© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
P. S. Mohammed Yazeen et al.Broadbanding Techniques for RadomesSpringerBriefs in Electrical and Computer Engineeringhttps://doi.org/10.1007/978-981-33-4130-2_3

3. Broadbanding Techniques Based on Metallic Wiregrids

P. S. Mohammed Yazeen1  , C. V. Vinisha2, S. Vandana3, M. Suprava4 and Raveendranath U. Nair5
(1)
Centre for Electromagnetics (CEM), CSIR-National Aerospace Laboratories, Bengaluru, Karnataka, India
(2)
Centre for Electromagnetics (CEM), CSIR-National Aerospace Laboratories, Bengaluru, Karnataka, India
(3)
Centre for Electromagnetics (CEM), CSIR-National Aerospace Laboratories, Bengaluru, Karnataka, India
(4)
Centre for Electromagnetics (CEM), CSIR-National Aerospace Laboratories, Bengaluru, Karnataka, India
(5)
Centre for Electromagnetics (CEM), CSIR-National Aerospace Laboratories, Bengaluru, Karnataka, India
 
 
P. S. Mohammed Yazeen
Email: mohammedyazeen@gmail.com

Substantial enhancement in EM performance over a broadband is one of the mandatory requirements for modern airborne radar systems. Different methods for broadbanding of radomes have been observed in the literatures (Harder and Gaurino 1964; Richmond 1964; Tricoles 1958). Techniques based on embedded metallic wire grids in the radome panels also have been widely used for improving the EM performance of radomes (Cary 1983; Kay 1958; Miller and Brown 1957; Robinson 1958; Worthington 1958; Walton 1966).

Radome structures having high strength-to-weight ratio, multilayered wall configuration is chosen over monolithic half-wave wall for manufacturing streamlined airborne radomes. C-sandwich configuration offers better power transmission characteristics than A-sandwich for a range of incidence angles.

For analyzing the EM performance using wiregrids, the power transmission characteristics of an optimized core C-sandwich configuration over a broadband of 2–18 GHz is considered.

The EM performance parameters can be improved up to a certain extent by the addition of metallic structures in the skin and core layers of the radome. Thus, design parameters of the wire grids should be optimized to provide enhanced EM performance for normal incidence and high incidence angles.

3.1 EM Design Aspects of Metallic Wiregrids Embedded C-sandwich Radome Panel

C-sandwich wall consists of two skins, two cores and a middle layer, with each core being embedded between a skin and the middle layer. In the current literature, the skin and the middle layer is considered as glass composite (relative permittivity, εr = 4.0; electric loss tangent, tanδe = 0.015) with two identical foam cores (εr = 1.15; tanδe = 0.002). For C-sandwich, wall configuration thickness of the center layer is kept at 1.5 mm, and an equal thickness of 0.75 mm is given to the inner and outer skin layers. An optimum thickness of 5.44 mm is assigned to each core to achieve maximum power transmission across the frequency band of 2–18 GHz.

As shown in Fig. 3.1, planar array of wire grids made up of parallel wires having circular cross sections is symmetrically embedded in the center plane of each core. Along the length of the wire material characteristics of the wire grid are the same. Besides the polarization of the incident wave, the pitch and diameter of the wires influences the EM performance parameters. When the electric field of the incident wave is polarized in the direction of the wires, the effect of the wiregrid will be maximum.
../images/467918_1_En_3_Chapter/467918_1_En_3_Fig1_HTML.png
Fig. 3.1

Cross section of C-sandwich radome panel with metallic wire grid embedded in the mid-plane of the core

To obtain superior EM performance, the capacitive susceptance of the dielectric material should match with the inductive susceptance of the wire grid, which is obtained by optimizing the design parameters of wiregrids. The optimized design parameters of the wire grid are calculated at 10 GHz which is given in Table 3.1.
Table 3.1

Design parameters of metallic wire grids

Angle of incidence (°)

Polarization

Optimum diameter (mm)

Optimum pitch (mm)

0

–

1.4

95.2

45

Perpendicular

1.4

79.6

60

Perpendicular

0.9

65.2

3.2 EM Performance Analysis of Metallic Wiregrids Embedded C-sandwich Radome Panel

The equivalent transmission line method is used for the estimation of EM performance parameters as explained in Chap. 2. An equivalent transmission line model can be derived from the metallic wiregrids included C-sandwich radome with different sections corresponding to skin, core, and wire grids. Discontinuity in the line caused by variation of the characteristic impendence from free space to the C-sandwich radome wall configuration is a major cause for incident wave power reflection on the structure. A matrix consisting of Ai, Bi, Ci, and Di parameters represents ith dielectric layer. Hence, the whole configuration can be represented by a single matrix obtained by the multiplication of matrices corresponding to individual layers.

