Design of Radar Absorbing Structures Utilizing Carbon-Based Polymer Composites

Abstract

Radar absorbing structure (RAS) is a composite laminate with a low reflection coefficient for the electromagnetic illumination in microwave frequency range, and thereby can be used in the stealth technology and electromagnetic compatibility (EMC). In this study, microwave absorbing properties of a two-layer composite laminate (carbon black impregnated rubber sheet attached to the carbon fiber–epoxy composite panel) has been investigated. Complex permittivity and permeability of the composite materials were measured in C- and X-band frequencies (4–12 GHz) by reflection/transmission technique using a coaxial waveguide and network analyzer. Complex permittivity can be controlled with the amount of carbon black in the rubber composite. High values of dielectric constant and dielectric loss are observed in the carbon fiber composite. Optimization of microwave absorption is conducted for the two-layer RAS on the basis of transmission line theory. It is found that microwave absorption is strongly sensitive to carbon black content in the rubber composite and its layer thickness. For the rubber sheet containing 10% carbon black (with dielectric constant ≍5), the maximum microwave absorption (30 dB) is predicted at 10 GHz.

1. Introduction

Conventional ferrite absorbers in tile or composite form are attached on the existing metal structures and thereby reduce the wave reflections from the conductive substrate. For this metal-backed (short-circuited) absorber, many studies were carried out to design the zero-reflected absorber and to improve the microwave absorbing properties^1–9. However, in movable semi-anechoic chamber or other types of moving vehicles, the structures are preferable as light as possible. For this demand, the metal parts can be replaced by carbon fiber polymer composites with high mechanical strength and low weight. Furthermore, the carbon fiber composites can be used as a microwave reflector, due to its high electrical conductivity^10–12. Therefore, a two-layered absorber consisting of the carbon black and carbon fiber composite substrate can be proposed as a light-weight structural absorber having low microwave reflections^13–15.

The purpose of this study is to investigate the microwave absorbing properties of carbon black composite attached on the carbon fiber polymer composite substrate. On the basis of wave propagation theory, a modified equation for wave-impedance-matching at the front surface of absorbing layer is proposed. It is demonstrated that the microwave absorbance of front carbon black-absorbing layer is strongly influenced by the electrical properties of the attached carbon fiber polymer composite.

2. Reflection and Absorption Loss of Two-Layer Ras

Consider a situation that a plane wave illuminates the microwave absorber attached by a quasi-reflective substrate, as illustrated in Figure 1(a) . The situation is analogous to that of terminated transmission line as schematically shown in Figure 1(b) , where Z₀ is free-space impedance (= 376.7 ω), Z_c1(2) is characteristic impedance of substrate (designated by 1) and absorbing layer (designated by 2), and Z_in1(2) is input impedance at the front surface of reflecting substrate and absorbing layer, respectively.

Figure 1

Schematic description of (a) two-layered RAS and (b) its equivalent circuit

If the relative permeability and permittivity of the substrate and absorbing layer are designated by μr₁₍₂₎ and εr₁₍₂₎, respectively, the characteristic impedance Z_c1(2) and propagation constant v₁₍₂₎ in the two medium is expressed as

$$Z_{c1(2)}=Z_0\sqrt{\frac{\mu c1(2)}{{\epsilon }_{r1(2)}}}$$

(1)

$${\upsilon }_{c1(2)}=j\left(\frac{2\pi f}{C}\right)\sqrt{{\mu }_{r1(2)}{\epsilon }_{r1(2)}}$$

(2)

where f is frequency and c is velocity of light. Z_in1(2) is a function of material constants (μ _r ε _r ) and layer thickness (d₁ and d ₂ for the substrate and absorber, respectively), expressed as

$$Z_{in1(2)}=Z_{c1(2)}\times \frac{Z_0+Z_{c1(2)}\tanh {\upsilon }_{1(2)}{d}_{1(2)}}{Z_{c1(2)}+Z_0\tanh {\upsilon }_{1(2)}{d}_{1(2)}}$$

(3)

When the wave is incident normally on the boundary between two media, part of incident wave is reflected while another part is transmitted into the second medium. The amplitude of the reflected wave (E) is related to that of the incident wave (E) by the reflection coefficient (Γ), defined by

$$\Gamma =\frac{E_r}{E_i}$$

(4)

The reflection loss (RL), in decibels, is then given by

$$RL=20\log \left|\Gamma \right|$$

(5)

For normal incidence, the reflection coefficient at the front surface of the absorbing layer is given by

$$\Gamma =\frac{Z_{in2}-Z_0}{Z_{in2}+Z_0}$$

(6)

In the case of matched line (Z_in(2) = Z₀), there is no reflected wave from the absorber (Γ = 0). Since Z_in2 is a function of not only Z_c2 and V₂ but Z_in1 as well, the electromagnetic properties and dimension of the reflective substrate influence on the microwave absorbing properties of the front absorbing layer.

