In recent years, geostationary orbit (GEO) satellites have been increasingly employed in satellite communication, broadcasting, monitoring, and data relay systems [1–7]. These satellites are situated above the target ground stations or areas, enabling continuous communication or monitoring by matching their orbital speed to the Earth’s rotational speed [8, 9]. For this purpose, they are generally operated at altitudes of around 36,000 km. However, such high altitudes result in high transmission path losses, which can cause serious communication errors between satellites and ground stations. To transmit signals between satellites and the Earth’s surface, extremely high-gain antennas are typically required to compensate significant path loss caused by long-distance transmission under atmospheric attenuation. In addition, satellite antennas must possess broadband characteristics to perform various missions using a limited number of antennas. Among the antennas that satisfy these requirements are reflector antennas, which are widely employed in various satellite missions [10–14]. However, to use reflector antennas at high operating altitudes, such as in GEO satellites, the reflector volume must be increased to achieve high gain characteristics. Unfortunately, this increases the weight of the total antenna system. To resolve this problem, extensive research has been conducted on deployable reflector antennas to dramatically reduce their stowed volume by replacing the heavy metal reflector with a lightweight conductive mesh and deployable rib structure [15–18]. A rib-type deployable mesh reflector antenna is composed of multiple ribs and joints, which enables efficient deployability. This serves to reduce the antenna volume when it is loaded onto a rocket but increases mechanical errors during deployment [19–22]. Since deployment errors can lead to degradation in antenna performance, they need to be analyzed extensively. However, most recent studies on deployable reflector antennas have focused on deriving optimal shapes and performance. Consequently, there is a lack of research on antenna performance analysis that accounts for errors, such as reflector surface errors and feed antenna misalignment, that can cause performance degradation. Moreover, it is essential to identify the error that has the greatest impact on the performance of a deployable reflector antenna.

In this paper, we analyze performance degradation resulting from mechanical errors in rib-type deployable mesh reflector antennas to propose error tolerance levels that can be used as a reference when designing such antennas. In rib-type deployable mesh reflectors, five types of errors may occur: joint stop angle error, feeder alignment error, feeder pointing error, defective surface error, and wrinkled surface error. In this study, we investigate the antenna performance degradation caused by these mechanical errors, based on which we suggest error tolerances pertaining to a reduction in boresight gain by 1 dB, 2 dB, and 3 dB. For this analysis, we employed CST Studio Suite [23], along with a previously studied deployable reflector antenna [24] and a feed horn antenna [25]. The error tolerances at which 1-dB performance degradation occurred for each error type are as follows: 0.32° at 10 GHz for joint stop angle error, 9.5% at 3 GHz for defective surface error, 0.0071 m at 10 GHz for wrinkled surface error, 0.016 m at 10 GHz for feeder alignment error, and 23.6° at 3 GHz for feeder pointing error. According to these results, the joint stop angle error is the most sensitive and critical error. Therefore, it must be minimized when designing and fabricating rib-type deployable mesh reflector antennas.

Fig. 1 illustrates the geometry of a reference rib-type deployable mesh reflector antenna. As shown in Fig. 1(a), it consists of a rib-type deployable mesh reflector [24] and a double-ridge horn antenna [25]. The mesh reflector is constructed using a deployable frame structure and flexible conductive mesh to reduce its volume when stowed in a rocket’s payload. To achieve efficient deployability, N_r ribs with joints are used, with the conducting mesh attached to the upper surface of the structure. The mesh forms a curved surface owing to the tension caused by rib expansion, which creates multiple flat subdivisions on the surface. Since there are two joints in the model depicted in Fig. 1(a), three flat subdivisions (N_sub) are created between each rib. Fig. 1(b) presents the side view of the reflector antenna. The reflector’s curvature was determined using a parabolic equation (Eq. 1), which is conventionally used for designing reflector antennas:

where D represents the diameter of the reflector when it is fully deployed, and F is the focal point of the parabolic reflector. Focal point F denotes the single spot where all incoming radio waves are concentrated based on the parabolic geometry of the reflector. The feed antenna (a 3D metal double-ridge horn antenna) is situated at this point. Notably, the presented reflector antenna was optimized to exhibit high gain characteristics. Its detailed parameters are listed in Table 1.

