Enhancing Circular Polarization Performance of Low-Profile Patch Antennas for Wearables Using Characteristic Mode Analysis

A wearable antenna functioning in the 2.4 GHz band for health monitoring and sensing is proposed. It is a circularly polarized (CP) patch antenna made from textiles. Despite its low profile (3.34 mm thickness, 0.027 λ0), an enhanced 3-dB axial ratio (AR) bandwidth is achieved by introducing slit-loaded parasitic elements on top of analysis and observations within the framework of Characteristic Mode Analysis (CMA). In detail, the parasitic elements introduce higher-order modes at high frequencies that may contribute to the 3-dB AR bandwidth enhancement. More importantly, additional slit loading is investigated to preserve the higher-order modes while relaxing strong capacitive coupling invoked by the low-profile structure and the parasitic elements. As a result, unlike conventional multilayer designs, a simple single-substrate, low-profile, and low-cost structure is achieved. While compared to traditional low-profile antennas, a significantly widened CP bandwidth is realized. These merits are important for the future massive application. The realized CP bandwidth is 2.2–2.54 GHz (14.3%), which is 3–5 times that of traditional low-profile designs (thickness < 4 mm, 0.04 λ0). A prototype was fabricated and measured with good results.


Introduction
Due to the restrictions on cost, reliability, productivity, safety, and robustness, as well as the requirement for a good user experience in advanced communications and wireless body area networks (WBAN) for health care, health monitoring, sensing, and athlete training, etc., a tremendous effort has been devoted to minimizing traditional rigid antennas [1,2]. However, as a compromise, the miniaturization sacrifices the antenna performance since the antenna gain is essentially related to its dimensions [3]. Alternatively, flexible wearable antennas based on textiles [4][5][6], polyimide [7], PDMS [8][9][10], etc., are supposed to be good candidates for maintaining good performance and user experience while relieving the dimension restriction. For instance, [6] reports a wearable antenna for energy harvesting applications; however, the reported antenna has a low front-to-back ratio (FBR) without ground shielding. It is well known that the unshielded design results in a significant gain decrease (e.g., it decreases by a factor of 2 or more in [6]) due to the coupling and power absorption caused by the vicinity loading of the lossy human body. In contrast, patch antennas are reported to be insensitive to the human body and can obtain high FBR due to their shielding ground, which can benefit wearable applications. Their merits of low profile and low cost are also favorable for massive usage. Additionally, one needs to address the issue of polarization mismatch, which inevitably happens due to unpredictable movements in realistic circumstances when linearly polarized (LP) antennas are used. Hence, CP

Antenna Configuration
The geometry of the antenna is depicted in Figure 1. The antenna is composed of a corner-truncated patch surrounded by parasitic elements. The patch is with a cross-slot at the center. The antenna is deposited on top of a grounded single substrate layer made of felt (ε r = 1.35, tan δ = 0.03). Both the patch and the ground are made of conductive textiles with a conductivity of σ = 1.18 × 10 5 S/m (Shieldit Super from LessEMF Inc, Latham NY, USA.). The materials are flexible so that the antenna is friendly to be worn on the body. A ground shielding topology rather than unshielded ones [6,33] is adopted to reduce the human body loading effect on the antenna performance. Since a large area is available on the body, the antenna ground can be kept large to have higher gain and less radiation exposure issues. The thickness of the felt substrate and the conductive textiles are 3 mm and 0.17 mm, respectively. This results in a low-profile structure whose thickness is only 0.027 λ 0 . An antenna prototype is fabricated, as shown in Figure 9a. All the materials were cut manually. The textile radiator, the ground layer, and the felt substrate were ironed together with thermal melting glue. An SMA connector was soldered to the ground and to the patch to feed the antenna for measurements using a temperature-tunable soldering iron to avoid burning the textile.

Characteristic Mode (CM) Theory
To ease the illustration of the working mechanism of the CP bandwidth enhancement, here we review the main theoretical elements of CMA first.