The transmitted wave is attenuated by the material loss (dielectric or magnetic) inside the material. Absorption loss (AL), in decibel, is given by

$$AL=8.686\alpha d[dB]$$

(7)

In Eq. (7), a is attenuation constant (real part of propagation constant), which is a increasing function of loss tangent (tanδ) as expressed in Eq. (8)

$$\alpha =\mathrm{Re}(\upsilon )=\frac{\pi \sqrt{2{\delta }^{\text{'}}}}{c}{(\sqrt{1+{\tan }^2\delta }-1)}^{1/2}-[Np/m]$$

(8)

where tanδ is given by

$$\tan \delta =\frac{{\delta }^{"}}{{\delta }^{"}}=\frac{{\mu }_r{}^{\text{'}}{\epsilon }^{"}{}_r+{\mu }_r{}^{"}{\epsilon }^{\text{'}}{}_r}{{\mu }_r{}^{\text{'}}{\epsilon }^{\text{'}}{}_r-{\mu }_r{}^{"}{\epsilon }^{"}{}_r}$$

(9)

3. Experiment

Carbon fiber–epoxy composites were prepared by lamination technique with commercially available prepreg with 0°/45° orientation and Bisphenol–A type epoxy resins. The carbon fiber fabric was cut by 15 cm × 15 cm and dipped in epoxy resin. After drying at 80°C in a vacuum oven, the prepreg was laminated by using uniaxial press with automatic temperature and pressure controller. The lamination temperature was 130°C.

The absorbing layer was prepared from the mixture of carbon black and silicone rubber. The dielectric lossy material used as filler was carbon black and its amount was varied in the range 10–40% in volume. The mixture was molded in a coaxial die with a dimension of 3 mm in inner diameter and 7 mm in outer diameter.

The complex permeability and dielectric constant were determined by using a network analyzer. Measurements were made in the C- and X-band frequencies (4–12 GHz). The precisely machined toroid samples were inserted between the inner and outer conductors of standard coaxial line. The complex permeability and dielectric constant were determined from the measured reflected and transmitted scattering parameters. ¹⁶

4. Results and Discussion

4.1 Material Parameters (μ_r, ε_r)

Figure 2 presents the frequency dispersion of complex permittivity (ε _r = ε _r ″ – jε _r ′) measured in the composites of carbon black of 30%. Nearly constant value of real (ε′ _r ≈ 15) and imaginary value (ε″ _r ≈ 2) of complex permittivity is observed. Complex permittivity can be controlled with the amount of carbon black. Both ε′ _r and ε′ _r increase with increase of carbon black (ε′ _r ≈ 5, ε′ _r ≈ 0 for 10% and ε′ _r ≈ 25, ε′; _r ≈ 4 for 40%), as depicted in Figure 3 . Complex permeability (μ _r = μ′ _r – jμ″ _r ) value of the composites was μ′ _r ≈ 1, μ″ _r ≈ 0, due to nonmagnetic property of carbon black and rubber matrix. The electrical conductivity is very low due to the insulating properties of binder matrix.

Figure 2

Material parameters of carbon black-silicone rubber composite with carbon black content of 30% in volume

Figure 3

Complex permittivity of carbon black-silicone rubber composites at different contents of carbon black (measured at 9.0 GHz)

Figure 4 presents the material parameters of carbon fiber–epoxy composite specimens. Fiber content was approximately 60% in volume. High value of dielectric constant (nearly constant value of ε _r ‘ ≈ 25) and dielectric loss (of which value decreases with frequency from e _r ” ≈ 60 at 4 GHz to ε″ _r ≈ 20 at 12 GHz) was observed in the composites. Frequency dispersion of dielectric constant of composite specimens containing conductive particles or laminates was explained by Hippel. ¹⁷ The space change polarization between parallel carbon fibers (conductors) separated by epoxy matrix (insulator) can lead to high dielectric constant. The imaginary part of dielectric constant is resulting from the ohmic loss along the longitudinal axis of fibers. ¹¹ However, the apparent electrical conductivity of the composite panels is low (∼10⁻³ S/cm) due to the insulating properties of binder matrix. A constant value of μ′ _r ≈; 1.1 (nearly equal to free-space impedance) and μ″ _r ≈ 0 was observed, which is also due to nonmagnetic property of carbon fiber and epoxy resin.

Figure 4

Material parameters of carbon fiber-epoxy composite (fiber content = 60% in volume)

4.2 Reflection and Absorption Loss of Carbon Fiber Composites

When a composite layer having low intrinsic impedance and high loss such as carbon fiber composites is illuminated by incident plane wave, the microwave reflection occurs at the front surface due to impedance mismatching and the penetrated wave is attenuated inside due to material loss. The reflection and absorption loss can be predicted from the material parameters by using equation (5) and (7).