Fig. 2 presents conceptual figures of typical mechanical errors observed in rib-type deployable mesh reflector antennas. We examined five types of mechanical errors commonly encountered in rib-type deployable mesh reflector antennas, analyzing their impact on performance. With regard to the reflector, three types of errors—joint stop angle error, defective surface error, and wrinkled surface error—are frequently observed, as illustrated in Fig. 2(a), 2(b), and 2(c), respectively. The joint stop angle error occurs when the antenna deployment process cannot be completed due to mechanical failure or unexpected factors causing reflection surface errors. Furthermore, defective surface errors take place when the ribs unfold too quickly or the mesh is pinched by the structure, while wrinkled surface errors may result from thermal stress, physical stress, or aging during operation. In the case of the feed antenna, two types of errors may occur: feeder alignment error and feeder pointing error. As shown in Fig. 2(d), feeder alignment error may occur in all directions. When this error occurs in a plane parallel to the reflector aperture (xy-plane), it tilts the main lobe direction of the reflector antenna. Conversely, when the error occurs along the z-axis, the main lobe direction remains unchanged, but the boresight gain characteristics decrease significantly. The feeder pointing error, depicted in Fig. 2(e), also leads to the critical degradation of the boresight gain. However, in this case, the main lobe direction is not significantly tilted. For example, when the pointing error is 40°, the main lobe direction is tilted by only 1°. In the following chapters, we analyze the performance degradations caused by these five errors.

Fig. 3 shows the simulated performance degradation results for the joint stop angle error. Fig. 3(a) provides a detailed illustration of the joint stop angle error, where ϕ_n,1 refers to the angle error of Joint 1 in n-th rib (n = 1, 2,…, N_r) and ϕ_n,2 denotes the angle error of Joint 2 in n-th rib. Each error occurred independently and randomly, following a normal distribution within the range of 1°–10°. The average angle (ϕ_a) was calculated using Eq. (2):

Fig. 3(b) presents the boresight gain and half-power beamwidth (HPBW) attained in relation to ϕ_a at 3 GHz. It is observed that when ϕ_a is 1.35°, the boresight gain decreases by 1 dB and the HPBW increases by 0.35°. Furthermore, when ϕ_a is 1.99°, the boresight gain decreases by 2 dB and the HPBW increases by 0.77°. To verify the feasibility of these results, the Ruze formula—a conventional method for evaluating performance degradation caused by antenna surface errors—was implemented [26]. The root mean square error (RMSE) of the joint stop angle error was estimated to be 1.78 dB, showing good agreement with the simulation results. Fig. 3(b) also shows that when ϕ_a is 2.32°, the boresight gain decreases by 3 dB and the HPBW increases by 1.29°. Furthermore, Fig. 3(c) presents the sidelobe level (SLL) and the main lobe direction, indicating that when ϕ_a increases, the SLL decreases from 27.1 dB to 10.4 dB, whereas the main lobe direction remains nearly unchanged.

Fig. 4 shows the simulated results for performance degradation caused by the defective surface error. A detailed illustration of the error is presented in Fig. 4(a), where A_dn denotes the defective mesh area. To analyze antenna performance, the defective mesh ratio (A_r) was calculated using Eq. (3), as follows:

where N_d refers to the total number of defective meshes, and D is the diameter of the mesh reflector. Fig. 4(b) presents the boresight gain and HPBW pertaining to A_r at 3 GHz, showing that when A_r is 9.5%, the boresight gain decreases by 1 dB and the HPBW remains unchanged. Furthermore, the boresight gain decreases by 2 dB when A_r is 18.9%, and by 3 dB when A_r is 27.5%. Fig. 4(c) depicts the SLL and main lobe direction, where the SLL decreases to 14 dB as the A_r increases, while the main lobe direction remains unchanged.

Fig. 5 depicts the simulation results for performance degradation caused by the wrinkled surface error. Fig. 5(a) provides a detailed illustration explaining the error, where d_w represents the depth of the wrinkles on the surface, with its value set to be uniform between each rib. Fig. 5(b) presents the variations in boresight gain and HPBW with regard to d_w at 3 GHz. It is observed that d_w of 0.018 m results in a 1 dB decrease in boresight gain and a 0.54° increase in the HPBW. Furthermore, as d_w increases to 0.027 m, the boresight gain decreases by 2 dB, while the HPBW increases by 1.18°. Again, when d_w is 0.037 m, a 3-dB boresight gain reduction is attained, with the HPBW increasing by 1.8°. To verify the feasibility of these results, the Ruze formula was applied. The RMSE of the wrinkled surface error was calculated to be 0.62 dB, indicating good agreement with the simulation results. Fig. 5(c) shows the SLL and main lobe direction, demonstrating that the SLL decreases from 27.1 dB to 18.5 dB as the d_w increases, whereas the main lobe direction remains almost unchanged.