Characteristic Mode (CM) Theory
To ease the illustration of the working mechanism of the CP bandwidth enhancement, here we review the main theoretical elements of CMA first.
According to the CM theory [34], an impedance matrix Z can be written as where R and X are the real and imaginary parts of the impedance matrix, respectively. Accordingly, a generalized eigenvalue problem is defined as: where J n is the nth characteristic current mode of a conductive structure and λ n is the corresponding eigenvalue of the nth mode. For each mode, modal significance MS is defined as [35]: It is an intrinsic property of the structure and is independent of external excitations. Thus, by investigating the MSs of a certain structure, the properties of the structure can be envisioned and modified. Especially for λ n = 0, i.e., MS = 1, the nth mode is in resonance. If we take an antenna as an example, with proper feeding excitation, the antenna may effectively radiate.
Another important factor for antennas design in CM theory is the characteristic angle (CA), which is defined as [35]: It presents the constant phase lag between the current J n and the tangential component of characteristic fields E n , where E n is the field produced by current J n .
To design a CP antenna, in practice, it is required that two orthogonal modes be effectively excited, and their MSs be close. Meanwhile, the characteristic angles should have a phase difference of nearly 90 • (70 • -110 • ).

Characteristic Mode Analysis (CMA) of the Low-Profile CP Antenna
CMA Multilayer Solver in CST studio 2020 is applied to carry out the predesign and analysis of the proposed antenna. Figure 2 shows the design in 3 steps. The design starts from a traditional corner-truncated patch, and then a cross-slot and four parasitic elements are adopted to introduce extra resonant modes in the frequency band of interest. Afterward, slits are cut on the parasitic elements to further broaden the bandwidth. Figure 3 illustrates the MSs and CAs of the first six modes of the three-step design, and Figures 4-6 illustrate the corresponding modal current distributions. As we can see in Figure 3a, mode 1 and mode 2 have large MSs in the 2.5-2.8 GHz band, while the MSs of mode 3-6 are almost 0, which means mode 1 and mode 2 could be excited. However, the MS and CA conditions to generate CP waves are effective in a limited bandwidth, i.e., 2.62-2.72 GHz, indicated in the colored zone 1 in Figure 3b. This also explains the natural narrow CP bandwidth of traditional corner-truncated patch antennas [21,22,36].
To increase the bandwidth, four parasitic elements are utilized to introduce extra modes in the interested band in the second step. The MSs and CAs for the interested mode 1-6 are shown in Figure 3c  GHz as long as all the modes can be effectively excited. Notably, the resonant frequencies of mode 1 and mode 2 are lower than the ones in step 1. This is due to the introduction of the cross-slot at the patch center and due to the coupling between the parasitic elements and the patch. This can be seen from the modal current distributions of mode 1 and mode 2, as shown in Figure 4a,b and Figure 5a,b. Such coupling can be modeled using LC model methods [5,28]. Moreover, it is worth mentioning that the parasitic patches and the traditional center patch without slot-loading in step 1 induce a strong capacitive effect with the antenna ground. This makes a traditional high-profile design preferable since a long feed probe can be used to compensate for the capacitive effect by its intrinsic inductance. However, for a wearable design with low-profile restrictions, the feed probe is too short to fulfill this requirement. Hence, a cross-slot is cut at the center patch to reduce the capacitive effect and to release the need for a long probe.         