3.6 Electromagnetic characteristics
Complex permittivity \(\varepsilon\) and complex permeability \(\mu\)are two parameters required for studying the absorption properties of
materials. Generally, they are expressed by Eq. 3 and Eq. 4. The real
parts \(\varepsilon\)’ and \(\mu^{\prime}\) indicate the degree of polarization
or magnetization of the absorbing material under the influence of an
electric field or magnetic field. The imaginary parts\(\varepsilon"\text{\ and}\) \(\mu"\) respectively represent the
measurement of the loss caused by rearrangement of the electrical moment
or magnetic moment of the absorbing material under the influence of an
applied electric field or magnetic field. The larger the two imaginary
parts, the greater the dielectric loss and magnetic loss capability of
the absorbing material[38].
\(\varepsilon=\varepsilon^{\prime}-j\varepsilon"\) (Eq. 3)
\(\mu=\mu^{\prime}-j\mu"\) (Eq. 4)
Groups O, C2 and C2S1 are selected for the electromagnetic parameter
test. The results are demonstrated in Figure 14-15.
The real and imaginary parts of the complex permittivity of different
groups are shown in Figure 14. The values of \(\varepsilon\)’ and\(\varepsilon"\) of Group O are both small, with the range of 1.6-2.5
and 0-0.5, respectively. As can be seen from the chemical composition of
cement (see Table 1), the tested cement itself contains a small content
of the metal oxides Al2O3,Fe2O3, and MgO. Under the influence of
an applied electromagnetic field, they will undergo dielectric
polarization, bringing the foam concrete with a certain dielectric loss
capability which is poor and negligible. For group C2 mixed with
0.6wt.% carbon fiber, the values of \(\varepsilon\)’ and\(\varepsilon"\) are between 5.9-8 and 0.5-2.2, respectively, which are
significantly improved compared with those of group O. Besides, the
average value of the imaginary parts is about 1.75 in 4-5 GHz frequency
band, indicating that the foam concrete has a larger dielectric loss
factor (Eq. 5) and a better dielectric loss capability in this frequency
band. For group C2S1, the values of \(\varepsilon\)’ and\(\varepsilon"\) range between 7.9-10.9 and 0.9-3.3, respectively, which
are higher than those of the other two groups. The average value of the
imaginary parts in 2.2-3 GHz band is about 2.75, which is about 1.75
higher than group C2.
(Eq. 5)
Figure 15 shows the real and imaginary parts of the complex permeability
of foam concrete. The real part values of the complex permeability of
three groups have little difference at various frequencies, with the
range of 0.25-1.4. The imaginary part values of the complex permeability
of three groups are between 0 and 0.7, and the two groups mixed with
absorbents have higher values in the 0.5-5 GHz band compared to group O.
Furthermore, compared with the complex permittivity in Figure 13, carbon
fiber and graphite have a relatively poor effect on increasing the
values of \(\mu^{\prime}\) and \(\mu"\) of foam concrete. This also corresponds
to the loss mechanism of carbon fiber and graphite on electromagnetic
waves, which is resistance loss rather than magnetic loss.
The loss characteristics of the material can be characterised by the
attenuation constant α (Eq. 6), where f is the frequency of
the electromagnetic wave and c is the speed of light, and the
larger the value, the more the electromagnetic waves tend to
dissipate[39,40]. The calculation results are presented in Figure
16.
(Eq. 6)
The attenuation constant values of Group O are low at different
frequencies with the maximum value of only 19.23. It indicates that foam
concrete without absorbents has poor electromagnetic wave loss
capability, corresponding to the previous conductivity test results. For
group C2 with the addition of 0.6wt.% carbon fiber, the attenuation
constant value increases with the increasing frequency and the
absorption peak appears between 2.5-3.5 GHz with the value of 47.18. At
3.5-5 GHz, the attenuation constant continues to rise and the maximum
value is 70.07, increased by 264.38% over that of group O. Group C2S1
has roughly the same change trend of the attenuation constant as group
C2, but the absorption peak is earlier and 11.95 higher than that of
group C2. The maximum value is 94.6, which is 391.94% higher and
35.01% higher than those of group O and group C2, respectively. As a
result, the electromagnetic wave absorption and loss capacities of
specimens are improved by adding carbon fiber alone. For Group C2S1, the
absorption peak occurs earlier, which widens the bandwidth with the
large attenuation constant.
Reflection loss (RL) is a criterion for the electromagnetic wave
absorption characteristics of single-layer planar materials, as in
equation 7, and a value of less than -10 dB indicates that more than
90% of the electromagnetic wave is absorbed by the material[41].
The results of RL calculations for three sets of specimens from 0 to 10
mm thickness are shown in Figures 17 to 19.
(Eq. 7)
In this equation: Zin -Input impedance of the
material
μ r-Relative permeability
ε r-Relative permittivity
Z0 -Wave impedance of free space
μ0 -Permeability of free space
ε0 -Permittivity of free space
d -Thickness of material
Figure 17(a) shows the 3d mapped surface plot of the reflection loss for
Group O at different thicknesses and frequencies, and Figure 17(b) shows
the corresponding two-dimensional curve. It can be seen from Figure 17
that the Group O has almost no electromagnetic wave loss capability and
the reflection loss value reaches its minimum value of -3.58 dB at a
thickness of 10 mm. As can be seen from Figure 18, the electromagnetic
wave loss capability of group C2 is significantly higher than that of
group O. The reflection loss value decreases with increasing specimen
thickness and appears to be less than -10 dB, with effective bandwidths
of 0.8 GHz, 1.7 GHz and 1 GHz at thicknesses of 6, 8 and 10 mm,
respectively. The reflection loss reaches a minimum value of -38.47 dB
at 10 mm thickness, an increase of 34.89 in absolute value compared to
group O. This indicates that the addition of carbon fibre has a
significant improvement in the electromagnetic wave loss performance of
the foam concrete. The reflective loss of the foam concrete with
graphite compounding at different thicknesses is shown in Figure 19,
where the value also decreases with increasing thickness, with effective
bandwidths of 2.5 GHz, 1.4 GHz and 0.9 GHz at thicknesses of 6, 8 and 10
mm respectively.