Free space characteristic impedance is given as Z0, and the characteristic impedances of the skin, core, and wire grid are represented by Zs, Zc, and ZG, respectively. Electrical length of each layer is represented as Φ, which is a function of the angle of incidence $$(\theta )$$, complex permittivity $$(\varepsilon *)$$ of dielectric layer, thickness of the dielectric layer (d), and wavelength of incident wave (λ).

The electrical length (each layer) can be represented as
$$ \Phi = \frac{{2\pi d\sqrt {\varepsilon ^{*} - \sin ^{2} \theta } }}{\lambda } $$
(3.1)

The matrix representation of each layer of C-sandwich wall is represented as:

The outer skin:
$$ \left[ {\begin{array}{*{20}c} {A_{1} } & {B_{1} } \\ {C_{1} } & {D_{1} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}l} {\cos \Phi_{1} } \hfill & {j\frac{{Z_{\text{s}} }}{{Z_{0} }}\sin \Phi_{1} } \hfill \\ {j\frac{{Z_{0} }}{{Z_{\text{s}} }}\sin \Phi_{1} } \hfill & {\cos \Phi_{1} } \hfill \\ \end{array} } \right] $$
(3.2)
In the current wall configuration, the wire grid is placed in the center of each core. Hence, each core can be divided into two similar sections with wire grid embedded in between them. Then, each section of the outer core can be represented by
$$ \left[ {\begin{array}{*{20}c} {A_{2} } & {B_{2} } \\ {C_{2} } & {D_{2} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}l} {\cos \Phi_{2} } \hfill & {j\frac{{Z_{\text{c}} }}{{Z_{0} }}\sin \Phi_{2} } \hfill \\ {j\frac{{Z_{0} }}{{Z_{\text{c}} }}\sin \Phi_{2} } \hfill & {\cos \Phi_{2} } \hfill \\ \end{array} } \right] $$
(3.3)
Let AWG, BWG, CWG, and DWG be the elements of the matrix representing wire grid. Then,
$$ \left[ {\begin{array}{*{20}c} {A_{{{\text{WG}}}} } & {B_{{{\text{WG}}}} } \\ {C_{{{\text{WG}}}} } & {D_{{{\text{WG}}}} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 1 & 0 \\ j_{{B_{{\text{G}}} }} & 1 \\ \end{array} } \right] $$
(3.4)

Here, BG represents the shunt susceptance of the wire grid.

For perpendicular polarization,,
$$ B_{\text{G}} = \frac{ - 1}{{\left( {\frac{P}{\lambda }} \right)\sqrt {\varepsilon_{\text{c}} - \sin^{2} \theta } \left[ {\log_{\text{e}} \left( {\frac{P}{\pi \,D}} \right) + 0.6\left( {\frac{P}{\lambda }} \right)^{2} \left( {\varepsilon_{\text{c}} + 2\;\sin^{2} \theta } \right)} \right]}} $$
(3.5)

P, D,$$\varepsilon_{c}$$ and λ represent pitch of the wire grid, wire diameter, dielectric constant, and wavelength, respectively.

The middle layer:
$$ \left[ {\begin{array}{*{20}c} {A_{3} } & {B_{3} } \\ {C_{3} } & {D_{3} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}l} {\cos \Phi_{3} } \hfill & {j\frac{{Z_{\text{s}} }}{{Z_{0} }}\sin \Phi_{3} } \hfill \\ {j\frac{{Z_{0} }}{{Z_{\text{s}} }}\sin \Phi_{3} } \hfill & {\cos \Phi_{3} } \hfill \\ \end{array} } \right] $$
(3.6)
Like the outer core, each equal section of the inner core is denoted by
$$ \left[ {\begin{array}{*{20}c} {A_{4} } & {B_{4} } \\ {C_{4} } & {D_{4} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}l} {\cos \Phi_{4} } \hfill & {j\frac{{Z_{\text{c}} }}{{Z_{0} }}\sin \Phi_{4} } \hfill \\ {j\frac{{Z_{0} }}{{Z_{\text{c}} }}\sin \Phi_{4} } \hfill & {\cos \Phi_{4} } \hfill \\ \end{array} } \right] $$
(3.7)
The inner skin:
$$ \left[ {\begin{array}{*{20}c} {A_{5} } & {B_{5} } \\ {C_{5} } & {D_{5} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}l} {\cos \Phi_{5} } \hfill & {j\frac{{Z_{\text{s}} }}{{Z_{0} }}\sin \Phi_{5} } \hfill \\ {j\frac{{Z_{0} }}{{Z_{\text{s}} }}\sin \Phi_{5} } \hfill & {\cos \Phi_{5} } \hfill \\ \end{array} } \right] $$
(3.8)
The entire wiregrid embedded C-sandwich wall configuration is denoted by
$$ \begin{aligned} \left[ {\begin{array}{*{20}c} A & B \\ C & D \\ \end{array} } \right] & = \left[ {\begin{array}{*{20}c} {A_{1} } & {B_{1} } \\ {C_{1} } & {D_{1} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {A_{2} } & {B_{2} } \\ {C_{2} } & {D_{2} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} 1 & 0 \\ {jB_{\text{G}} } & 1 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {A_{2} } & {B_{2} } \\ {C_{2} } & {D_{2} } \\ \end{array} } \right] \\ & \quad \left[ {\begin{array}{*{20}c} {A_{3} } & {B_{3} } \\ {C_{3} } & {D_{3} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {A_{4} } & {B_{4} } \\ {C_{4} } & {D_{4} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} 1 & 0 \\ {jB_{\text{G}} } & 1 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {A_{4} } & {B_{4} } \\ {C_{4} } & {D_{4} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {A_{5} } & {B_{5} } \\ {C_{5} } & {D_{5} } \\ \end{array} } \right] \\ \end{aligned} $$
(3.9)
Therefore, using Eq. (3.9), power transmission coefficient is given by
$$ P_{{{\text{tr}}}} = \left| T \right|^{2} = \left[ {\frac{4}{{(A + B + C + D)^{2} }}} \right] $$
(3.10)
And, the power reflection coefficient is given by
$$ P_{{{\text{rf}}}} = \left| R \right|_{m}^{2} = \left[ {\frac{A + B - C - D}{{A + B + C + D}}} \right]^{2} $$
(3.11)

3.3 Numerical Results and Discussion

The EM performance parameters are computed for C-sandwich radome wall with wiregrid embedded having optimized core thickness. The analysis is done for perpendicular polarization at normal incidence, 45° and 60° incidence angles. This section depicts the comparative study of EM performance of C-sandwich radome wall with wiregrid embedded with that of C-sandwich wall alone. Figure 3.2a shows power transmission characteristics of wiregrid embedded C-sandwich and C-sandwich alone over the frequency band 2–18 GHz at normal incidence. It is evident from the figures that the power transmission characteristic of C-sandwich alone is poor as compared to C-sandwich radome wall with wiregrid embedded which is having a considerable transmission efficiency of 95% throughout the frequency band up to 16 GHz, after which it starts degrading and the power transmission ends up to 70% at 18 GHz.
../images/467918_1_En_3_Chapter/467918_1_En_3_Fig2_HTML.png
Fig. 3.2

a Transmission efficiency of C-sandwich radome wall configurations at normal incidence. b Reflection characteristics of C-sandwich radome wall configurations at normal incidence. c Insertion phase delay (IPD) of C-sandwich radome wall configurations at normal incidence

Figure 3.2b shows the power reflection characteristics of the wiregrid embedded C-sandwich and C-sandwich alone at normal incidence. It is observed that the power reflection characteristic of C-sandwich alone at normal incidence is increasing significantly beyond 12 GHz and for C-sandwich with wiregrid embedded the power reflection is reduced considerably.

Figure 3.2c shows the IPD characteristics of modified C-sandwich configuration with wiregrid which characterizes better performance than that of C-sandwich alone at normal incidence.

Figure 3.3a–c shows the power transmission, power reflection, IPD of the wiregrid embedded C-sandwich and C-sandwich alone over the frequency band 2–18 GHz at 45° incidence angle. The characteristics are almost similar, and only slight variations can be noticed as compared to the normal incidence case.
../images/467918_1_En_3_Chapter/467918_1_En_3_Fig3_HTML.png
Fig. 3.3

a Transmission efficiency of C-sandwich radome wall configurations at 45° incidence angle. b Reflection characteristics of C-sandwich radome wall configurations at 45° incidence angle. c Insertion phase delay (IPD) of C-sandwich radome wall configurations at 45° incidence angle

Figure 3.4a–c shows the power transmission, power reflection, IPD of the wiregrid embedded C-sandwich and C-sandwich alone over the frequency range 2–18 GHz at 60° incidence angle.
../images/467918_1_En_3_Chapter/467918_1_En_3_Fig4_HTML.png
Fig. 3.4

a Transmission efficiency of C-sandwich radome wall configurations at 60° incidence angle. b Reflection characteristics of C-sandwich radome wall configurations at 60° incidence angle. c Insertion phase delay (IPD) of C-sandwich radome wall configurations at 60° incidence angle

The power reflection characteristics of the C-sandwich radome wall with wiregrid embedded shows excellent performance as compared to the C-sandwich wall alone, which will minimize the side lobe level degradation to a greater extent.

The IPD characteristics of C-sandwich radome wall with wiregrid embedded are better than that of C-sandwich alone at the mentioned three incidence angles. Hence, the modified structure will offer better boresight error (BSE) characteristics.

3.4 Conclusion

The EM performance analysis for wiregrid embedded C-sandwich radome wall with optimized core thickness has been explained in the section. It was found that EM performance characteristics are better for C-sandwich wall configurations with wiregrids embedded. For planar radome applications, C-sandwich wall with wiregrids embedded is a better choice as compared to the conventional C-sandwich radome. The strength-to-weight ratio of the wall configuration can be improved by embedding the wire-grids in the core of the C-sandwich radome.