To increase the bandwidth, four parasitic elements are utilized to introduce extra modes in the interested band in the second step. The MSs and CAs for the interested mode 1-6 are shown in Figure 3c,d. It can be seen that mode 1 and mode 2 are the dominant ones and satisfy the CA requirements for generating CP waves around 2.34 GHz (colored zone 1, 2.3-2.39 GHz), while other modes around 2.34 GHZ have low MSs so that they can be ignored. Similarly, mode 2 and mode 3/4 contribute to a potential CP around 2.45 GHz (colored zone 2), mode 3/4 and mode 5 contribute to the frequency band of 2.47-2.51 GHz (colored zone 3), and mode 5 and mode 6 contribute to 2.51-2.55 GHz (colored zone 4). To sum up, the antenna may theoretically have a CP bandwidth in the frequency band of 2.3-2.55 GHz as long as all the modes can be effectively excited. Notably, the resonant frequencies of mode 1 and mode 2 are lower than the ones in step 1. This is due to the introduction of the cross-slot at the patch center and due to the coupling between the parasitic elements and the patch. This can be seen from the modal current distributions of mode 1 and mode 2, as shown in Figures 4a,b and 5a,b. Such coupling can be modeled using LC model methods [5,28]. Moreover, it is worth mentioning that the parasitic patches and the traditional center patch without slot-loading in step 1 induce a strong capacitive effect with the antenna ground. This makes a traditional high-profile design preferable since a long feed probe can be used to compensate for the capacitive effect by its intrinsic inductance. However, for a wearable design with low-profile restrictions, the   To increase the bandwidth, four parasitic elements are utilized to introduce extra modes in the interested band in the second step. The MSs and CAs for the interested mode 1-6 are shown in Figure 3c,d. It can be seen that mode 1 and mode 2 are the dominant ones and satisfy the CA requirements for generating CP waves around 2.34 GHz (colored zone 1, 2.3-2.39 GHz), while other modes around 2.34 GHZ have low MSs so that they can be ignored. Similarly, mode 2 and mode 3/4 contribute to a potential CP around 2.45 GHz (colored zone 2), mode 3/4 and mode 5 contribute to the frequency band of 2.47-2.51 GHz (colored zone 3), and mode 5 and mode 6 contribute to 2.51-2.55 GHz (colored zone 4). To sum up, the antenna may theoretically have a CP bandwidth in the frequency band of 2.3-2.55 GHz as long as all the modes can be effectively excited. Notably, the resonant frequencies of mode 1 and mode 2 are lower than the ones in step 1. This is due to the introduction of the cross-slot at the patch center and due to the coupling between the parasitic elements and the patch. This can be seen from the modal current distributions of mode 1 and mode 2, as shown in Figures 4a,b and 5a,b. Such coupling can be modeled using LC model methods [5,28]. Moreover, it is worth mentioning that the parasitic patches and the traditional center patch without slot-loading in step 1 induce a strong capacitive effect with the antenna ground. This makes a traditional high-profile design preferable since a long feed probe can be used to compensate for the capacitive effect by its intrinsic inductance. However, for a wearable design with low-profile restrictions, the  feed probe is too short to fulfill this requirement. Hence, a cross-slot is cut at the center patch to reduce the capacitive effect and to release the need for a long probe. Last, we find that the topology with slit-loadings on the parasitic elements proposed in step 3 has similar MSs, CAs, and modal currents as in step 2 (see Figures 3e,f and 6). The potential CP bandwidth is 2.26-2.52 GHz. This is due to the fact that all the modal currents of modes 1-6 on the parasitic elements flow along the x or y direction so that slits  Last, we find that the topology with slit-loadings on the parasitic elements proposed in step 3 has similar MSs, CAs, and modal currents as in step 2 (see Figure 3e,f and Figure 6). The potential CP bandwidth is 2.26-2.52 GHz. This is due to the fact that all the modal currents of modes 1-6 on the parasitic elements flow along the x or y direction so that slits along x or y directions have limited impact on the modal currents and the characteristic properties. Thanks to this, narrowing down the size of parasitic patches in step 2 by means of additional slits increases the parasitic inductance and decreases the capacitance while keeping the characteristic properties, meaning that a short, less inductive feeding structure may be sufficient to feed and excite the antenna. Overall, this approach with slits and the cross-slot is significantly different from the thick multilayer designs in [14,29], which need extra disks and pins for impedance matching.

