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Post by JohnH on Feb 8, 2017 14:23:53 GMT -5
One thing (ok one amoung many!) that I'm not understanding is how you are getting the output plots derived from impedance measurements. When I calculate such things from equivalent components, I need to end up with reducing the system to two impedances (each with real and imaginary parts) forming a voltage divider. Then I can get a ratio of input to output voltage given a virtual voltage source with a flat response. I cant get the result with just one overall impedance.
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Post by ms on Feb 8, 2017 15:33:16 GMT -5
One thing (ok one amoung many!) that I'm not understanding is how you are getting the output plots derived from impedance measurements. When I calculate such things from equivalent components, I need to end up with reducing the system to two impedances (each with real and imaginary parts) forming a voltage divider. Then I can get a ratio of input to output voltage given a virtual voltage source with a flat response. I cant get the result with just one overall impedance. John, here is the answer from an earlier post. This is exactly what I am doing: So start with the measured impedance; it includes all four of the elements in the above representation. Suppose we find the C value somehow. (It seems practical to do this at the resonance by fitting to a model that incorporates the eddy current effects over a narrow frequency range so that Rse can be assumed constant over that range.) This C can be "unparalleled" leaving an impedance, call it Zu. The real and imaginary parts of this impedance are shown in the impedance plots shown earlier (green and yellowish lines), and the accuracy of the C measurement is shown by the removal of the shape of he peak from Zu. Now Zu and C can be used to make a voltage divider. That is, Zu replaces the three series elements in the above pickup model. Then the frequency response can be directly computed from the impedances of Zu and C. This is the idea I am trying, but it is necessary to measure the frequency response directly in order to check the results. I can do that with the same system used to measure the impedance, modified a bit. Here is the Python routine used to do the calculation: # Function to compute the frequency response from the impedance # Inputs are the frequency array, the complex impedance, without C, the C # value, and the R value (load, across the C) def frfZ(freqs, Zu, C, R): pt = pupc.pupc(fext = freqs) Zc = pt.fZC(C) return pt.vdiv(Zu, pt.par(Zc, R)) vdiv calculates the response of a voltage divider. It is a method in the class I listed here earlier.
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Post by JohnH on Feb 8, 2017 16:09:52 GMT -5
Ok thanks and sorry for missing that earlier. I see how once you have identufied a value for C and seperated it from the other impedances, then maths will provide the outputs.
But there is a very important difference between that model and the ones I play with in that the extra damping beyond 3 basic RLC components is all done by adding impedance in series with the basic R and L, whereas my models add a parralel impedance across the output. I see eddy currents as acting primarily as a load rather than as an impedance change (though that happens as a consequence).
It could be that these two different approaches can be shown to be equivalent. Or it may be that there is a fundamental priciple in play.
In adding parallel impedance, I adjust the basic L and R to keep measured properties the same at low frequency.
I think one demo of validity would be if a single model can be used with external components to match tested results with two different external load conditions.
Do you think these are valid questions and if so can you forsee how they could be resolved?
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Post by antigua on Feb 8, 2017 16:32:37 GMT -5
Ok thanks and sorry for missing that earlier. I see how once you have identufied a value for C and seperated it from the other impedances, then maths will provide the outputs. But there is a very important difference between that model and the ones I play with in that the extra damping beyond 3 basic RLC components is all done by adding impedance in series with the basic R and L, whereas my models add a parralel impedance across the output. I see eddy currents as acting primarily as a load rather than as an impedance change (though that happens as a consequence). It could be that these two different approaches can be shown to be equivalent. Or it may be that there is a fundamental priciple in play. As far as principles go, eddy currents are part series impedance, and partly a direct attenuation upon the AC source itself, which is to say it's external to the circuit. It's like if someone is talking into a microphone and you put a burlap sack over their head, you're attenuating the subject, not the microphone or it's circuit. The eddy currents that oppose the guitar string are doing something similar to that. I think the six part model only resembles eddy current losses by virtue of introducing a counter resonance that causes a mild band stop filter effect. We see a similar band stop with veratone circuits. It's like you're making a veratone that approximates eddy losses.
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Post by JohnH on Feb 8, 2017 21:16:30 GMT -5
I agree that they may need to be a function on input voltage. Im curious about why eddy's would necessarily be represented by added series impedance, as compared to added parallel load. They may be equivalent if the theory would align with transformers, such as described here: www.insula.com.au/physics/1221/L17.htmlIt shows how the effect of a loaded secondary (which eddy currents could be considered as analogous to with poor coupling) can be represented either by parallel or by series impedances. Or, consider a thought experiment, and possibly a real experiment: Consider two pickups of comparable DCR, resonant frequency and L, one being a simple but overwound alnico single, the other is a low wind humbucker with a poor cover, both with very similar low frequency properties in terms of DCR and measured inductance. The humbucker produces a much flatter softer peak. Which will have the greater impedance at resonance? If the damping is best represented by added series impedance, then the more highly damped humbucker should show a greater impedance at resonance than the single.
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Post by antigua on Feb 8, 2017 23:31:11 GMT -5
The reason you get an impedance at resonance because of the resonance itself, and if you introduce something that prevents the inductance and capacitance from resonating, by way of series resistance, or in giving the current a bypass by way of parallel load, you lose that sharp resonant peak. We know that eddy currents cause the resonant Q to drop, so which of these two things is it doing: the former, preventing the L and C from interacting, or the latter, giving current a route around the LC reactance?
What I would really like to know is why, in my eddy current experiments where the pickup and driver coil were a few inches apart, the Q factor dropped even when the source the eddy currents (aluminum block) was hugging the driver coil, and was nowhere near the pickup.
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