 turn loop, then connecting the scope probe across the 1 turn loop.  That enables you to see the resonance peak but now the probe capacitance is not across the coil so you can use smaller values there.  A simple way to make small capacitors is to twist some magnet wire into a twisted pair then you get capacitance between the two wires.  You can cut the twisted pair into smaller lengths to get smaller values, but of course you need to measure each one to know what the capacitance is.  Or measure a long length to establish the distributed capacitance value (pF per metre) then cut to the required length.  It would be interesting to see the full mu v. frequency curve to see if we could use that permeability peak somehow.

One thing is clear, the new core will enable you to work at frequencies up to 1MHz which is what we wanted.  So you might be tempted to make the whole bucking coil transformer thingy and do some power transfer measurements at those higher frequencies.

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Re: A closer look at a simulated Negative resistance coil. « Reply #83 on: 2015-02-18, 10:26:01 »

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Quote from: orthofield on 2015-02-17, 21:13:14
Hi Smudge,

I haven't looked at your 'precession' paper yet... 
Still examining the paper on using the permeability peak, which I find quite interesting.
 
I can imagine a circuit where the core is in a tank circuit along with a varactor or other frequency changing element. A pulse is introduced at the peak mu frequency, adjusted by the biased varactor. As soon as the decaying oscillation starts, the varactor bias is shut off, and the frequency drops. With the drop in frequency, the increase in mu causes an increase in current in the coil which can be tapped for power.
I also wonder, if a weak signal is introduced at this high frequency permeability peak, will the presence of this signal control the low frequency mu? It's pretty well known that mu can be increased, and hys. losses decreased by superimposing a small HF signal on a core. The superimposed signal can be smaller magnitude than the LF signal. This was patented in the 1920s.
Also, I'm still trying to find a patent in my files that shows a method for changing mu of a 'dielectric' ferrite by superimposing an electric field on it. 

orthocoil

You almost got it, but your varactor would have to lower the capacitance to create an increase in frequency to get the increased permeability.  Don't know about the superimposed HF but it would be worth trying.  Perhaps this permeability peak idea should be on a different thread since it is not associated with bucking coils (but there again this thread title does not mention bucking).

Smudge
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #84 on: 2015-02-18, 19:18:10 »

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Hi Smudge
Thanks for the help.
I used thicker insulated wire and twisted it and then measured the cap using my LCR each time, the problem is that with no capacitance (No wire & open coil) i can still only go up to 378KHz, i have 4 coils all open on this toroid, 2 primary & 2 secondary.

Here's the data, going off now to do some power tests, i will choose 300kHz for a starter  O0


wire 33.55pf 277kHz
30.74pf 284kHz
28.94pf 284kHz
26.94pf 287kHz
23.7pf 297kHz
19.16pf 304kHz
15.95pf 312kHz
12.71pf 328kHz
8.65pf 342kHz
5.7pf 347kHz
2.98pf 362kHz
no capacitance 378kHz (Open circuit coil)
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #85 on: 2015-02-18, 19:50:52 »
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Hi Smudge,

The way I was thinking of this was that the circuit would start at the high frequency with the initial impulse, and then the frequency would be dropped into the range where mu was lower. The reduction of mu (and L) would lead to a rise in current in the decay oscillation (parametric amplification).

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Re: A closer look at a simulated Negative resistance coil. « Reply #86 on: 2015-02-18, 20:04:49 »

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OK i  took scope shots of first across the primary CSR 1 Ohm & Across L at different frequencys and then went back and took load snaps at the same frequencys.

as follows at
312khz
500khz
762khz
1.02mhz
1.52mhz
2.02mhz
2.5mhz
2.98mhz
3.91mhz


Pin = Vrms * Irms *cos(phi)
Pout = Irms^2 * R R=1 Ohm so Pout=Irms^2
COP=Pout/Pin
312khz Vrms=186mv Irms=64.4ma VLrms=12.4mv Pin=11.978mW Pout=153.76uW COP 0.0129
500khz Vrms=283mv Irms=64.4ma VLrms=12.7mv Pin=18.2252mw Pout=161.29uw COP 0.00884
762khz Vrms=418mv Irms=64.2ma VLrms=13mv Pin=26.8356mw Pout=169uw COP 0.00629
1.02mhz Vrms=552mv Irms=62.7ma VLrms=13.7mv Pin=34.6104mw Pout=187.69uW COP 0.0054229
1.52mhz Vrms=758mv Irms=60.7ma VLrms=14.6mv Pin=46.0106mw Pout=213.16uw COP 0.004633
2.02mhz Vrms=967mv Irms=58.2ma VLrms=15.9mv Pin=56.2794mw Pout=252.81uw COP 0.004492
2.5mhz Vrms=1.12v Irms=55ma VLrms=18.4mv Pin=61.6mw Pout=338.56uW COP 0.005496