Full-Wave Simulation
Summarized, topology 3 has the potential to obtain a wide CP bandwidth if the desired modes 1-6 are effectively excited with proper feeding. In the following, a coaxial probe (inner-pin diameter is 1 mm, outer-shell diameter is 4.1 mm) is used as feeding, and full-wave simulations are carried out to validate the proposed design. The final optimized parameters are given in Figure 1. The simulated reflection coefficient and AR results of the three topologies are shown in Figure 7. The full-wave simulation results agree with the above-analyzed results very well. It is clear that the proposed LPCPA with slit-loadings has significantly improved the performance of the low-profile antennas of topology 1 and topology 2. Its impedance bandwidth (S 11 < −10 dB) and CP bandwidth (AR < 3 dB) are 2.2-2.64 GHz and 2.29-2.53 GHz, respectively.  The Specific Absorption Rate (SAR) over 10 g of tissue is simulated by CST Studio 2020 according to the IEEE C95.3 standard. For realistic wearing applications, the antenna is placed about 5 mm above the body most of the time due to the insertion of air gaps and mid-layers to prevent scratching, potential allergic reactions, etc. Figure 8 shows the simulation model, which has been validated in [37,38]. The permittivity of the fat, skin, and muscle is 5.28, 38.01, and 52.73, respectively [39]. The simulated SAR result is 0.0159 W/kg at 2.4 GHz. The simulated SAR value is significantly lower than the European standard threshold of 2 W/kg. This is a benefit of the ground shielding of the proposed design. The Specific Absorption Rate (SAR) over 10 g of tissue is simulated by CST Studio 2020 according to the IEEE C95.3 standard. For realistic wearing applications, the antenna is placed about 5 mm above the body most of the time due to the insertion of air gaps and mid-layers to prevent scratching, potential allergic reactions, etc. Figure 8 shows the simulation model, which has been validated in [37,38]. The permittivity of the fat, skin, and muscle is 5.28, 38.01, and 52.73, respectively [39]. The simulated SAR result is 0.0159 W/kg at 2.4 GHz. The simulated SAR value is significantly lower than the European standard threshold of 2 W/kg. This is a benefit of the ground shielding of the proposed design. simulation model, which has been validated in [37,38]. The permittivity of the fat, sk and muscle is 5.28, 38.01, and 52.73, respectively [39]. The simulated SAR result is 0.0 W/kg at 2.4 GHz. The simulated SAR value is significantly lower than the Europ standard threshold of 2 W/kg. This is a benefit of the ground shielding of the propo design.

Measurement and Discussion
The fabricated antenna was measured in an anechoic chamber with a Vector Netw Analyzer 8510 system. Three scenarios were considered: free-space, on-body, and phantom. The measurement setups are shown in Figure 9. Since a wearable antenn inevitably bent when being worn on the body in practice, bent antennas with curvat radii of 5 cm and 8.5 cm (i.e., conformal situations) were measured for the free sp scenario. Further, the reflection coefficient of on-body scenarios, for example, on-arm a on-chest, was measured. As for the AR measurements, body tissue simulating liq MSL2450v2 [40] was used to mimic the body loading due to the fact that a human m move during the measurement and cause unstable transmissions and reflections cylinder with a 10 cm diameter and a liquid bag packed with a 10-mm-thick foam w used as phantoms to mimic the on-arm and on-chest situations, respectively.

Measurement and Discussion
The fabricated antenna was measured in an anechoic chamber with a Vector Network Analyzer 8510 system. Three scenarios were considered: free-space, on-body, and onphantom. The measurement setups are shown in Figure 9. Since a wearable antenna is inevitably bent when being worn on the body in practice, bent antennas with curvature radii of 5 cm and 8.5 cm (i.e., conformal situations) were measured for the free space scenario. Further, the reflection coefficient of on-body scenarios, for example, on-arm and on-chest, was measured. As for the AR measurements, body tissue simulating liquid MSL2450v2 [40] was used to mimic the body loading due to the fact that a human may move during the measurement and cause unstable transmissions and reflections. A cylinder with a 10 cm diameter and a liquid bag packed with a 10-mm-thick foam were used as phantoms to mimic the on-arm and on-chest situations, respectively.

Reflection Coefficient
As shown in Figure 10a, in free space, the impedance bandwidth (S11 < -10 dB) is 2.2-2.64 GHz in simulation and 2.18-2.61 GHz in measurement when the antenna is flat. The slight discrepancy between simulation and measurement may be caused by manual fabrication errors. For the conformal cases, a slight frequency shift is observed. Nevertheless, the antenna still shows a good performance. Further, the on-body results are shown in Figure 10b. The simulated impedance bandwidth is 2.21-2.64 GHz, and the measured bandwidth of on-arm and on-chest is 2.18-2.59 GHz. It is evident that, due to the benefit of ground shielding, the proximity of the body results in a limited influence when the antenna is worn on the arm and on the chest. Overall, we can conclude that the simulation and the measurement results match well. The antenna shows a robust impedance performance in free space and on-body scenarios.

