Shields and Skin Depth

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The
following short
article is about
shields, Litz wire,
braid, and skin
depth.

Related pages

Coaxial and Shielded Lines 

Magnetic
Shielded Loops

Coaxial Cable Leakage

Common Mode Current

How
does a shield work?

We occasionally
hear that
time-varying
magnetic fields
penetrate a
non-ferrous
“shield”
on a shielded loop
or coaxial cable,
while electric
fields are blocked.
Here is an easy to
replicate experiment
showing how a thin
copper wall behaves
at radio
frequencies.

Below. I used a 10-inch
square ~.015 inch
thick copper sheet.
A standard BNC
connector was
soldered to the
center of this
sheet. (The lower
foreground shows two
small magnetic pick
up coils about 1/2
inch diameter)….

 

BELOW. The rear of the
sheet has two tabs
positioned directly
opposite the BNC
connector
connections. These
tabs mark the exact
location of the BNC
center and shield
pins….

These tabs
provide a reference
point for
measurements
directly opposite
the BNC connector on
the rear wall of the
sheet. Only a very
thin wall of copper
15/1000th inch thick
(.015″ thick) separates the rear
terminals from the
front side BNC
connector connection
points.

MEASUREMENTS

Is it possible
for energy to flow
directly through the
15/1000th inch thick
copper wall? How
would the signal get
to the back side of
the wall? To
answer these
questions we can
make two basic
measurements over
the area of the
sheet.

1. We can
   directly inject
   a signal into
   the sheet and
   directly read
   potential across
   a probe
2. We can use a
   small coupling
   loop for
   injection and a
   similar coupling
   loop for
   detection

We can move the
probes and loops
over the surface to
map signal levels.

The most
convenient device I
have for measuring
level change is
my spectrum analyzer
with a marker delta
function. By placing
a probe at the
injection point
where a high level
signal is injected
and zeroing the
marker delta
function, we can
directly read the difference in signal
levels at other
points.

 

Below. The copper sheet
is marked in
inches….

 

BELOW. The analyzer
probe is connected
and the marker zero
button pressed. Now
we have a reference
level of zero dB…

 

BELOW. The probe is
moved laterally one
inch. The analyzer
indicates signal
level change…

 

BELOW. The probe contact
point is moved
outwards and once
again the analyzer
indicates level
change…

The connection
points are moved one
inch at a time all
the way around to
the rear. The last
measurement is at
the two terminals
exactly behind the
generator input
connector.

How much signal
do you think there
is directly behind
the generator
attachment point?
This point would
have only .015 inch
of copper wall
thickness separating
the terminals. Do
you think the path
directly through the
.015 inch thick
copper wall would
have more level than
a lateral move of
one inch, where the
signal has to flow
laterally one inch
to one terminal and
then back laterally
for a total of two
inches? Does the
.030 inch round trip
directly through the
wall have less
attenuation than a
lateral trip of at
least two inches?

The following
readings were
observed at 500kHz:

Front					front edge	rear edge		rear center
0″ = 0db	1″ = -11dB	2″ = -24dB	3″ = -35dB	4″ = -43dB	5″ = -55dB	5″= -65dB	4″ = in noise	in noise

We see signal
level decreases
steadily towards the
edge. As we work around to the other side, we find no measurable signal directly
through the very thin copper wall!

This proves the
skin depth of the
copper prevents
coupling to the far
side. The isolation is as good
as if the back side
were totally
isolated from the
front, except for
what spills over the
edge of course.

What happens when
small loop probes
are substituted for
direct connections?
The small loop
probes are resonated
at 6.5 MHz. One loop
was fixed at the
center, the other
was moved along the
surface. The loop
was always aligned
for maximum reading.
The  following
readings were
obtained at 6.5
MHz::

Front					front edge	rear edge		rear center
0″ = 0db	1″ = -20dB	2″ = -38dB	3″ = -46dB	4″ = -53dB	5″ = -55dB	5″= -62dB	4″ =  in noise	in noise

Neither time
varying magnetic
flux nor
time-varying
electric flux can
pass directly
through a conductive
wall more than
several skin depths
thick. A shielded or
coaxial loop
only  receives
signals from the
outside wall, with
the gap becoming the
feedpoint. Our
Handbooks are
correct. The outer
wall of a coaxial
cable is a
“third
conductor”, the
outer wall is
isolated from the
inner shield wall by
skin effect.

Faraday
Screens

Don’t confuse an
intentionally gapped
screen with a completely walled or closed screen. Each behaves differently.

This is a Faraday
Screen etched on a double sided PC board. I developed
this screen in the 1980’s for a
medical
application…

 

(This applicator design is patented.) To satisfy FDA requirements, we had to
make hundreds of E and H field measurements. We need to provide a stable
magnetic field level. To reduce the effect of applicator-patient spacing on
tuning, and to prevent dielectric heating of areas near the surface, I needed to
reduce direct capacitive coupling to high voltage points inside the applicator.