Fig. 6 shows the simulation results for performance degradation caused by the feeder alignment error. Fig. 6(a) explains the error in detail, with d_ex, d_ey, and d_ez representing feeder misalignment distances along the x-, y-, and z-axes, respectively. Fig. 6(b) illustrates that when the feeder alignment error occurs along the x-axis, the maximum gain decreases and HPBW increases. Meanwhile, Fig. 6(c) presents the SLL and main lobe direction, showing that SLL decreases from 27.1 dB to 11.6 dB as d_ex increases, with the main lobe direction also changing significantly. For instance, when d_ex is 0.047 m, the main lobe direction tilts by 5°, which closely corresponds to the misalignment angle from the z-axis calculated using Eq. (4).

This angle is formed by misalignment between the optimum and error positions relative to the reflector center. Furthermore, as shown in Fig. 6(d), when the feeder alignment error occurs along the y-axis, the maximum gain decreases while the HPBW increases. Fig. 6(e) clarifies that the SLL decreases to 10.8 dB, and the main lobe direction changes in such a scenario. Fig. 6(f) illustrates the variations in boresight gain and HPBW with regard to d_ez at 3 GHz. It is observed that when d_ez is 0.068 m, the boresight gain decreases by 1 dB while the HPBW remains unchanged. As the misalignment increases to 0.091 m, a 2-dB reduction in boresight gain is observed. Upon further increasing d_ez to 0.125 m, a boresight gain reduction of 3 dB is attained. Meanwhile, as evident from Fig. 6(g), the SLL variation does not exhibit a consistent trend as d_ez increases, while the main lobe direction remains unchanged.

Fig. 7 illustrates the simulated results for performance degradation caused by the feeder pointing error. Fig. 7(a) presents a detailed figure explaining the error, where θ_error refers to the angular error of the feeder’s direction from the reflector center. In Fig. 7(b), the impact of θ_error on boresight gain and HPBW at 3 GHz is depicted, demonstrating that a misalignment of 23.6° results in a 1-dB reduction in boresight gain, although the HPBW does not change. As θ_error increases to 33.2°, the boresight gain decreases by 2 dB. Furthermore, when θ_error increases to 40.4°, the boresight gain decreases by 3 dB. In addition, Fig. 7(c), which displays the SLL and main lobe direction, shows that SLL decreases from 27.1 dB to 11.2 dB as θ_error increases, while the main lobe direction increases gradually, shifting by 1°, 2°, and 3° when θ_error is 17.3°, 32°, and 48.2°, respectively.

The performance analysis conducted for the five types of errors, as described in Section III, was repeated at 6 GHz and 10 GHz to derive the error points at which the boresight gain decreases by 1 dB (20.6%), 2 dB (36.9%), and 3 dB (50%) at both frequencies. Notably, these boresight gain reduction levels are widely adopted as intuitive indicators of antenna performance degradation. Tables 2–6 present the observed changes in performance in relation to each error.

Table 2 lists the degradation of boresight gain caused by the joint stop angle error. It is evident that the degradation value increases with the error value at each frequency. For example, at 3 GHz, 1-dB degradation occurs at 1.35°, 2-dB degradation occurs at 1.99°, and 3-dB degradation occurs at 2.32°. Furthermore, it is observed that as the frequency increases, these levels of degradation occurs at smaller error values. For instance, the 1-dB degradation point is 1.35° at 3 GHz, 0.62° at 6 GHz, and 0.32° at 10 GHz.

