1. Introduction
Antennas, as indispensable components of wireless communication systems, directly impact the efficiency and reliability of the entire system [
1]. With the rapid development of communication technologies, the performance requirements for antennas are increasingly demanding. As highly integrated electronic equipment, antennas feature complex mechanical structures and feed networks. Enhancements in antenna performance involve multiple disciplines, including structural, thermal, and electromagnetic aspects [
2,
3,
4]. Regardless of whether it involves a thermal or structural design, all antenna design work must ensure the antenna’s electrical performance. Analyzing this performance is an essential research step in various antenna designs. In traditional analyses of antenna electrical performance, the process begins by establishing a computational model of the antenna’s electrical characteristics. This is followed by setting multiple operating conditions based on input parameters to perform comparisons, thereby summarizing the impact of relevant parameters on the antenna’s electrical performance to guide its design and optimization. This method is not only time-consuming but also inefficient. This is particularly true in the design of phased array antennas, where the antenna’s electrical performance is influenced by multiple input parameters. To comprehensively understand the impact of each parameter, the number of required operating conditions can increase exponentially.
Currently, many scholars researching antenna design and compensation also explore the analysis of antenna electrical performance. In the field of electrical design for antennas, the references [
5,
6,
7,
8,
9,
10] employed interval analysis to compute the impact range of random amplitude-phase errors, for which the probability distribution is unknown, on the performance of array antennas. These studies derived the relationship between the boundaries of the power directional pattern and the phase errors of the antenna array. Additionally, representative numerical settings are used to validate the method under different cases. Reference [
11] proposed a method to address the deterioration of the electrical performance in airborne array antennas caused by blockages from fixed obstacles. It identified the main shadow areas affected by electromagnetic propagation when the array antenna encounters fixed obstructions. The shadowed area was divided into small scattering units to reduce the solution range. Based on the characteristic modes of the units and coordinate transformations, a correlation model between the fixed obstacle–conformal array system and isolated units was established. Using this model, multiple operating conditions are applied to coaxially fed microstrip antenna conformal arrays as examples, verifying the accuracy of the derived electric field expressions for the conformal array and the multi-scatterer–conformal array system. Reference [
12] introduced a method that combines scattering matrix techniques with microblog network theory for a trade-off between in-band scattering and radiation performance in broadband phased arrays. This method can effectively predict the radiation and scattering performance of effective phased arrays with unit-independent matching networks or loads. The design work verified that the scattering of the array is significantly reduced over the entire operating bandwidth after using this method.
In the field of antenna structural design, considerations often include the effects of manufacturing and installation errors or operational conditions causing structural deformations on the antenna’s electrical performance. In [
13], the structural damage of large HF reflector antennas operating outdoors after exposure to environmental factors such as wind, rain, snow, and solar radiation was discussed. It proposed an optimization method for sub-reflector array active control and an active compensation method for electrical performance. Based on this approach, multiple operational conditions are applied using dual-reflector antennas as examples. By the real-time adjustment of the phase plane of the distorted aperture field, the method compensates for the antenna’s electrical performance. This addresses the inaccuracies in position error representations caused by systemic errors, which in turn affect the antenna’s electrical performance. Similarly considering structural errors’ impact on antenna electrical performance, reference [
14] derived an estimation algorithm for the influence of channel correlation, hardware damage, and position errors on the uplink channel of array antennas. The algorithm accounts for channel correlation because, in practical applications, antenna arrays are often affected by multipath effects from surrounding objects, such as buildings, which alter the phase and amplitude of the received signals, thus impacting the entire system’s electrical performance. By analyzing the channel model, the algorithm can predict signal propagation losses and phase changes, providing directions for adjusting antenna design. Position errors can cause incorrect beam steering and distortion of the radiation pattern of the array. The algorithm provided a more accurate method for antenna correction by precisely simulating the impact of the positional inaccuracies of each antenna element on the electrical performance of the array antenna. Reference [
15] introduced a γ conical representation method to account for the γ-order position correlation of continuous array elements. It compared the existing conical representation methods with the proposed γ conical representation method, generating simulated data for positional errors. Utilizing antenna theory and Feko, the corresponding electrical performance due to positional errors is calculated. A prediction model was established based on a linear programming support vector regression algorithm to evaluate the capabilities of different representation methods. Multiple operational conditions are presented to demonstrate the superiority of the γ conical representation method. Reference [
