Q factors; eddy currents versus wire resistance

[antigua]

It's been a while since we worked on eddy current modeling, but one thing I personally didn't around to was trying to map the equivalent series resistance that is imposed by eddy current losses. Since eddy currents increase with frequency, of course it's not exactly like "real" resistance, but there is an effective resistance at the resonance as a result of eddy currents.

So how much resistance? Someone on another forum asked about this www.strat-talk.com/threads/57-62-pickups-which-is-which.443031/#post-2849879 , so I thought I'd look into this more thoroughly. 


AlNiCo Single Coil

This plot below shows a Fralin Vintage Hots pickup, a typical Strat pickup set with AlNiCo 5 pole pieces and a hot bridge (guitarnuts2.proboards.com/thread/7814/lindy-fralin-vintage-analysis-review)



The LCR values for the neck pickup is 2.3H, 105p and 6.0k ohms. The unloaded peak reaches 13.3dB (pink line above). With these values plugged in, I can get a similar peak at 9.8kHz, but with a 14.8dB peak (green line below):



So there's a 1.5dB difference between the recorded 13.3dB in the real bode plot and the theoretical 14.8dB peak in the LTSpice plot, apparently owing to eddy currents that are not accounted for in the LTSpice model. It requires a total series resistance of 11k in order to bring the peak dB down to 13.3 (blue line), which is 5k ohms more than the 6.0k ohms of real copper wire resistance, at unloaded resonance, so it could be said that the eddy currents are equivalent to 5k ohms of added series resistance at that particular frequency.

With load (470pF and 200k parallel in order to simulate pot controls and guitar cable), the peak frequency drops to 4.2kHz and the peak amplitude reaches 6.7dB, and according to the spice model, with that 200k ohms parallel to the pickup, it takes no additional series resistance to get precisely 6.7dB at 4.2kHz.



In summary, eddy currents from the AlNiCo 5 poles add 5k ohms worth of series resistance at the true resonance, and virtually no resistance at the lower, loaded resonance with parallel load resistance.




PAF Style Humbucker


This Seymour Duncan SH-5 was uncovered (guitarnuts2.proboards.com/thread/7763/seymour-duncan-custom-analysis-review):



Here is a model with the values input:


The "pure" modeled peak comes out to +10dB (green line in LTSpice), but the recorded plot (black line in real bode plot) shows +5.2dB, and in order to get the plot peak down to 5dB, so that both plots match, the series resistance must be set to 80k, which is 65k ohms greater than the series resistance alone.


Here is the "loaded" SH-5 plot:



Here is what is required to curve match the loaded plot:



The theoretical peak is 1.5dB (green line in LTSpice), but the real peak is 1.0dB (black line in real bode plot), and to get that -0.5dB drop, a total of 38k series resistance is required, which is about 23.5k ohms of additional resistance represented by eddy current resistance.



In summary, the eddy current losses are more observable as the frequency increases, which is obvious enough, but more interesting is that the AlNiCo pole pieces represent only about 5k ohms resistance at true resonance, and almost no resistance in situ, with a guitar cable, where as a humbucker with steel poles and screws have equivalent losses in the double digits, 65k at self resonance, and 23.5k with a simulated guitar cable.

A take away from this is that, if considering only the pickup itself, the Q factor of a humbucker, or other steel core pickup, is determined mostly by eddy currents, and only somewhat by the wire resistance, whereas the Q factor of AlNiCo single coils is almost entirely determined by copper wire's resistance.

[ms]

Jul 8, 2017 16:10:40 GMT -5 antigua said:

A take away from this is that, if considering only the pickup itself, the Q factor of a humbucker, or other steel core pickup, is determined mostly by eddy currents, and only somewhat by the wire resistance, whereas the Q factor of AlNiCo single coils is almost entirely determined by copper wire's resistance.

Yes, the results such as this are the basis of my comment that increasing the conductivity by about 6% through the use of silver rather than copper wire is not a significant effect.  If it were, then so would many other effects, some of them hard to control.  It would be very difficult to produce a product sufficiently consistent so advertising claims would have any significance at all. Oh wait...

[reTrEaD]

Jul 9, 2017 5:58:05 GMT -5 ms said:

increasing the conductivity by about 6% through the use of silver rather than copper wire

Jul 9, 2017 5:58:05 GMT -5 ms said:

advertising claims

*giggle*

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From SD:

"Summary

A high-definition humbucker set that gives you more of everything you love about your guitar, with the finest components available.

Description

The Zephyr series was born from a challenge issued to Vice President of Engineering Kevin Beller to come up with a pickup that wasn’t constrained by the usual considerations of costs or materials: just dream it, design it and build it. The result is a tone with unprecedented treble clarity, vibrant harmonics and incredible dynamics, where your guitar simply feels like it has more of everything. More highs, fuller yet tighter lows, fatter mids and greater responsiveness. Compared to the bridge model has a slightly more aggressive feel and more output than the neck, while the neck model has a lower output and more high end which allow it to match well with the bridge model.

The sound is what immediately stands out about the Zephyr, but how we get there involves careful selection and implementation of the highest-quality materials available. We use silver wire – the only material with a lower CD resistance per unit length than copper (5.36%). Silver wire doesn’t boost highs and lows; it just does a better job of transmitting them. And silver’s softness compared to copper allows for an exceptionally even, neat coil form with increased immediacy whether you play with your pick or fingers.

We also use Bi-Metallic pole pieces with 440C Stainless Steel around a pure nickel core; the Stainless Steel delivers high saturation levels and extends the dynamic range, while the nickel core responds more quickly to subtle changes. We also use Glass Fiberfill Nylon Bobbins which are more resistant to microphonics than plastic and are more physically stable. Finally we use Cryogenic treatment which has been proven to enhance the detail available from audio equipment.

We hope you’ll love the Zephyr Silver Pickups as much as we do. If you want the best for your tone, Zephyr pickups are a true investment in your sound.

www.seymourduncan.com/pickup/zephyr-humbucker-set
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Wow.