(10.20)
where x is the shield thickness, in meters; the resistivity of the shield, in ohm meters; µ
r
the
relative permeability of the shield material; the skin depth of the material; and F the
frequency of the wave.
From
Table 4.1
the resistivity of copper is
Cu
= 1.72 × 10
-8
·m, whereas pure iron is
Fe
=
10 × 10
-8
·m and steel ranges from 1.2 to 120 times the resistivity of pure iron. The relative
permeability of iron and/or steel ranges from 110 to 14,800; however, ranges from 300 to
1000 are typically used for shielding calculations. Thus, although pure copper is more
conductive (less resistive) then iron-based metals, the iron-based metals allow less
penetration (recall that increased permeability decreases the skin depth). This is important
except for conditions where the shield is thin (x << ). When the shield is thin, most of the
shielding is accomplished due to reflection, and a higher-conductivity metal such as copper
would be an advantage.
For materials other then sheet metal, such as conductor impregnated plastic,
equation
(10.20)
is generalized as
(10.21)
where q is a constant that varies with the conductive material or coating and x is the
thickness. For conductive surface coatings, q will vary from 0.2 to 1.0 [
White, 1986
].
Reflection is, of course, the other parameter that determines shield effectiveness (SE).
Shield effectiveness due to reflection is defined as
(10.22)
where Z
shield
is the per square impedance of the shield (the same as the equivalent metal
surface impedance in ohms per square for sheet metal, or this number is provided in data
sheets for special shield materials), and Z
wave
is the wave impedance at the distance of the
shield. Again, the shield effectiveness is a measure of the decrease in radiated emissions
[
White, 1986
].
For wave impedance values much higher than the shield impedance, as is usually the case
for conductive shields,
equation (10.22)
reduces to
(10.23)
where the wave impedance is 377
in the far field or can be derived for the near field from
equation (10.8)
or
equation (10.3)
, depending on the nature of the radiator. One can see that
for low-impedance waves, such as in the near field of a low-impedance loop radiator, it may
be difficult to get reflective performance from the shield.
Notice that unlike penetration performance, reflective performance from thin shields is not a
function of frequency. Thus, thin conductive shields can be implemented successfully using
primarily reflection as a shielding mechanism. The condition to avoid with such a shield is, of