16] proposed a statistical analysis method that considered the mutual coupling effects between array elements, using modal coupling to describe these interactions. Through multiple comparative operational conditions, it was shown that at the same magnitude, the normal errors in element positions more readily cause fluctuations in antenna radiation characteristics than the lateral errors in radiation element positions. However, the latter had a greater impact on mutual coupling effects. The findings underscore the necessity of meticulously allocating positional tolerances for radiating elements when designing high-precision antenna arrays. In [
17], the random errors in the manufacturing and assembling process of millimeter-wave phased array antennas are investigated to establish the theoretical model of the excitation amplitude quantization error, on the basis of which the influence of different amplitude quantization steps on the antenna directional map is simulated by giving multiple sets of working conditions as an example of a 16 × 16 two-dimensional array antenna, and the analysis reveals the influence of the error on the antenna’s electrical performance.
In the field of thermal design for antennas, the thermal power dissipation of the T/R components on the antenna array surface is substantial, leading not only to a decline in device performance but also to the structural thermal deformation of the antenna array surface, both of which deteriorate the electrical performance of the antenna. Reference [
18] presented a combined application of comprehensive impact parameters and finite element methods to perform thermal compensation control for phased array antennas, addressing the changes in the shape and alignment of phased array antenna panels caused by temperature variations. Multiple operational conditions are provided to validate that by adjusting and compensating for thermal deformations, the antenna can operate efficiently and accurately in various thermal environments. This method has been shown to not only reduce the complexity of thermal deformation modeling but also enhance predictive accuracy. In [
19], the structural deformations of active phased array antennas, caused by thermal loads, were addressed. A phase compensation method and an amplitude-phase compensation method based on least squares were used. The electrical performance of the deformed antenna was compensated under the premise of obtaining the excitation adjustment value of the antenna unit, and the compensation effects of different methods are compared by setting up comparative working conditions.
From the aforementioned studies, it can be seen that the analysis of antenna electrical performance is an essential aspect of various research areas related to antenna electromagnetics, structure, and thermal properties. When researchers identify an error factor that impacts antenna electrical performance or seek to compensate for such an error, they typically summarize their findings by setting up multiple operating conditions. Rarely do studies derive formulas that quantitatively reflect the impact of these factors on antenna electrical performance. During research on the tolerance design of array antenna element positions, the author found that the impact of element position errors on antenna electrical performance, as reflected by sensitivity calculation formulas in mechanical design, is consistent with the impacts derived from different cases. This led to the idea of directly quantifying the impact of parameters on antenna electrical performance through sensitivity to these parameters, offering a more intuitive and reliable approach. Based on this, the paper proposes a sensitivity-based method for analyzing antenna electrical performance, which quantitatively assesses the impact of various parameter changes on antenna performance, providing a more scientific and systematic means of analysis. Through this method, designers can not only see the specific effects of parameter changes on performance visually but can also guide the initial antenna parameter settings more effectively, which largely improves the precision and efficiency of the design.
For the purpose of protecting an array antenna from the adverse effects of the service environment, the antenna is often equipped with a corresponding radome. Although the radome plays the role of protecting the antenna, it also brings certain negative effects. For example, the reflection of the electromagnetic waves emitted by the antenna on the surface of the radome and the absorption within the dielectric layer of the radome will cause power loss and reduce the distance of the electronic system. However, in the research on the analysis of the electrical performance of array antennas, more studies focus on the antenna array, and few studies comprehensively consider the effect of the radome on the electrical performance of the antenna. However, the electrical performance of the array antenna with hood is jointly determined by the radome and the antenna array, and it is necessary to consider the influence of the radome in the electrical performance analysis. Therefore, this paper takes the antenna with hood array as the research object to verify the effectiveness of the sensitivity-based electrical performance analysis method. Firstly, we use the sensitivity-based electrical performance analysis method proposed in this paper to analyze the influence of relevant parameters on the electrical performance of the antenna, and then we use the traditional method of enumerating cases to analyze the influence of the same parameters on the electrical performance of the antenna, and compare the results.