Reflection Coefficient
As shown in Figure 10a, in free space, the impedance bandwidth (S 11 < −10 dB) is 2.2-2.64 GHz in simulation and 2.18-2.61 GHz in measurement when the antenna is flat. The slight discrepancy between simulation and measurement may be caused by manual fabrication errors. For the conformal cases, a slight frequency shift is observed. Nevertheless, the antenna still shows a good performance. Further, the on-body results are shown in Figure 10b. The simulated impedance bandwidth is 2.21-2.64 GHz, and the measured bandwidth of on-arm and on-chest is 2.18-2.59 GHz. It is evident that, due to the benefit of ground shielding, the proximity of the body results in a limited influence when the antenna is worn on the arm and on the chest. Overall, we can conclude that the simulation and the measurement results match well. The antenna shows a robust impedance performance in free space and on-body scenarios.

Axial Ratio
The simulated and measured AR results of the antenna in free-space and on-phantom scenarios are shown in Figure 11. They are evaluated on the normal axis (θ = 0 • ) of the antenna. For the free-space scenario (see Figure 11a), the simulated flat antenna has a Sensors 2023, 23, 2474 9 of 12 CP bandwidth (AR < 3 dB) of 2.29-2.53 GHz, and, accordingly, the measurement result is 2.2-2.54 GHz. The measurement bandwidth is wider than that of the simulation. This may be caused by fabrication errors during the manual fabrication process. The measured results when the antenna is bent show a frequency shift (depression) compared to the flat scenario. This is due to the symmetry of the structure that is broken. In detail, the modal currents of the dominant modes at high frequencies, i.e., modes 3-6 in Figure 6c-f, mainly flow on the rotationally symmetric parasitic elements. So, when the symmetric is broken, the CP waves cannot be effectively generated at high frequencies, and a frequency shift (depression) is observed. As for the on-phantom scenarios (see Figure 11b), a similar phenomenon can be observed.

Reflection Coefficient
As shown in Figure 10a, in free space, the impedance bandwidth (S11 < -10 dB) is 2.2-2.64 GHz in simulation and 2.18-2.61 GHz in measurement when the antenna is flat. The slight discrepancy between simulation and measurement may be caused by manual fabrication errors. For the conformal cases, a slight frequency shift is observed. Nevertheless, the antenna still shows a good performance. Further, the on-body results are shown in Figure 10b. The simulated impedance bandwidth is 2.21-2.64 GHz, and the measured bandwidth of on-arm and on-chest is 2.18-2.59 GHz. It is evident that, due to the benefit of ground shielding, the proximity of the body results in a limited influence when the antenna is worn on the arm and on the chest. Overall, we can conclude that the simulation and the measurement results match well. The antenna shows a robust impedance performance in free space and on-body scenarios.

