Shielding
Theory
There are two ways of approaching the theory of shielding: the
use of circuit theory, or the use of wave theory. The EMC industry
uses a wave theory approach to shielding theory using abstract
mathematical modeling techniques to yield a value of merit classified
as “shielding effectiveness”. Shielding effectiveness
is then used as a measurement to gauge the attenuation of the Electromagnetic
(EM) fields through shielding barrier material.
The problem with the use of shielding effectiveness is that there
can be a significant differential between the attenuation of the
electric E fields, magnetic H fields, and power, where the difference
can exceed 100 dB. The actual difference will vary as a function
of variables associated with specific applications where the literature
on the shielding of radiated EM fields does not address these conditions.
The result is a significant confusion factor in the selection of
shielding barrier material, facing design engineers who are required
to meet EMC radiated emission and susceptibility requirements.
The circuit theory approach (included herein) employs mathematical
modeling techniques consistent with college course work and yields
a predicted field strength at any given distance from the shielding
barrier material. The results can also be used to predict the shielding
of a seam or gasketed joint in the barrier material (or enclosure).
The circuit theory approach given below examines the wave as it
penetrates a barrier and yields a value of the E and H fields as
the wave exits the barrier.
Introduction
A radiated electromagnetic (EM) wave is generated by the action
of driving a current through a wire. An example is that of Figure
1 which represents a sending/receiver circuit on a PC card.
Figure
1

The wire (or PC card trace) acts as a transmitting antenna, as
an emitter of EM interference and as a receptor with regard to
EM susceptibility. A common method of reducing (or eliminating)
the possibility of the PC trace being an emitter or receptor is
by the use of a shielding barrier.
When an EM wave is impinged on a metallic (conductive) shielding
barrier, currents are caused to flow in the barrier. As the wave
penetrates the barrier, the current is attenuated (i.e., reduced
in amplitude as illustrated in Figure 2) by a force called skin
effect.
Figure
2

The power of the wave as it leaves the barrier is approximately
equal to the current squared times the impedance of the barrier,
and is in watts per meter squared.
As we learned above, currents flow in the shielding barrier as
a function of the radiated wave being impinged on the barrier.
When the current crosses a seam in the barrier (created by maintenance
covers, etc.),
a voltage is created across the seam, where the value of the voltage
is equal to the current times the impedance of the seam. The seam
then becomes a radiating antenna where the impedance and pattern
is similar to that of a slot antenna. EMI gaskets are used to reduce
the impedance of the seam and subsequent power radiating from the
seam.
Generation
and Propagation of EM Fields
Figure 3

The undergraduate courses on EM theory introduce the concept
of an EM wave by driving a pair of parallel plates with an AC
voltage source as illustrated in Figure 3.
The current that flows through the wire comes from the top plate
and is stored in the bottom plate. The overpresence of the electrons
on the bottom plate is illustrated by
and the absence of electrons on the top plate and is illustrated
by
. This creates an EM wave which is illustrated in
Figure 4. The EM wave consisting of the
straight lines is classified as a displacement field and is in
Amperes per meter squared. The magnitude of the E field is equal
to the voltage differential between the plates divided by the
distance between the plates in meters. The resultant E field is
in Volts per meter (e.g., a set of parallel plates is used for
performing E field susceptibility testing to MILSTD461/462).
Figure 4

As is illustrated in Figure 4, the lines of flux in the center of
the plates are straight and flow from the bottom to the top plate.
At the edges they bow out, where the fields or lines of flux repel
each other, forcing the bowing. The field that bows out represents
a radiated EM wave. The radiated EM wave emanating from the trace
of Figure 1 is similar to the radiated EM wave illustrated in Figure
4. The electric “E” field is tangent to the lines of
flux (displacement current) as illustrated in Figure 4. The magnetic “H” field
is a field perpendicular to the displacement current and points out
of the paper (right hand rule).
The set of plates as illustrated in Figure
4 produce a field similar to that of the PC card trace of Figure
1 (and of an electric dipole antenna). If the transmitted power
is known, the field strength can be calculated using the dipole
antenna equation, i.e.,
And power equation (poynting vector):
If the power is not known, the value of the electric field can
be approximated using the following equation:
Suppression
(Shielding) of EM Fields
Figure 5

When we place a shielding barrier in the path of the EM wave,
the force of the wave causes current to flow in the barrier. As
is illustrated in Figure 5, the excess electrons in the bottom
plate create a force on the electrons in the barrier. This force
causes the electrons to flow away from the point of contact. In
a similar manner, the lack of electrons on the upper plate will
create an excess of electrons on the barrier at the upper point
of contact. This current flow in the barrier is called the "surface
current density" in amperes/meter, and is approximately
equal to the H field incident on the barrier when the direction
of the wave is perpendicular to the barrier. The current flowing
in the barrier is attenuated by skin effect.
The current on the transmitted side is equal to
(i.e., the current on the incident side attenuated by skin effect).
The impedance of the field emanating from the barrier is equal to
the impedance of the barrier. The values of
and
are as illustrated in Figure 5 and are as
follows.
Field
Strength Through Shield
Figure
6

From antenna theory we know that the power from an antenna is
reduced as the square of the distance from its source. Shielding
theory proposes that the wave as it passes through a barrier is
attenuated but not changed with regard to direction. As such, the
loss of power is a function of the distance from the original source
of the wave as illustrated in Figure 6.
The power at a distance
from the barrier is equal to the following:
The impedance of the field will vary from a low impedance (impedance
of the barrier) to 377 ohms when the distance .
The value of E and H can be closely approximated at a distance using
the following equalities:
Gasketed
Joint Shielding
Figure 7

When a radiated EM wave is impinged on a metallic shielding barrier,
a current (surface current density in amps/meter) is generated
in the material. When the current flows across a gasketed maintenance
cover as illustrated in Figure 7, a voltage e is generated across
the gasket. The value of e is equal to
the current in amps/meter times the impedance of the joint (transfer
impedance in ohmmeters).
The EM force field illustrated in Figure 7 is generated by the
voltage across the gap and has the characteristics of a low impedance
slot antenna.
The value of the radiated EM fields can be estimated from the
example of Figure 7 as follows:
