Variable thickness design is capable of yielding excellent electromagnetic (EM) performance for streamlined airborne radomes. The traditional optimization method using evolutionary computation (EC) techniques can yield variable thickness radome (VTR) design with optimal EM performance but uncontrollable thickness profile, leading to manufacturing difficulties. Thickness profile design based on average incident angle is an efficient way for VTR design with smooth thickness profile, whereas the boresight error (BSE) is relatively large. In this work, insertion phase delay (IPD) correction is introduced in the efficient thickness profile design process to realize a better balance between EM performance and thickness profile smoothness of airborne radomes. The thickness profile obtained from average incident angle is adjusted for IPD distribution symmetry with respect to the antenna axis under scan angles with large BSE. Results indicate that the proposed method can effectively improve the BSE characteristics at the expense of slight deterioration of computational efficiency and thickness profile smoothness.
Radomes are used in various applications to protect antennas such as reflector antennas and phased array antennas. [
Incident angle is an important factor in determining the transmission characteristics of radomes. Streamlined radome shapes introduce asymmetric incident angle distribution varying during antenna scanning, which tends to degrade the EM performance. Through analyzing the incident angle variation characteristics for different radome areas, thickness can be accordingly designed to compensate the adverse effect of incident angle. Average incident angle with proper modification is effective in efficiently designing the thickness profile through the half-wave thickness expression [
Asymmetric insertion phase delay (IPD) is the main cause of radome BSE. Essentially, the half-wave thickness implies optimal transmission efficiency and gives little consideration to BSE characteristics. In this work, on the basis of the thickness profile obtained by the average incident angle method in [
Through changing the radome thickness, the IPD correction is meant to improve the IPD distribution under particular antenna scan angles, thus reducing the BSE. As IPD asymmetry is the main cause of radome BSE, it is considered to realize IPD distribution symmetric to antenna aperture center. The IPD caused by the radome longitudinal curvature along the thickness profile is the main target of symmetry, whereas the effect of radome lateral curvature on IPD is further considered through scale factor. At different antenna scan angles, the required radome thickness profiles can be different. The IPD correction is therefore a compromise of optimal thickness value under different scan angles to yield minimum BSE.
As in [
Radome IPD, cause of the phase distortion, depends on 3 parameters of radome: thickness, permittivity, and shape (which relates to the incident angle and polarization angle). As shown in Figure
2D case of the antenna-radome system. (a) Overall view. (b) Partial view with IPD.
In fact, for a particular scan angle, the corresponding IPD distribution can be changed through thickness adjustment to reduce the BSE. Figure
IPD correction for symmetry. (a) Without scale factor. (b) With scale factor for right side correction.
Figure
3D case of antenna-radome system.
Radome IPD can be calculated via the following formula:
Radome IPD can be modified to be a particular value through thickness adjustment. As shown in Figure
The thickness profile can then be obtained by cubic-B-spline interpolation [
From a given thickness profile, the BSE w.r.t. antenna scan angle can be calculated. Then, the 2D case IPD curve under the scan angle corresponding to the maximum BSE can be changed. It should be noticed that the changed thickness profile will affect the EM performance under some other scan angles. As shown in Figure
The scan angle range affected by a part of the thickness profile.
For a set of scale factors
The inner “max” operator is to find the maximum BSE for all scan angles within
The IPD correction procedure can be summarized as follows: Calculate the BSE curve of a given thickness profile (using the average incident angle method in [ Find the optimal scale factor and side (left or right) within ASAR using ( Return to step 1 with the new thickness profile and repeat the IPD correction. When the maximum BSE after IPD correction is no less than the original value, the procedure can be terminated.
It should be noticed that even if at one iteration, the maximum BSE is not reduced by the IPD correction and further correction may yield smaller maximum BSE. Thus, it is suggested to calculate the correction iteration by 5 times and then start the termination judgment. In this way, the thickness design procedure can be refined as the flow chart shown in Figure
Efficient thickness design procedure.
The tangent-ogival radome used in [
The tangent-ogival radome.
Verification of the EM performance analysis method can be found in [
The scale factor range is set as [0.9, 1.1] with a step of 0.01. In IPD correction, it is necessary to properly discretize the thickness profile into a series of points along radome height. If the discrete points are too sparse, the precision of IPD symmetry in LSC or RSC will degrade, whereas the final thickness profile is prone to be ragged when the points are too dense. For the case in this work, a step of 0.04 m or 0.03 m will be a good compromise between IPD correction precision and thickness profile smoothness. To realize the best results, the 0.04 m step is mainly employed, i.e., 1, 0.96, 0.92, …, 0.28, 0.24, and 0.19 (unit: m), whereas in Section
Based on the 3D design method with an incident angle modification factor of 0.75 in [
The maximum BSE during IPD correction iteration.
Iteration | BSE (mrad) | Scale factor | Side | TL (dB) |
---|---|---|---|---|
Initial | 1.388 | — | — | 0.53 |
1 | 1.374 | 1.00 | Right | 0.53 |
2 | 1.027 | 1.06 | Left | 0.53 |
3 | 1.000 | 1.00 | Right | 0.53 |
4 | 0.927 | 0.99 | Right | 0.53 |
5 | 0.758 | 1.00 | Left | 0.53 |
6 | 0.706 | 1.01 | Left | 0.53 |
7 | 0.739 | 0.95 | Right | 0.54 |
As shown in Table
Thickness profile of VTRs obtained by different methods.