EDIT** i think i should have used I^2*R for power in the load as the voltage is really a current, but as my resistor is 1 Ohm it does not alter my results, i will change the above text to reflect this later after work  O0
2.98mhz Vrms=1.27mv Irms=51.5ma VLrms=19.5mv Pin=65.405mw Pout=380.25uW COP 0.005814
3.9mhz Vrms=1.53mv Irms=39.8ma VLrms=21.9mv Pin=60.894mw Pout=479.61uw COP 0.007876
« Last Edit: 2015-02-19, 18:17:06 by Peterae »
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #87 on: 2015-02-19, 08:49:41 »

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Peter,

Your Pin should be Pin=Vrms*Irms*cos(phi) where phi is the phase angle between V and I.  It appears you haven't measured phi.  Did you check that phase angle?  If it is well away from 0 degrees it will seriously affect the result.  Measuring that phase angle can be problematical when you use the voltage across a NIR for getting the current, since you need a scope that can do waveform subtraction.

Edit.  I have just looked at your waveforms and it is clear that the phase angle between input V and I is close to 90 degrees so the input power is way down on those quoted.

Edit 2.  In fact it is so close to 90 degrees that the input power is almost zero, so great difficulty in getting an accurate measurement. As the input impedance is close to being purely inductive I suggest you concentrate on the lower frequency range between 300KHz and 1.5Mhz.  Use a series capacitor to resonate the input L at the chosen frequency so that the input current and voltage are in phase, then use the Pin=Vrms*Irms formula.  Of course the capacitor must be between your NIR and the coil, and the voltage must be taken across the series C and coil.

Edit 3.  And you could try higher values of load resistor.

Edit 4.  Having blown up your images it looks like the phase angle is about 80 degrees so your input powers are all overstated by about 6.  Improves the COP's slightly.  I would expect better COP's with higher load resistance.

From your inductance measurements using resonance it is clear that the coils have a self resonance indicating self capacitance and that is not surprising.  So the apparent large rise in inductance at the higher frequencies is an artefact.  I think we can say that the cores meet the 3C90 spec and are good up to 400KHz and beyond.  I am playing with the negative resistance calculation to include the losses expected form the core using the 3C90 complex permeability data.  They give u' and u" that are the real and imaginary components of the mu.  So the inductance formula using u' gives the inductance value and that same formula using u" and multiplied by omega yields the effective core losses as a resistance value in series with the L (I think :-\ ).  I'll post the results when done.

Smudge
« Last Edit: 2015-02-19, 15:53:40 by Smudge »
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #88 on: 2015-02-19, 18:02:16 »

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Hi Smudge Thanks.
so if i need to take into account the phase angle then the above yellow trace would need inverting, and it looks like there's an offset for some reason, the yellow trace does not look as if on the zero line despite the cursor saying so and this would give a false phase angle, i will try a calibration, poor scope has had a hammering in the past.

Quote
Your Pin should be Pin=Vrms*Irms*cos(phi) where phi is the phase angle between V and I.  It appears you haven't measured phi.  Did you check that phase angle?  If it is well away from 0 degrees it will seriously affect the result.  Measuring that phase angle can be problematical when you use the voltage across a NIR for getting the current, since you need a scope that can do waveform subtraction.
My scope does not do phase angle, although it does have a basic math function, i cannot do maths on the rms values but the waveforms on the scope probes i can.

I thought the phase angle in an inductor should be 90Deg, so surely it is safe to use 90 Deg in our above scope shots?

Lets choose 750KHz to work on, if there is a way to work out the optimum load that could help me.

EDIT i will edit the above results to show Pin using *cos(phi)

EDIT that did not work out as cos(90) = 0  C.C So i now see what you mean our input power needs to be gained by other methods or by measuring the angle precisely which is not possible with my scope, so i will try your series cap method  O0

I suspect we will be limited by the self capacitance regarding our trial frequency, if i calculate the series cap value using my LCR inductance of 4.45mH then i get 10pf, we already know we cannot get parallel LC above 370khz, i will do some tests but i suspect we may need to test at 300khz.
« Last Edit: 2015-02-19, 18:36:22 by Peterae »
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #89 on: 2015-02-19, 19:38:28 »

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Peter,

The series cap does not tune with the secondary inductances so forget the 5mH.  Measure the input inductance of your bucking primary windings (100's of uH) and tune to that.  You'll soon know whether it is right because you will see the V and I in phase on your scope (in fact you can adjust frequency to get them in phase).

You can deduce the phase on your scope by taking the timing from zero cross overs of V and I.  I did this not by actual times but by graticule markings. Then since the graticule distance for a full cycle is easy to determine, and that represents 360 degrees, you get the phase from 360*phasegraticule/cyclegraticule (edited cos I got it wrong :-[ ).

