Reference: Robert Hooko's post 13 Jan 02 Re: JSPI etc.
Here's my theory of metallic iron response, seen primarily from a VLF viewpoint, but it sheds some light on PI as well.
Iron is a low-conductivity metal. However, its phase response internally is like a high-conductivity target, because although the electrical conductivity is low, its magnetic permeability produces an increase in the inductance of the eddy-current path.
Externally, the magnetic permeability of the iron also distorts the magnetic field, independently of the fact that the iron is conductive and can support eddy currents. In a VLF machine, we look for signals while the field is changing, so we see this effect, which is similar to that of ferrite. Superimposed on that effect is the eddy current effect.
If the reactive component of the magnetic permeability response were equal in magnitude to the reactive component of the eddy current response, the two would cancel and you'd have a target with a 90 degree magnetic loss angle, which would appear as a target having a zero degree electrical angle (i.e., resistive). This can happen on flat iron the plane of which is oriented at right angles to the field, minimizing the permeability effect.
If we ignore such special cases, and restrict ourselves to things like nails and lumps of iron, then we have the following situation.
It is an observable fact that regardless of frequency (or pulsewidth, if you prefer) iron doesn't come close to a 0 degree loss angle like ferrite, nor does it come close to a 90 degree loss angle like salt water. It may bounce all over the place, but it stays away from those two limits. It's always somewhere in the broad middle region.
When the resistive and reactive components are demodulated and then differentiated and divided to get apparent phase, then you're looking at phase trajectories. If you interpret this as actual phase (as is the custom) then you'll often find apparent phase coming close to the 0 and 90 degree limits or even going beyond momentarily. We will limit the discussion here to the actual phase as seen when looking at the static signals without "motion circuits".
So, what keeps iron away from the 0 and 90 degree loss angle boundaries?
If the iron has fairly low permeability due to its composition or orientation, then the permeability effect produces a fairly weak vector in the direction of ferrite (0 degrees). If all else were equal, then the reactive component (180 degrees) of the eddy current vector would be strong in comparison, and the target would look nonferrous.
However, if the permeability is low, then the inductance of the eddy current loop is also low, and internally the iron acts as though it were lower conductivity, with a corresponding reduction in its 180 degree reactive component. So, the 0 and 180 degree reactive components tend to maintain their relationship of balance toward 0 degrees.
So, with low permeability, why doesn't the resistive component push the result toward the 90 degree loss axis?
High permeability attracts the magnetic field to the target, increasing the magnitude of its eddy currents the same as though it were nonferrous and had been immersed in a stronger field. (You gold prospectors know how loud a signal a tiny iron wire whisker can give, especially if surrounded by magnetic rust!) Reducing the permeability reduces the total eddy current, and hence its resistive component.
The result is that iron tends to fall somewhere in the broad midrange between 0 and 90 degree magnetic loss angle, regardless of the material permeability or orientation.
So why does the permeability component always dominate, keeping the loss angle below 90 degrees? I have two explanations, but am not sure if either of them is the right one.
First explanation: Because the iron attracts a magnetic field from a region larger than itself, the permeability effect acts like a bigger target. (In magnetics engineering this effect is called "effective permeability", which is always greater than unity for magnetic materials).
Second explanation: the permeability vector is at 0 degrees, whereas the eddy current vector is somewhere between 90 and 180 degrees. If we assume that the eddy current vector cannot have a magnitude greater than the permeability vector, then the reactive component of the eddy current vector will always have a smaller absolute magnitude than that of the permeability vector.
"REACTIVE COMPONENT" IN PULSE INDUCTION
For the sake of convenience, in pulse induction we frequently say that the period during which current is flowing in the transmitter coil corresponds to the reactive component, and the decay afterwards corresponds to the resistive component. Although this provides a convenient analogy to VLF practice, it is not mathematically correct.
A lossless nonferrous target (i.e. a superconductor) would respond only during the transmit/flyback period, and would produce no detectable decay afterwards. On an IB loop, it would look like ferrite, but upside down. This effect, like that of an ideal ferrite, is independent of frequency.
An actual target, however, has reactive responses which are frequency-dependent. If you were to take all the independent reactive sinusoids over the frequency spectrum and superimpose them, they would not reproduce the time-domain transmit/flyback pulse. The resulting waveform would be doing lots of interesting stuff during the "decay period" as well.
WHY THE DECAY CURVE OF IRON HAS A DIFFERENT SHAPE
The high permeability of iron tends to restrict magnetic fields and hence eddy currents to a thinner skin depth than an otherwise similar nonferrous material. Skin depth varies with frequency. In the case a nonferrous material, as the geometry of the eddy current path changes over (decay) time, the inductance and resistance of that path change as well.
In the case of iron, we have a third variable: effective permeability. That, too, is dependent on geometry. It does not vary in proportion to the unity-permeability inductance of the current path; and, what's more, its effect on field distribution influences the geometry of the eddy current distribution.
--Dave J.
