# Extremely Low-Profile Monopolar Microstrip Antenna with Wide Bandwidth
## 2 Antenna Design and Analysis
### Operation Principle and Field Distributions  
Figure 2 shows the simulated frequency responses of the proposed antenna to variations of the substrate thickness, \(t\). The \(t\) was varied from 0.127 mm (10 mils) to 0.787 mm (31 mils) with fixed \(\varepsilon_{r}\) of 2.2 using commercially produced RF and microwave dielectric substrate. As can be seen from the results, when the \(t\) was changed, the dual resonant couplings varied, and lowered resonant mode was kept at around 5.0 GHz to 5.3 GHz. It was observed that the geometric configuration only determined the lower resonant mode. However, the substrate thickness of t may determine the upper resonant frequency with different coupling factors. In the case of the \(t=0.254\), the upper resonant modes clearly occurred at two different frequencies. Figure 1: Configuration of the proposed antenna. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Description** & **Dimension (mm)** \\ \hline \(p\) & Length of the feeding hexagonal patch & 17.7 \\ \(pts\) & Upper length of the radiating trapezoidal patch & 10.2 \\ \(ptl\) & Lower length of the radiating trapezoidal patch & 20.4 \\ \(g\) & Coupling gap size between feed and radiator & 0.2 \\ \(w\) & GND wire width occurred from inner radiator & 0.2 \\ \(w_{G}\) & GND wire width occurred from between radiator & 0.6 \\ \(lf\) & Soldering pad length of the feed in the GND & 9.7 \\ \(lbs\) & GND slot length of the upper side of trapezoid & 5.4 \\ \(lbl\) & GND slot length of the equilateral triangle & 2.9 \\ \(D\) & Diameter of the substrate & 70 \\ \(t\) & Thickness of the substrate & 0.254 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimized all of dimensions of the proposed antenna parameters. Figure 2: Simulated frequency responses of the proposed antenna for substrate thickness variation. Figure 3 illustrates the simulated electric field distributions for understanding the dual resonant phenomenon, that is, the operation principle of the proposed antenna. As mentioned in the previous section, we used a monopolar microstrip antenna as a validated model in [31]. The omni-directional radiation is realized by utilizing the non-fundamental 1.5-wavelength resonant TM\({}_{02}\) mode like the conventional monopolar microstrip antenna. And this hexagonal microstrip antenna as a validated mode was conducted on the implementation of one operating frequency band and the improvement of the radiation performance by reducing \(Q\)-factor using the mesh ground using one resonator in [31]. In other words, although the proposed antenna has the same configuration in [31], the degenerated mode due to the substrate thickness is not considered at all. As shown in Figure 3a,b, two equivalent magnetic current densities in opposite directions are formed. By these two looped currents, which are mathematically equivalent to the electric line current density, the proposed antenna can form an omni-directional radiation pattern at two different frequencies. Thus, the proposed antenna showed only one single-layered single resonator with adjacent frequencies. Additionally, the identical modes, that is, the omni-directional radiations, were sustained at two different frequencies. Accordingly, the proposed antenna can accomplish the successful degenerated TM\({}_{02}\) modes for omni-directional radiation. As shown in the edge patch radiator of Figure 3a,b, the electric field phase was opposite, and the electric field magnitude was identical. It can be seen that this phenomenon is the same as the degenerated mode of the dual-mode filter introduced in [32]. In detail, the degenerated mode in the dual-mode filter technology is the difference in electrical length of two diagonals, and the same resonance occurs at two frequencies that are close to each other.