Axial Ratio
The simulated and measured AR results of the antenna in free-space and on-phantom scenarios are shown in Figure 11. They are evaluated on the normal axis (θ = 0°) of the antenna. For the free-space scenario (see Figure 11a), the simulated flat antenna has a CP bandwidth (AR < 3 dB) of 2.29-2.53 GHz, and, accordingly, the measurement result is 2.2-2.54 GHz. The measurement bandwidth is wider than that of the simulation. This may be caused by fabrication errors during the manual fabrication process. The measured results when the antenna is bent show a frequency shift (depression) compared to the flat scenario. This is due to the symmetry of the structure that is broken. In detail, the modal currents of the dominant modes at high frequencies, i.e., modes 3-6 in Figure 6c-f, mainly flow on the rotationally symmetric parasitic elements. So, when the symmetric is broken, the CP waves cannot be effectively generated at high frequencies, and a frequency shift (depression) is observed. As for the on-phantom scenarios (see Figure 11b), a similar phenomenon can be observed.  Figure 12 shows the LHCP and RHCP realized the gain pattern of the LPCPA at 2.3 GHz and 2.4 GHz for both the free space and the on-phantom scenarios. The LHCPs are 10 dB larger than the RHCPs, which means the main polarization of the antenna is lefthanded circular polarization. In free space (Figure 12a,b), the flat antenna has a measured realized gain of 8.9 dBic and 7.1 dBic at 2.3 GHz and 2.4 GHz, respectively. Correspondingly, the estimated proximate efficiencies are 52.96% and 44.12% based on the half-power beamwidth [41]. Compared to the literature in Table 1, the designed lowprofile antenna has achieved the highest peak gain even with lossy textile materials rather than the less-lossy PCB substrates that are used in [13,14]. Due to the bending, a decrease in the LHCP gain is observed. The measured realized gain is 8.7 dBic (2.3 GHz) and 5.4 dBic (2.4 GHz) when the antenna is bent with a curvature radius of 5 cm. As for the onphantom scenario, see Figure 12c,d, the measured realized gains at 2.3 GHz are 8.6 dBic for on-chest and 8.4 dBic for on-arm, respectively, and at 2.4 GHz the corresponding ones are 7.1 dBic and 5.9 dBic. According to the patterns, we can also obtain the FBR values. The evaluated FBR values are all larger than 18 dB, and the peak one is 35 dB for the flat antenna in free space, which shows good radiation shielding due to the presence of the ground. As for positions having limited space or with drastic bending, for example, the  Figure 12 shows the LHCP and RHCP realized the gain pattern of the LPCPA at 2.3 GHz and 2.4 GHz for both the free space and the on-phantom scenarios. The LHCPs are 10 dB larger than the RHCPs, which means the main polarization of the antenna is left-handed circular polarization. In free space (Figure 12a,b), the flat antenna has a measured realized gain of 8.9 dBic and 7.1 dBic at 2.3 GHz and 2.4 GHz, respectively. Correspondingly, the estimated proximate efficiencies are 52.96% and 44.12% based on the half-power beamwidth [41]. Compared to the literature in Table 1, the designed low-profile antenna has achieved the highest peak gain even with lossy textile materials rather than the less-lossy PCB substrates that are used in [13,14]. Due to the bending, a decrease in the LHCP gain is observed. The measured realized gain is 8.7 dBic (2.3 GHz) and 5.4 dBic (2.4 GHz) when the antenna is bent with a curvature radius of 5 cm. As for the on-phantom scenario, see Figure 12c,d, the measured realized gains at 2.3 GHz are 8.6 dBic for on-chest and 8.4 dBic for on-arm, respectively, and at 2.4 GHz the corresponding ones are 7.1 dBic and 5.9 dBic. According to the patterns, we can also obtain the FBR values. The evaluated FBR values are all larger than 18 dB, and the peak one is 35 dB for the flat antenna in free space, which shows good radiation shielding due to the presence of the ground. As for positions having limited space or with drastic bending, for example, the wrist, the ground should be decreased accordingly for good wearing comfortability. Alternatively, the materials could be changed to more flexible and stretchable ones.

Conclusions
A wearable low-profile antenna with circular polarization is designed. Slitparasitic elements are used to improve the CP bandwidth in the 2.4 GHz band. CM is used to reveal the modal current distributions of the antenna. According to these c distributions, we find that the antenna can achieve a wide CP bandwidth by loadin on the parasitic elements whilst the antenna profile remains low. Full wave simu and measurements validate our design. The size of the prototype antenna is 1.04 × 1 while the profile is only 0.027 λ0. The antenna has an impedance bandwidth of 2.1 GHz (18%) and a CP bandwidth of 2.2-2.54 GHz (14.3%) and realized a peak gain dBic. Compared to other low-profile wearable designs in the 2.4 GHz band, this achieves a bandwidth that is 3-5 times larger.

Conclusions
A wearable low-profile antenna with circular polarization is designed. Slit-loaded parasitic elements are used to improve the CP bandwidth in the 2.4 GHz band. CM theory is used to reveal the modal current distributions of the antenna. According to these current distributions, we find that the antenna can achieve a wide CP bandwidth by loading slits on the parasitic elements whilst the antenna profile remains low. Full wave simulations and measurements validate our design. The size of the prototype antenna is 1.04 × 1.04 λ 0 2 while the profile is only 0.027 λ 0 . The antenna has an impedance bandwidth of 2.18-2.61 GHz (18%) and a CP bandwidth of 2.2-2.54 GHz (14.3%) and realized a peak gain of 8.9 dBic. Compared to other low-profile wearable designs in the 2.4 GHz band, this design achieves a bandwidth that is 3-5 times larger.