Phase
Angle:
The difference in phase between two sinusoidally varying quantities.
Capacitive
Reactance:
A property of a circuit containing capacitance that together with
any resistance makes up its impedance.
Inductive
Reactance:
A property of a circuit containing inductance that together with
any resistance makes up its impedance.
Display
 Complex Impedance Plane (eddy scope)
Electrical
Impedance (Z),
is the total opposition that a circuit presents to an alternating
current. Impedance, measured in ohms, may include resistance (R),
inductive
reactance (X_{L}),
and capacitive
reactance (X_{C}).
Eddy current circuits usually have only R and (X_{L})
components. As discussed in the page on impedance, the resistance
component and the reactance component are not in phase, so vector
addition must be used to relate them with impedance. For an eddy
current circuit with resistance and inductive reactance components,
the total impedance is calculated using the following equation.
You will recall that this can be graphically displayed
using the impedance plane diagram as seen above. Impedance
also has an associated angle, called the phase
angle of the circuit, which can be calculated by the
following equation.
The impedance plane diagram is a very useful way
of displaying eddy current data. As shown in the figure below,
the strength of the eddy currents and the magnetic permeability
of the test material cause the eddy current signal on the impedance
plane to react in a variety of different ways.
If the eddy current circuit is balanced in air and
then placed on a piece of aluminum, the resistance component will
increase (eddy currents are being generated
in the aluminum and this takes energy away from the coil, which shows up as resistance) and the inductive reactance of the coil decreases (the
magnetic field created by the eddy currents opposes the coil's
magnetic field and the net effect is a weaker magnetic field to
produce inductance). If a crack is present in the material,
fewer eddy currents will be able to form and the resistance will
go back down and the inductive reactance will go back up. Changes
in conductivity will cause the eddy current signal to change in
a different way.
When a probe is placed on a magnetic material such
as steel, something different happens. Just like with aluminum
(conductive but not magnetic), eddy currents form, taking energy away from the coil, which shows up as an
increase in the coils resistance. And, just like with the
aluminum, the eddy currents generate their own magnetic field
that opposes the coils magnetic field. However, you will note
for the diagram that the reactance increases. This is because the
magnetic permeability of the steel concentrates the coil's magnetic
field. This increase in the magnetic field strength completely
overshadows the magnetic field of the eddy currents. The presence
of a crack or a change in the conductivity will produce a change
in the eddy current signal similar to that seen with aluminum.
In the applet below, liftoff curves can be generated
for several nonconductive materials with various electrical conductivities.
With the probe held away from the metal surface, zero and clear
the graph. Then slowly move the probe to the surface of the material.
Lift the probe back up, select a different material and touch
it back to the sample surface.
Experiment
Generate a family of liftoff curves for the different materials available in the applet using a frequency of 10kHz. Note the relative position of each of the curves. Repeat at 500kHz and 2MHz. (Note: it might be helpful to capture an image of the complete set of curves for each frequency for comparison.)
1) Which frequency would be best if you needed to distinguish between two high conductivity materials?
2) Which frequency would be best if you needed to distinguish between two low conductivity materials?
The impedance calculations in the above applet are
based on codes by Jack Blitz from "Electrical and Magnetic
Methods of Nondestructive Testing," 2nd ed., Chapman and
Hill.
