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NARRATOR: Skin effect-- describes
the tendency for high frequency currents
to be near surfaces of conductors.
Skin effect does not involve electromagnetic waves.
But it's rather a magnetic diffusion phenomenon.
One dimensional magnetic diffusion
can be pictured as the result of driving
a current from this source through this metal slab.
To make the current density and magnetic field intensity
depend only on x.
This configuration calls for the use of parallel plates
that make electrical contact with a slab.
The current is alternating.
At very low frequencies, the resulting current density
in the slab is uniform, and the magnetic field intensity
is a linear function of x.
At low frequencies, the magnetic field
falls from the current imposed by the source
to 0 At the insulating end.
B is the thickness of the slab.
Delta is the skin depth.
Omega is the angular frequency.
The skin depth is inversely proportional to the square root
of the frequency.
Mu is the permeability, and sigma is
the conductivity of the slab.
A high frequency implies a short skin depth.
As the frequency is raised, so that the skin depth becomes
shorter than the length of the slab,
the field decay is more rapid than a linear decay.
This decay reflects the fact that the current density
is crowding to the edge of the conductor, nearest the source.
The current density is distributing itself,
so as to lower the magnetic flux enclosed
by an average current loop.
To demonstrate this phenomenon, the slab
is this section of aluminum.
Rather than trying to find conducting sheets that
are even more conducting than the aluminum,
we extend this slab in the y direction
and make it the secondary of a transformer.
Here's the transformer primary.
Here's the transformer core.
The aluminum is the secondary of a step down transformer.
In effect, the secondary is composed of one turn
that is shorted on itself.
We will use this transverse probe
to measure the distribution of flux density.
Here's the experiment.
The section where essentially one
dimensional magnetic diffusion occurs is here.
By making the conductor long in the y direction,
we provide enough length for the current distribution
to become primarily dependent on x over the middle cross
section.
To avoid an influence of the magnetic core on the field
distribution here at the center, we placed it to one end.
This transfers probe can be inserted
so that it samples the vertical magnetic field intensity
over the span of the conductor.
The field component normal to the flat phase is measured.
The slit is little more than large enough for the probe.
The top trace is the current in the primary of the transformer,
the driving current.
The bottom trace is the probe signal, the magnetic flux
density.
As we pull the probe out, we see the field distribution with x.
The frequency is 60 hertz.
Here, we're at 3 centimeters, half the slab thickness.
It appears that the decay is somewhat more
rapid than linear.
So it looks like the skin depth at 60 hertz
is less than the thickness of the aluminum.
Let's evaluate the skin depth in aluminum at 60 hertz.
Aluminum has the permeability of free space,
a conductivity of 3.5 times 10 to the seventh siemens
per meter.
So at a frequency of 60 hertz, the skin depth
is less than the conductor thickness.
The skin depth of 1.1 centimeters
is small compared to a conductor thickness of 6 centimeters.
Here's a prediction of the field decay,
with distance from the left edge of the conductor.
This curve is for 60 hertz.
In going from 0 to 1 centimeter here on the 60 hertz curve,
we should see the field decay by 40%.
If we measure decays to about 50% of its original value.
Remember, the skin death is inversely
proportional to the square root of the frequency.
So if we increase the frequency to 240 hertz,
4 times the frequency, the skin depth is half as much,
and the decay should be more rapid.
This is the decay at 60 hertz.
Here, we're at 1 centimeter.
Here, we're at 3 centimeters.
Now we raise the frequency to 240 hertz.
This is the decay at 240 hertz.
1 centimeter, 3 centimeters.
The decay at 1 centimeter and 240 hertz plots like this.
These are additional data points.
Here's the major decay at 240 hertz, here at 60 hertz.
The discrepancy is probably due to the finite length
of the aluminum in the direction of current circulation.
Our one dimensional theory strictly
applies only where the currents have had sufficient development
length.
When the skin depth is short compared to the conductor
thickness, the current distribution
takes the form of a wave.
We've been observing the decay of this wave.
There's also a phase shift with x,
caused by the propagation of this diffusion wave
into the conductor.
By looking at the probe signal on an oscilloscope,
we can see this phase shift as the probe is withdrawn.
The top trace is the excitation current.
The bottom one the probe current.
Sync to the excitation current.
The frequency is 240 hertz.
So as the probe is withdrawn, the field decays rapidly.
To see the phase shift associated
with the propagation, let's put the probe signal
on top of the driving signal.
Watch the position of a peak in the probe signal,
relative to that of the driving current,
as the probe is withdrawn.
As the probe is pulled into the conductor,
it measures a field that is increasingly delayed in phase.
The magnitude of the magnetic diffusion wave
decays exponentially into the conductor,
with a decay length that is the skin depth.
The phase shift shows that the wave has phases that
propagate into the conductor.