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Re: A closer look at a simulated Negative resistance coil. « Reply #90 on: 2015-02-19, 19:40:57 »
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Hi Peterae-

If I may suggest a different test layout that will simplify your resonance testing. See the attached schematic which is pretty much self explanatory. The idea is to create a ringing between the known capacitance Cx and the unknown inductance Lx which can then be easily measured with a scope automatically or manually with cursors. The scope probe capacitance is in parallel with Cx.

Also attached is a scope shot of a test using this circuit on a 51mm toroid in P7070 material with 9 turns on the core and Cx is only the scope capacitance of 8pfd along with I'm sure a few pfd of strays.

Hope this is of some help.

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Re: A closer look at a simulated Negative resistance coil. « Reply #91 on: 2015-02-19, 19:43:55 »

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Primary LCR Test in series bucking mode @ 10KHz
L=15uH
R=0.0488R
Q=19.4
Z=0.94R

So for 750khz thats 3.0021nF  O0

Thanks
Not got to the bench yet but will head down shortly to try it out
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #92 on: 2015-02-19, 21:20:20 »

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OK
This test used a 100 OHM load, the 100 Ohm was metal film hopefully thats ok, the primary NIR was still 1 Ohm

I will describe the setup first for you to check i understood correctly.

My sig gen positive connected to one end of NIR i have my yellow probe either side of NIR, my cap connects to other end of NIR as does my other scope probe earth, so both scope probe earths are together, the other side of the cap connects to inductor and the other end of inductor connects to the earth of the sig gen and my green probe tip.

Green chan is inverted, so green chan is across series LC and yellow probe across NIR

I had to set my cap box to 16nF to obtain a frequency of approx 771khz where i could adjust to get the phases of current and voltage to align.

So first shot is green Voltage across LC and yellow across 1 Ohm NIR res 771khzpriyeli-greenv

Then i dosconnected the green chan leaving the yellow across the 1 Ohm primary NIR resistor and connected the green across the 100 Ohm load which gives the second shot sec100ohmload771khzgreenloadyellowcur

So Green is across 100 Ohm load and yellow the primary current. PS i had the load probe wrong way hence phase inversion.

Not crunched any numbers yet, if i get a chance i will append the results  O0


EDIT

green 228mv
yellow 52.9
Pin=12.0612mw

Pout = V^2 / R
Pout = 7.3mW
Ok i was right to use V^2/R for Pout because if it's I^2*R then i have a Pout of 73Watts LOL and my little resistance should have been glowing red.

Tomorrow night i need to try some higher resistance loads as a 1OHM load gave me
Pout = 121uw
Pin = 12mw
« Last Edit: 2015-02-19, 22:19:52 by Peterae »
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #93 on: 2015-02-20, 11:17:54 »

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Peter,

From your description
Quote
My sig gen positive connected to one end of NIR i have my yellow probe either side of NIR, my cap connects to other end of NIR as does my other scope probe earth, so both scope probe earths are together, the other side of the cap connects to inductor and the other end of inductor connects to the earth of the sig gen and my green probe tip.
I don't think you are measuring what you think you are measuring.  Can you supply a diagram in case I am misreading your description.  I also think you have serious issues with the earth connections of scope and sig gen shunting away signals.

Smudge 
 
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #94 on: 2015-02-20, 18:20:41 »

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Hi Smudge see schematic, my DSO is connected to a laptop on bAttery powr and as the s econdary & load is not connected to anything else i did not think it would matter if the scope probe earth was connected to anything?

I dont need to monitor the primary current while doing the load shot, so i will do jujst the load connected on it's own the primary reading would not change.
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #95 on: 2015-02-20, 20:38:08 »

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OK 3 Tests.

1MHz 200 Ohm load
1Mhz 510 Ohm load
744KHz 510 Ohm load

All primary waveforms are Green across LC & Yellow I across 1 Ohm NIR
Secondary is green with yellow probe disconnected.

1MHz 200 Ohm Load
Primary 1mhz200load-grelc-yeli
V=383mv
I=54ma
Pin=20.682mw
Secondary 1mhz-200ohmload
V=1.66V
Pout=13.778mw
COP=0.666
-----------------------------------
1MHz 510 Ohm Load
Primary 510ohm-pri-glc-yi
V=749mv
I=46.1mv
Pin=34.5289mw
Secondary 510ohmload1mhz
V=3.41V
Pout=22.80mw
COP=0.660
-----------------------------------
744KHz 510 Ohm Load
Primary 744-510ohm-pri-glc-yi
V=689mv
I=44.3mv
Pin=30.5227mw
Secondary 744-load510ohm
V=3.52V
Pout=24.29mw
COP=0.7958
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #96 on: 2015-02-21, 15:15:24 »

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Away from home in motorhome (RV) using laptop on low battery so might not get this post finished.  Although your DSO is on battery power its chassis will have a self capacitance to earth so there will be shunt path across to the sig gen earth.  This will be more prominent at the higher frequencies and will affect only the input measurements, effectively you have placed an unwanted capacitor across the input terminals that could be much greater than that of a scope probe.  If your scope can do subtraction you can put the NIR at the earthy end of the primary, then both scopes probes connect to the common earth.  One scopes the NIR voltage and the other scopes the sum of the NIR voltage and the wanted input voltage.  So a subtraction gives you the input voltage.  Then you eliminate any unwanted shunt paths.