This paper is divided into four sections. The first section introduces the research background, the current state of research, and the structural arrangement of the article. In the second section, the electrical performance calculation model and sensitivity analysis model of the antenna with hood array are derived. In the third section, the effects of three influencing factors, namely the current, array element position, and radome thickness, on the electrical performance of the antenna are analyzed by using the sensitivity-based analysis method and the method of enumerating working conditions, respectively, and the analysis results are compared to verify the effectiveness of the sensitivity-based analysis method. The fourth section summarizes the whole work and gives an outlook on the research that can be carried out in the next step.
3. Simulation Analysis
For a phased array antenna with a radome operating at 9.375 GHz, which corresponds to a working wavelength of 32 mm, the radome is made of quartz glass material. At room temperature, the material has a relative dielectric constant of 3.45 and a loss tangent of 0.0004, resulting in a theoretical radome thickness of 8.6 mm. The array arrangement is shown in
Figure 6, which is based on a 20 × 20 rectangular grid plane array and is designed to demonstrate specific special conclusions. The distribution of the excitation current amplitude is shown in
Figure 7, with both uniform amplitude and phase weighting and Taylor weighting, and the excitation current phase is 0. The element positions are modified by changing the element spacing and arrangement, divided into 12 operational conditions to study the electrical performance of the antenna, as shown in
Table 1.
3.1. Impact Analysis of Excitation Current Amplitude (Case 1 and 2)
Using the parameters of Case 1 and Case 2 which can be based on Equation (10), the sensitivity distribution plots and contours of the effect of the excitation current amplitude on the antenna’s electrical performance can be calculated as shown in
Figure 8 and
Figure 9.
in the figure shows the sensitivity of the antenna electrical properties to the current amplitude. According to
Figure 8 and
Figure 9, it can be predicted that the excitation current amplitude has the most significant effect on the electrical performance of the antenna in the interval of
, followed by the interval of
. According to Equations (11)–(13), the sensitivity distribution plots and contours of the influence of the position of the Case 2 array element on the electrical performance of the antenna can be calculated.
Both Case 1 and Case 2 are phased array antennas with octagonal arrays in the unshrouded case, but Case 1 uses equal-amplitude in-phase excitation and Case 2 uses Taylor-weighted excitation. Using Equation (2), the field strength direction diagram at
can be calculated as shown in
Figure 10, and the corresponding electrical performance index comparison is shown in
Table 2.
It can be clearly seen that when the distribution of the excitation current amplitude changes, the most obvious changes in the electrical properties are found in , the changes in the field strength amplitude in are also accompanied by changes in the main flap beamwidth, and the changes in the electrical properties in the other intervals are relatively weak.
3.2. Array Element Location Impact Analysis (Case 2–10)
According to Equations (11)–(13), the sensitivity distribution plots and contours of the influence of the position of the Case 2 array element on the electrical performance of the antenna can be calculated, as shown in
Figure 11 and
Figure 12.
Since the array element position rows are centrosymmetric, all the sensitivity distributions in
Figure 11 and
Figure 12 are also centrosymmetric.
Figure 12 clearly shows that the positional sensitivity of the field strength maximum about the z-direction of the array element is two orders of magnitude higher than that about the x-direction and the y-direction, so the change in the position of the array element in the z-direction has a more obvious effect on the antenna’s electrical performance than the change in the position of the array element in the x-and y-directions.
