## 3 Working Mechanism
### 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].  
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 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.  
Figure 3: MSs and CAs evolution of the LPCPA. (**a,b**) MSs and CAs of Step 1. (**c,d**) MSs and CAs of Step 2. (**e,f**) MSs and CAs of Step 3. Colored zones present where the CA phase differences are in the range of 70\({}^{\circ}\)-110\({}^{\circ}\).  
Figure 2: Evolution of the LPCPA design. (**a**) Step 1, a traditional corner truncated patch antenna. (**b**) Step 2, a corner truncated patch with cross-slot and parasitic elements. (**c**) Step 3, the proposed LPCPA with slit-loading.  
Figure 4: Modal current distributions of basic corner-truncated structure. (**a**) Mode 1. (**b**) Mode 2.  
Figure 5: Modal current distributions of the structure without slit-loading. (**a**–**f**) are Mode 1–6.  
Figure 6: Modal current distributions of the structure with slit-loading. (**a**)–(**f**) are Mode 1–6.  
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.