EM performance of VTRs obtained by different methods. (a) BSE. (b) TL.
Results of different methods.
BSEmax (mrad) | TLmax (dB) | Number of EM computations | |
---|---|---|---|
Optimization method | 0.499 | 0.53 | 10000 |
Efficient design (previous) | 1.389 | 0.53 | 61 |
Efficient design (proposed) | 0.706 | 0.53 | 237 |
It can be seen from these results that the proposed efficient design method, compared with the previous one, can yield much better BSE (maximum value improved by about 50%) with slightly degraded thickness profile (smooth, but not as smooth as the previous one). The maximum BSE of the proposed method is close to that of the optimization method. All three methods yield similar TL characteristics, which is an indication of the insensitivity of TL to slight thickness variation. With the optimization method as reference, the efficiency of the efficient design is only deteriorated from 0.6% for the previous one to 2.4% for the present one. The proposed efficient design method can yield much better BSE with slightly degraded thickness profile smoothness and computational efficiency.
To show the effect of the IPD correction method, the thickness profile and the corresponding BSE characteristics in the iteration process are shown in Figure
The thickness profile and BSE curve during the IPD correction process. (a, b) Iterations 0 and 1. (c, d) Iterations 1 and 2. (e, f) Iterations 2 and 3. (g, h) Iterations 3 and 4. (i, j) Iterations 4 and 5. (k, l) Iterations 5 and 6.
In the design process, the selection of which side to be modified is implemented by computing both sides and choosing the one with the optimal BSE characteristics in each iteration. This is an important part of the computational cost. It would be interesting to see what happens when the side (either left or right) is fixed in the process.
Table
The maximum BSE during IPD correction iteration for LSC/RSC.
Iteration | BSE (mrad) | |
---|---|---|
LSC | RSC | |
Initial | 1.388 | |
1 | 1.397 | 1.374 |
2 | 1.373 | 1.027 |
3 | 1.363 | 1.083 |
4 | 1.367 | 1.240 |
5 | 1.401 | 1.199 |
6 | 1.471 | 0.974 |
7 | 1.399 | 0.918 |
8 | 1.444 | 1.044 |
Besides, the modification factor for average incident angle in [
Table
The maximum BSE during IPD correction iteration without incident angle modification factor.
Iteration | BSE (mrad) | |
---|---|---|
Scale factor [0.9, 1.1] | Scale factor [0.7, 1.1] | |
Initial | 2.919 | |
1 | 2.749 | 2.749 |
2 | 2.574 | 2.247 |
3 | 2.525 | 2.221 |
4 | 2.476 | 2.039 |
5 | 2.428 | 1.867 |
6 | 2.379 | 1.796 |
7 | 2.329 | 1.756 |
8 | 2.281 | 1.466 |
9 | 2.247 | 1.407 |
10 | 2.232 | 1.065 |
11 | 2.221 | 0.972 |
12 | 2.354 | 1.102 |
Figure
Thickness profile of VTRs obtained by the proposed method, one-side-correction-only method, and no-modification-factor method.
EM performance of VTRs obtained by the proposed method, one-side-correction-only method, and no-modification-factor method. (a) BSE. (b) TL.
Effect of side selection and modification factor.
BSEmax (mrad) | TLmax (dB) | Number of EM computations | |
---|---|---|---|
Efficient design—proposed | 0.706 | 0.53 | 237 |
One-side-correction only | 0.918 | 0.52 | 149 |
No modification factor | 0.972 | 0.50 | 651 |
From these results, it can be concluded that the proposed method has the overall best performance. Besides, some hints can also be recognized. In the proposed method, the adoption of the modification factor in fact makes the thickness profile obtained by half-wave expression approach the optimal thickness profile with better BSE characteristics, which is like a coarse-adjustment step, and the LSC-RSC method implements the fine-adjustment step.
In this work, IPD correction is introduced in the efficient thickness profile design of streamlined airborne radomes. Based on the half-wave wall design from average incident angle with a modification factor, the thickness profile is further adjusted for IPD symmetry at particular antenna scan angles. Both left-side correction (LSC) and right‐side correction (RSC) are considered in IPD correction. Several conclusions can be drawn: The proposed method can well improve the BSE characteristics of the half-wave wall design with slight increase of computational cost and deterioration of thickness profile smoothness. The scale factor range [0.9, 1.1] with a step of 0.01 is suggested. The modification factor and LSC-RSC method are both important in realizing the good performance, and the former essentially works as a coarse-adjustment step while the latter as a fine-adjustment step. Using the proposed method, the VTR can be efficiently designed with EM performance close to the traditional optimization design and thickness profile nearly as smooth as the efficient average incident angle method. A better balance between EM performance and thickness profile smoothness of airborne radomes is achieved.
All data generated or analyzed during this study are included in this article.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (Grant nos. 51605362, 51875431, and 51775405), Natural Science Basic Research Plan in Shaanxi Province of China (Grant no. 2018JQ5063), the Fundamental Research Funds for the Central Universities, and the 111 Project (B14042).