This applicator consisted of a large
pancake coil inside a metal “pan”. The pancake coil had a
large fixed copper plate at
the center, and the
outer edge was
grounded to the pan. A movable flapper-plate, grounded to the metal
coil-enclosure pan and centered on the fixed coil plate, tuned the pancake coil.
The large center plate had considerable voltage, and considerable capacitance to
anything placed within a few inches of the applicator face. This meant anything
near the applicator center had large displacement currents, which seriously
affected tuning and impedance.

My solution was installation of a unique “Faraday” screen. My screen employed
a double sided PC board, with opposing screens on both the inner and outer
surfaces. The inner interlaced screen was rotated 90-degrees from the outer
screen. This spread the electric field around over a wide area, preventing a
concentrated electrical field from appearing. The screen prevented direct
capacitive coupling, and reduced distance detuning of the application and
E-field heating of skin. This helped produce a more consistent field
intensity level deep in a
patient’s soft tissue. 

Many people think a screen like this reduces electric field to zero, by
shielding or screen the electric field. Factually, we cannot have a time varying
magnetic field without an accompanying time-varying electric field. What we can
do is change the field impedance by moving the field around, or changing the
ratio of electric to magnetic fields. In a screen like this, the electric
field is
concentrated at each
open tip. Since
alternating open tips appear
everywhere around
the
applicator’s perimeter, the
electric field is 
evenly distributed
without “hot
spots”. This
reduces direct
external coupling
through capacitance
to nearby objects.

This screen does not eliminate the electric field. If it did, all magnetic
coupling would also stop. Just a few inches from the surface, the
field is
nearly identical to
an unscreened applicator. This screen and
similar screens will
reduce direct
capacitive coupling
to objects a very
small distance away,
but they do NOT
take the
electric field to
zero as some people
might claim.

If this screen were solid, neither magnetic or electric fields would
penetrate the wall. Any excitation of the other side could only come from
current spilling over the screen edge. This is because skin depth prevents
magnetic and electric fields from penetrating any conductor more than several
skin depths thick.   

Skin
Depth and Its Effect
in Conductors

The best
explanation of skin
depth I have seen is
in Circuits and
Networks (by
Koehler) on page
196:

So we see, skin
effect occurs
because the outer
areas of a conductor
have less magnetic
flux surrounding
them than the inner
layers. While we
often consider the
effect on materials
without weaves,
think about how this
affects woven
conductors like
braiding or Litz
wire. Any individual
conductor has HIGHER
impedance when it
moves into the
center areas, and if
current finds an
alternate path it
moves out to the
lower-impedance
outer layer.

If strands touch
with high resistance
connections, it
effectively adds
unnecessary
resistance to the
path. The fact the
surface is rough
also DECREASES
effective surface
area for current for
a given occupied
physical area,
because there are
non-conductive air
gaps in the occupied
area! 

The increased
resistance (and
impedance) is why
braiding should
never be used for
high frequency high
current applications
unless it is
oversized to
compensate for
increased impedance
and dissipation.
Parallel stranding
decreases effective
current carrying
surface area at high
frequencies, but at
least avoids the
weave problems.

As a matter of
fact the weave is
what causes most of
the loss increase
when typical coaxial
cables are
contaminated by
water. The problem
occurs, even after
the cable is dry,
because the hundreds
of weave contact
points corrode and
make poor
connections,
increasing the
resistance.
Something similar
happens when we
“unpack” a
braid from a jacket.
The pressure between
weaves decreases,
and series
resistance (and
impedance)
increases!     

We could insulate
strands, and once we
establish a basic
loss in conductivity
caused by replacing
useful conductor
area with insulation
we would find the
impedance slope much
flatter with
frequency. If the
strands are
insulated (Litz
wire) and frequency
is increased,
eventually we reach
a point where the
conductor resistance
increases and we are
much worse off than
we would be with
braided or stranded
wire. The upper
limit point is
generally around 1
MHz for Litz wire.

From Radio
Engineering by
Terman:

   

 

In reality, the
real advantage of
Litz wire is NOT
reduced resistance
per unit length for
a given diameter.
The advantage is
less slope in
resistance with
frequency and
reduced eddy current
when the conductor
is in a multi-layer
coil or transformer.
The individual
strands are like
laminations in a
transformer core,
and below a certain
frequency they
greatly reduce eddy
currents by
decreasing the
“short
circuit” path
distance for
magnetic flux
induced currents
that are not in the
normal current flow
direction.

My own
measurements have
shown noticeably
lower ESR
(equivalent series
resistance) for a
given conductor size
when using a SOLID
wire as compared to
any Litz wire sample
I have tried above
300kHz (the lower
limit of my main
vector network
analyzers).

For a given wire
diameter and form
factor, I’ve always
been able to achieve
higher Q with solid
round or ribbon
conductors.

Also see mobile
and loaded antennas.

this
page since October
2005