It should be pointed out that the conclusion that the change in the position of the elements at the center of the array has a greater impact on the electrical performance of the antenna than the change in the position of the elements at the edge of the array is an empirical one [
22]. Sensitivity is a method of theoretically verifying and describing this empirical conclusion. This article quantifies the position error of array elements into x, y, and z directions, and analyzes the impact of array element position errors in these three directions on antenna electrical performance. But in reality, the position error of the array elements occurs simultaneously in three directions. Although the elements with the highest sensitivity in the x and y directions are not located at the center of the array, they still belong to the central region of the array. Furthermore, because the z-direction position of the array element has the greatest impact on the antenna’s electrical performance, when considering the impact of positional deviations in the three directions comprehensively, it is easy to conclude that the element located in the center still has the greatest impact on the antenna’s electrical performance.
Based on
Figure 11a and
Figure 12a, the maximum sensitivity of the electric field strength in the x-direction occurs at four array elements: (5,10), (5,11), (16,10), and (16,11). The sensitivity contours decrease concentrically around these points, forming ellipsoidal distributions. Similarly, according to
Figure 11b and
Figure 12b, the y-direction sensitivity exhibits a similar distribution pattern around the four array elements (10,5), (11,5), (10,16), and (11,16). From
Figure 11c and
Figure 12c, the maximum sensitivity of the electric field strength in the z-direction is observed at the central array elements (10,10), (10,11), (11,10), and (11,11), with the sensitivity decreasing concentrically from these points. The changes in the positions of the edge array elements have a more significant impact on the antenna’s electrical performance compared to the changes in the positions of the central array elements.
Case 3 to 5 randomly adjusted the position of the array element relative to the x/y/z direction of the phase reference point on the basis of Case 2, in which the adjustment of the position of the array element in the x/y direction can be realized by the adjustment of the spacing of the array element in the x/y direction. In order to facilitate the comparison of the results, the position adjustment values of each array element in the three directions are all taken as
and the same random number matrix is used, and the direction diagram is shown in
Figure 13.
Figure 13 uses a graph of the
UV direction of the antenna, where u denotes the wavelength
along the direction of the antenna, and v denotes the wavelength
perpendicular to the direction of the antenna, and the
UV coordinate system allows for the characterization of the radiation of the antenna in different directions. Comparing with
Figure 13, it can be clearly found that the deterioration of the antenna electrical performance caused by the position change in the z direction is more obvious than that in the x and y directions when the position change is of the same magnitude, which is in line with the prediction result of the sensitivity distribution graph.
Cases 6 to 10 involve adjusting the array element arrangement based on Case 2 and observing the impact of the element positions on the antenna’s electrical performance by removing or adding key array elements. Case 2 features an octagonal tangent array. In Case 6, the array is supplemented to form a full array. Case 7 presents a random tangent array addition. Case 8 involves a special arrangement matrix where the center element with the greatest influence on z-direction sensitivity is removed. Case 9 focuses on removing the center element that most affects x-direction sensitivity, and Case 10 removes the center element with the highest impact on y-direction sensitivity. The orientation diagram for these cases is shown in
Figure 14.
Comparing Case 2, Case 6, and Case 7, it can be found that the missing array element at the corner position basically does not cause the deterioration of the antenna’s electrical performance, and even the missing array element in Case 2 makes the antenna’s radiation performance more balanced in different directions. Comparing Case 2, Case 8, Case 9, and Case 10, it can be found that the absence of the array element at the key position has a serious effect on the electrical performance of the antenna. Case 8 and Case 3 also correspond to the adjustment of the x-direction array element position, Case 9 and Case 4 also correspond to the adjustment of the y-direction array element position, and Case 10 and Case 5 also correspond to the adjustment of the z-direction array element position, and the corresponding deterioration of antenna electrical performance has the same trend. The above antenna electrical performance calculation results are all in accordance with the prediction results of the sensitivity distribution diagram.