I note your COP's are now quite realistic whereas before they were dismal.  It is worth doing finer frequency increments to see if there is a sweet spot giving maximum COP.  The graph of COP against frequency would reveal whether the math behind the negative resistance is correct since that definitely shows a peak at a certain frequency.  Then it is a matter of accounting for the positive losses pulling the COP below 1.

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Re: A closer look at a simulated Negative resistance coil. « Reply #97 on: 2015-02-21, 15:36:17 »

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Quote
The graph of COP against frequency would reveal whether the math behind the negative resistance is correct since that definitely shows a peak at a certain frequency.
Any preference for load resistor value?
   
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Re: A closer look at a simulated Negative resistance coil. « Reply #98 on: 2015-02-21, 19:07:24 »

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OK i used 510R


215khz i=72.4 lcv=675 load=4.6 pin=48.87mw pout=41.49mw cop=0.849
245khz i=72.4 lcv=757 load=4.90 pin=54.80mw pout=47.08mw cop=0.859
297khz i=72.3 lcv=875 load=5.17 pin=63.26mw pout=52.41mw cop=0.828
378khz i=68.5 lcv=1.04 load=5.78 pin=71.24mw pout=65.51mw cop=0.920
510khz i=67.5 lcv=1.06v load=5.8 pin=71.55mw pout=65.96mw cop=0.922
744khz i=66.7 lcv=1.17 load=5.76 pin=78.04mw pout=65.05mw cop=0.834
892khz i=63.8 lcv=1.2 load=5.77 pin=76.56mw pout=65.28mw cop=0.853
1.14mhz i=63.3 lcv=1.28 load=5.6 pin=81.66mw pout=61.49mw cop=0.753
1.32mhz i=61.6 lcv=1.22 load=5.25 pin=75.15mw pout=54.04mw cop=0.719
1.56mhz i=62.5 lcv=1.26 load=5.16 pin=78.75mw pout=52.20mw cop=0.663
1.84mhz i=63.7 lcv=1.29 load=5 pin=82.17mw pout=49.02mw cop=0.597
2.15mhz i=57.6 lcv=1.16 load=4.40 pin=73.89mw pout=37.96mw cop=0.514
3.30mhz i=56.2 lcv=1.25 load=3.4 pin=70.25mw pout=22.66mw cop=0.323
4.81mhz i=42.4 lcv=1.45 load=2.49 pin=61.48mw pout=12.16mw cop=0.198
6.76mhz i=21.2 lcv=2.08 load=1.31 pin=44.09mw pout=33.65mw cop=0.763

Not sure what happened at 6.76MHz i will look at that sudden jump up a bit more

EDIT
The graph was not very good so have now replaced it with a better one.
« Last Edit: 2015-02-22, 08:00:18 by Peterae »
   
img  Smudge
Re: A closer look at a simulated Negative resistance coil. « Reply #99 on: 2015-02-22, 16:05:54 »

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Thanks for all those measurements.  The sudden jump at 6.76MHz is almost certainly due to a resonance outside our area of interest.  If you ignore that then we have graph rising to a peak value then falling off at the higher frequencies, which is exactly what I would expect.  It is that rise to a peak value that is of interest since that is indicative of some internal effect that eventually gets overridden by the HF core losses.  The two charts here show (a) the complex permeability values that were derived using math functions to fit the actual ones and (b) the negative resistance that appears using the formula in my original paper.  The actual values shown are of no interest since I can change a small parameter and get widely different ones.  What is of interest is the value increasing with increasing frequency (as per my formula) but then getting overridden by the increasing positive value from core losses.  I think your results show this tendency.

So I suggest you now concentrate at a fixed frequency where the COP is maximum between 378 KHz and 510 KHz.  Then create a plot of COP against different load resistor values.  You should find an optimum value where COP is greatest.  Since you are already at a COP greater than 0.9 this bodes well for getting near to unity even if not beyond that.  When you consider that (a) the core has losses and (b) the coils have losses then a COP near unity could well mean that there is an OU effect going on.  You might then try Litz wire to minimise coil losses.  Anyway it appears you now have something tangible to get your teeth into.  Well done!

Smudge
   
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