Tweet
One can attempt to model the circuit of a humbucker as an inductor with the resistance of the coil in series and with a capacitance and another resistance in parallel. This second resistance attempts to account for the losses due to eddy currents in the cores. This model does not work very well; one way of describing its inaccuracies is this: the the measurements, when compared to the model, appear to show that the inductance varies with frequency. Measurements with an LCR meter indicate something similar.
[A note about modeling electronic things: Maxwell's equations imply the concepts of resistance, inductance and capacitance. The ideal components used in circuit analysis are based on these concepts. All actual components are more complicated, having, at least to some degree, all three properties. Modeling a pickup means finding a circuit of ideal components that describes the behavior of the pickup with reasonable accuracy.]
So another way of looking at this is that one expects that there is one or more essential components missing from the model described in the first paragraph. That is, the impedance of the pickup, when measured across frequency, appears to imply a varying inductance, but the inclusion of the correct additional components should lead to good agreement without resorting to frequency variable components.
The rest of this post is a summary of the topics that need to be discussed later in order to show that the idea in the previous paragraph is correct. First are the measurements. They use the pickup meter described in Joe's discussion on designing an LCR meter. These new measurements include the phase of the impedance in addition to its amplitude. The phase might not be essential, but it does provide independent information and helps verify conclusions about the accuracy of the pickup model.
Next is the new model of the circuit for a pickup. It is based on the model for a non-ideal transformer. The magnetizing inductance from this model is the inductance of the pickup coil. This model also has an inductor which accounts for the leakage flux. A pickup has a lot of leakage flux because the cores are open, and so this inductance can be very large. In applying this model to a pickup, the effect of the eddy currents in the cores is represented by a resistive load on a one turn secondary. The inductance accounting for the flux leakage appears in series with this load, and it alters the effect of the eddy currents as a function of frequency.
Third, it is necessary to compare the predictions of this new model with the measurements. The effect of the leakage flux inductor is to improve the agreement between the model and the measurement. This is convincing evidence that the model has a physical basis. That is, it tells us how the pickup circuit works. Thus, from my point of view, saying the pickup has frequency variable inductance is a measurement issue rather than a useful way of describing how the circuit works.
The final topic concerns developing a method of deriving the values of the components in the model, as implied by the measurements, by means of a software technique. If successful, this would be one way to complete the pickup measuring process, and possibly make a practical effective instrument.
[A note about modeling electronic things: Maxwell's equations imply the concepts of resistance, inductance and capacitance. The ideal components used in circuit analysis are based on these concepts. All actual components are more complicated, having, at least to some degree, all three properties. Modeling a pickup means finding a circuit of ideal components that describes the behavior of the pickup with reasonable accuracy.]
So another way of looking at this is that one expects that there is one or more essential components missing from the model described in the first paragraph. That is, the impedance of the pickup, when measured across frequency, appears to imply a varying inductance, but the inclusion of the correct additional components should lead to good agreement without resorting to frequency variable components.
The rest of this post is a summary of the topics that need to be discussed later in order to show that the idea in the previous paragraph is correct. First are the measurements. They use the pickup meter described in Joe's discussion on designing an LCR meter. These new measurements include the phase of the impedance in addition to its amplitude. The phase might not be essential, but it does provide independent information and helps verify conclusions about the accuracy of the pickup model.
Next is the new model of the circuit for a pickup. It is based on the model for a non-ideal transformer. The magnetizing inductance from this model is the inductance of the pickup coil. This model also has an inductor which accounts for the leakage flux. A pickup has a lot of leakage flux because the cores are open, and so this inductance can be very large. In applying this model to a pickup, the effect of the eddy currents in the cores is represented by a resistive load on a one turn secondary. The inductance accounting for the flux leakage appears in series with this load, and it alters the effect of the eddy currents as a function of frequency.
Third, it is necessary to compare the predictions of this new model with the measurements. The effect of the leakage flux inductor is to improve the agreement between the model and the measurement. This is convincing evidence that the model has a physical basis. That is, it tells us how the pickup circuit works. Thus, from my point of view, saying the pickup has frequency variable inductance is a measurement issue rather than a useful way of describing how the circuit works.
The final topic concerns developing a method of deriving the values of the components in the model, as implied by the measurements, by means of a software technique. If successful, this would be one way to complete the pickup measuring process, and possibly make a practical effective instrument.
Comment