New impedance measurement geometry, not the same results

[ms]

What I want is an independent method of measuring changes in frequency, that is, decreasing inductance and increasing resistance as a result of eddy currents.  Results from the new method are not what I expected, but first let's look at how it works, and then the results later.

The top panel of the figure below shows my normal method of measuring impedance.  An ac voltage source drives the series combination of the pickup and a sense resistor (about 1K).  Input 1 (to the recording interface) measures the voltage across this series combination, and input 2 measures the voltage across the sensing resistor, which gives the current. The ratio is the impedance through the series combination.

A simplified model of a pickup is drawn inside the pickup box.  In order to examine the details of L and R, it is necessary to "unparallel" the impedance of the C.  This works fine, but it would be nice to have a method which removes the effect of the C in a different way.




The bottom panel of the figure shows such a different method.  An exciter coil is used to induce a voltage in the pickup coil.  The voltage is induced around each turn, but of course using Thevenin's theorem, this becomes a single series voltage source.  The exciter coil has an Rsense (165 ohms, value not critical, but needs to be known).  The exciter coil is as described by Ken Wiltmont.  Using the sense resistor is the easiest way to get accurate current information, both amplitude and phase.  As usual, input 1 is used as a reference in a cross-spectral measurement with input 2.

Rsense (input 2) is about 1K.  This is small enough so that the input C of the recording interface and the C of the pickup have little effect.  If we knew the value of that little voltage source, we would have a simple impedance measurement, similar to above.  However, only the L and R would matter.  Actually we only know the voltage to within a constant, and a 90 degree phase shift from the differentiation of the law of magnetic induction.  The constant can be found by a calibration at low frequencies, where R can be measured by an ohm meter and the impedance of L is small.

So that is a simple view of how it works; results later.

[ms]

Shown below is a measurement made with the alternate geometry shown in the lower panel  from the previous post.  The most striking difference between it and the "normal" measurement (shown further down) is that the imaginary part (the inductive reactance) does not bend over, but stays straight, up to the frequency where the measurement goes bad.  Also the real (resistive) part is not as large. Why?

[aquin43]

I think that the reason for the disagreement with the other measurement method is a phase problem at higher frequencies. The calculation assumes that the induced voltage leads the current through the exciter by 90 degrees. The field seen by the coil, however, is the combination of the exciter field and the re-radiated field of the pickup losses. The phase of this combined field lags behind the assumed 90 degree lead so that when you calculate the impedance it appears more inductive than it should be. This phase error in the calculation rotates part of the resistive component into the inductive.

[ms]

Feb 6, 2023 4:51:20 GMT -5 aquin43 said:

I think that the reason for the disagreement with the other measurement method is a phase problem at higher frequencies. The calculation assumes that the induced voltage leads the current through the exciter by 90 degrees. The field seen by the coil, however, is the combination of the exciter field and the re-radiated field of the pickup losses. The phase of this combined field lags behind the assumed 90 degree lead so that when you calculate the impedance it appears more inductive than it should be. This phase error in the calculation rotates part of the resistive component into the inductive.

I think you are saying that there are differences in the eddy current losses between the two different methods of excitation.  Maybe it works like this: when you excite by putting a voltage across the coil, eddy currents are induced in metal pieces by the B field made by the resulting current in the coil.  When excite with a B field, eddy currents are also induced in the metal pieces directly by this field.

I think that this has consequences for analyzing what the field from the vibrating string does.

There are a couple of ways to proceed experimentally.  First, increase the eddy current losses by using a cover.  I have some brass covers on order, but it appears that they are coming from China; I did not realize this when I made the order.  Also, I have a higher loss pickup (Filter'tron, or however that should be written) that I have started to measure.

[aquin43]

What I am really saying is that you can't get a known direct access to the pickup coil via magnetic excitation. There will always be a unknown filtering effect in play that will upset the phase relationship. Imagine that you went in via the shaded pole of my pole shading scheme. The coil excitation phase at high frequencies would be well below from the assumed 90 degrees lead. Phase shift is the real killer when making impedance measurements.

[ms]

But it is not just that "it appears more inductive than it should be";  its inductive reactance at all frequencies is that of the low frequency inductance of the normal method (straight line on log log scale where the measurement is good).

Here is the Fitler'tron with the new method:

and the original method:






The inductive reactance at all frequencies is also that expected from the low frequency inductance of the normal measurement.  The real part is even more reduced than that of the SDSH1N, approaching the low frequency value.

[aquin43]

I haven't done the algebra on this but I did try a spice simulation with a single mutually coupled loss. Assuming that 1/imag(short_circuit_current) represents the inductive reactance it does seem that the effective inductance is constant at high frequencies with or without the coupled loss. The loss R/L frequency is 820Hz.

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[ms]

I was hoping you would do a simulation. Thanks.  Circuits using mutually coupled inductors, especially when more than one k is involved, are difficult to  understand.  The skin effect, creating variable frequency resistors, makes more complication.  Here we have a circuit where an aspect of the response is simple.  It ought to be good for something.