Figure 5 presents the reflection and absorption properties determined in the carbon fiber composites as a function of layer thickness (d = 1–5 mm). The value of reflection loss decreases slightly with frequency from −2 dB at 4 GHz to −3.5 dB at 12 GHz and insensitive to the thickness, as depicted in Figure 5(a) . In average, approximately 50% power reflectance is predicted, which is due to high dielectric constant and dielectric loss of the carbon fiber composite. Figure 5(b) shows the attenuation constant determined by Eq. (8). Large value of attenuation constant greater than 400 Np/m is predicted over the frequencies 4–12 GHz, which is due to high dielectric loss of carbon fiber composites. Because of this large attenuation, absorption loss was also high, as depicted in Figure 5(c) . Absorption loss greater than 10 dB (90% in power absorption) was predicted with a thickness as small as 3 mm.

Figure 5

Reflection and transmission properties determined in carbon fiber-epoxy composite panels: (a) reflection loss, (b) attenuation constant, and (c) absorption loss

With the advantage of high values of microwave reflectance and absorption, the carbon fiver composites can be used as the terminal plate in multi-layer RAS. Since about 50% of incident wave is reflected at the boundary and 90% of the remained transmitted wave is attenuated inside the material, the penetrating wave through the composite panel is only 5% (20 dB in shielding effectiveness). The carbon fiber composites can thus be suggested as a good terminal material with high capability of microwave shielding in multi-layer RAS.

4.3 Microwave Absorbing Properties of Composite Laminate

As explained previously, microwave reflectance from the carbon fiber composites is as high as 50% due to low intrinsic impedance (high dielectric constant). Impedance transforming layer of high impedance (low dielectric constant) must be attached to the carbon fiber composites to diminish the microwave reflection. As the impedance transforming layer, carbon black-impregnated rubber composites of low dielectric constant can be used.

Figure 6 presents the reflection loss determined in the two-layer RAS composed of impedance transformer (carbon black-rubber composites with its thickness varied in the range d₂ = 2–4 mm) and carbon fiber composite (with a fixed thickness d₁ = 2.5 mm). Microwave absorption is strongly sensitive to the carbon black content and layer thickness. Absorbing band moves to lower frequency with increasing carbon content. For the composite containing 10% carbon black (ε′ _r ≈ 5), the maximum attenuation (—30 dB reflection loss) is predicted at 10 GHz with a thickness d ₂ = 3 mm, as shown in Figure 6(a) . The measured value of reflection loss determined in the coaxial waveguide is in good agreement with the calculated values, as depicted in Figure 7 . If carbon black content is increased to 20% (ε′ _r ≈ 11), the maximum absorption (17 dB) occurs at 4.5 GHz with a thickness d ₂ = 4.0 mm ( Figure 6(b) ). With more increase of carbon black (30%, ε′ _r ≈ 15), the absorption band moves to lower frequency below 4 GHz ( Figure 6(c) ).

Figure 6

Reflection loss determined in two-layer RAS of carbon black/carbon fiber composite laminate with increasing carbon black content: (a) 10%, (b) 20%, and (c) 30%. The thickness of carbon black composite was varied d₂ = 2–4 mm

Figure 7

Measured value of reflection loss of two-layered RAS composed of carbon black composite (thickness = 3 mm, carbon black content = 10%) and carbon fiber composite (thickness = 2 mm)

It is evident that absorbing frequency band is quite sensitive to the dielectric constant of impedance transforming layer. As presented in Figure 3 , dielectric constant increases with carbon black content. The wavelength in the dielectric medium is diminished with increase of dielectric constant. The matching thickness of impedance transforming layer is, therefore, reduced with increase of dielectric constant. The absorbing band moves to lower frequency with carbon black content in the impedance transforming layer at the same thickness. The similar relationship was verified in the conventional radar absorbing materials.

5. Conclusions

High value of microwave absorbance was demonstrated in the two-layer composite laminate of the carbon black impregnated rubber sheet attached to the carbon fiber–epoxy composite panel. In the impedance-transforming layer of carbon black composite, complex permittivity can be controlled by the amount of carbon black. High values of dielectric constant and dielectric loss were determined in the carbon fiber composite, which can thus be used as the reflecting substrate. On the basis of transmission line theory, highly absorptive RAS can be designed by laminating the carbon black and carbon fiber composites. For this two-layer structure with the rubber sheet containing 10% carbon black (with dielectric constant of ε′ _r ≈ 5), the maximum microwave absorption (30 dB) is predicted at 10 GHz.