3.3. Impact Analysis of Radome Thickness Effects (Case 2, 11, 12)
As shown in
Figure 15, the relationship between the transmission coefficient and the thickness of the radome is plotted, and the closer the transmission coefficient is to 1, the smaller the influence of the radome on the electrical properties of the antenna. In the range of
, there are two intervals
,
when the transmission coefficient is close to 1, and taking into account the stability of the radome structure, the thickness of the radome is not likely to fall in the
interval, and this paper uses the formula calculated radome thickness h of 8.6 mm in the
interval.
As shown in
Figure 16, the sensitivity distribution of the transmission coefficient with respect to the radome thickness is depicted. By comparing
Figure 15, it is evident that the interval in which the transmission coefficient has the smallest impact on the antenna electrical performance is the same as the interval in which the transmission coefficient has the highest sensitivity value on the antenna cover thickness.
Figure 17 shows the contour of the sensitivity distribution corresponding to
Figure 16, from which it can be seen that when the signal is vertically injected into the radome, the radome thickness has basically no effect on the transmission coefficient, and the larger the angle of incidence of the signal is, the more pronounced is the effect of the radome thickness on the transmission coefficient, and the effect is most significant in the interval of
.
Case 2, Case 11, and Case 12 are no radome, a radome with a thickness of 8.6 mm, and a radome with a thickness of 16 mm, respectively, with their radiation patterns shown in
Figure 18. Compared to Case 2, the main lobe field strength in Case 11 shows a slight decrease, with minimal overall changes in the radiation pattern. In Case 12, there is a comprehensive attenuation of field strength, resulting in a significant deterioration of the antenna’s electrical performance. This aligns with the predictions from the sensitivity distribution graphs regarding the impact of radome thickness on antenna electrical performance.
4. Conclusions
In this paper, a sensitivity-based method for analyzing the electrical performance of antennas is proposed, and a masked array antenna is used as the research object to verify the effectiveness of the method. Firstly, on the basis of the rectangular grid plane array factor direction map, the matrix characterizing the array layout form and the transmission coefficient characterizing the influence of the radome on the antenna’s electrical performance are introduced, and the electrical performance calculation model of the band-shrouded array antenna is deduced. Based on the electrical performance calculation model, the sensitivity model of the current amplitude, antenna array element x, y, z direction position, and radome thickness on the electrical performance of the antenna with shield array is deduced. Then, a numerical simulation example is given to analyze the trend of the parameters’ influence on the antenna electrical performance by using the sensitivity calculation model, and then analyze the influence of the same parameter on the antenna electrical performance by setting up several sets of working conditions by the traditional method, and the analysis results of the two methods are compared, and the results show a high degree of consistency, which proves the validity of the electrical performance analysis method based on the sensitivity proposed in this paper. Finally, in the process of analyzing the electrical performance of the band-mask antenna, it was found that under the conditions set in this paper, the excitation current amplitude has the most significant effect on the electrical performance of the antenna in the interval, the x-direction position of the four array elements (5,10), (5,11), (16,10), (16,11) has the most significant effect on the electrical performance, the y-direction position of the four array elements (10,5), (11,5), (10,16), (11,16) has the most significant effect on the electrical properties of the antenna, the z-direction position of the four array elements (10,10), (10,11), (11,10), (11,11) has the most significant effect on the electrical properties of the antenna, and the radome has the least effect on the electrical properties of the antenna in the interval.
Therefore, the method of analyzing the electrical performance of antennas based on sensitivity is practical and effective. In further research, this method can be extended to other types of antennas in the analysis of electrical performance. For antennas with simple and derivable formulas, the steps in this paper can be followed to calculate the sensitivity model of the antenna using the direct derivation method, which can quickly analyze the trend of the influence of various types of parameters on the antenna’s electrical performance; for antennas with complex or difficult to derive formulas for the calculation of electrical performance, the sensitivity model of the antenna can be obtained by the finite difference method and the Green’s function method. For antennas with complicated formulae or for which the electrical performance is difficult to derive, the sensitivity model of the electrical performance of the antenna can be obtained by the finite difference method and the Green’s function method, and then by analyzing the trend of the influence of the input parameters on the electrical performance.