Table 3 presents the levels of performance degradation observed for defective surface errors. At each frequency, the degradation value increases with the error value, exhibiting a trend similar to the joint stop angle error. However, in this case, as the frequency increases, the same levels of degradation occur at larger error values. For instance, the 1-dB degradation points are 9.5% at 3 GHz, 10.3% at 6 GHz, and 12.4% at 10 GHz. This further implies that, in general, higher frequencies result in higher sensitivity. To explore this phenomenon further, we analyzed the performance of a reflector antenna with a 1-m diameter at three frequencies: 3 GHz (λ = 0.1 m), 6 GHz (λ = 0.05 m), and 10 GHz (λ = 0.03 m). The electrical size of the reflector was observed to increase with frequency, corresponding to approximately 10λ at 3 GHz, 20λ at 6 GHz, and 33λ at 10 GHz. Moreover, when a fixed physical area (e.g., 0.1 m × 0.1 m) was defected, electrically equivalent areas of 1λ × 1λ at 3 GHz and approximately 3.3λ × 3.3λ at 10 GHz were measured. From these findings, it may appear that higher frequencies result in electrically larger defects. However, when the loss was normalized by the total electrical area of the reflector, the ratios were found to be similar—(1λ × 1λ) / (10λ × 10λ) at 3 GHz and (3.3λ × 3.3λ) / (33λ × 33λ) at 10 GHz. This suggests that, for a given defective area, the electrical area increases with the frequency, which may explain the similar relative performance degradation observed across different frequencies.

Table 4 presents the performance degradation associated with the wrinkled surface error. At each frequency, the degradation value increases with an increase in the error value (for example, at 3 GHz, 1-dB degradation occurs at 0.018 m, 2-dB degradation occurs at 0.027 m, and 3-dB degradation occurs at 0.0071 m). Furthermore, at higher frequencies, the same degradation is observed at reduced error values. For example, the 1-dB degradation point is 0.018 m at 3 GHz, 0.01 m at 6 GHz, and 0.0071 m at 10 GHz.

Table 5 details the performance degradation stemming from the feeder alignment error (z-axis). At each frequency, the degradation value increases with the error value. Moreover, the same level of degradation occurs at smaller error values as the frequency increases. Table 6 presents the performance degradation resulting from the feeder pointing error. In this case as well, the degradation value increases with the error value at each frequency. However, regardless of the frequency, the same level of degradation occurs corresponding to the same error value (e.g., the 1-dB degradation point is 23.6° at 3 GHz, 24.5° at 6 GHz, and 24.1° at 10 GHz).

These findings confirm that, except for defective surface error (Table 3) and feeder pointing error (Table 6), the degradation value increases with the error value at each frequency, while the 1-dB degradation error point decreases with an increase in frequency. The error tolerances at which a performance degradation of 1 dB was observed for each error type are as follows: 0.32° at 10 GHz for joint stop angle error, 9.5% at 3 GHz for defective surface error, 0.0071 m at 10 GHz for wrinkled surface error, 0.016 m at 10 GHz for feeder alignment error, and 23.6° at 3 GHz for feeder pointing error. These results highlight that while minimizing all types of errors is important, the most sensitive and critical one that should be addressed is the joint stop angle error, which must be minimized when designing and fabricating rib-type deployable mesh reflector antennas.

The detailed error tolerances at each frequency for each error type are presented in Tables 2–6. Notably, to address diverse operational scenarios, aperture efficiency was calculated using a commonly used equation [27], and the corresponding gain reduction values were estimated. Additionally, beam distortion—an important metric for evaluating the deviation of a beam shape from its intended pattern when an error occurs—was derived based on RMSE, as expressed in Eqs. (5) and (6):

Here, G_odB,lin denotes linear gain without any error, and G_ndB,lin refers to the linear gain when it is reduced by n dB (where n = 1, 2, 3).

In this paper, we analyzed performance degradation caused by mechanical errors in rib-type deployable mesh reflectors, subsequently proposing error tolerance levels that can be used as reference when designing antennas comprised of these reflectors. Five types of errors are commonly observed in such reflectors: joint stop angle error, feeder alignment error, feeder pointing error, defective surface error, and wrinkled surface error. We investigated the antenna performance degradation caused by each of these mechanical errors to subsequently suggest error tolerances pertaining to a reduction in boresight gain by 1 dB (20.6%), 2 dB (36.9%), and 3 dB (50%). The error tolerances at which a performance degradation of 1 dB occurred for each error type are as follows: 0.32° at 10 GHz for joint stop angle error, 9.5% at 3 GHz for defective surface error, 0.0071 m at 10 GHz for wrinkled surface error, 0.016 m at 10 GHz for feeder alignment error, and 23.6° at 3 GHz for feeder pointing error. These results reveal that the most sensitive and critical error is the joint stop angle error. Therefore, attention should be paid to minimizing this error when designing and fabricating rib-type deployable mesh reflector antennas.