# Design of Two Compact Wideband Monopoles Through Loading with Linear Approximated Lumped Components
## 2 Antenna Design
### Optimization of Loaded Monopoles  
Both loaded monopoles are optimized by GA optimization following a similar process to [33; 34; 35; 36] but using the loading technique described in Section 2.2 for accurately modeling practical load behaviors. To accurately perform simulations across a wide bandwidth, the frequency band was not sampled uniformly, but very densely at lower frequencies, viz. every 0.5 MHz from 30 to 40 MHz, every 1 MHz from 40 to 70 MHz, every 2 MHz from 70 to 120 MHz, every 5 MHz from 120 to 300 MHz, every 10 MHz from 300 to 600 MHz, every 20 MHz from 600 to 750 MHz and from 800 to 1500 MHz, and every 50 MHz from 1500 to 3000 MHz. Nonuniform sampling is important not only for increasing the relative weight of the gain in the lower portion of the frequency band, but also for eliminating possible narrowband dips in gain which have a tendency to appear at a lower frequency. Combining the loading technique described in Section 2.2 in the MoM solution with the AWE process, solution sweeping across an ultra-wide band with massive points could be carried out efficiently. The loaded elements for optimization are \(b_{R}\), \(b_{L}\), and \(b_{C}\) in (2), (5), and (6). The lower and upper bounds of these load parameter values were set to 0 \(<\) R \(<\) 2000 ohm, 0 \(<\) L \(<\) 400 nH, and 0 \(<\) C \(<\) 100 pF for the lower monopole and 0 \(<\) R \(<\) 2000 ohm, 0 \(<\) L \(<\) 25 nH, and 0 \(<\) C \(<\) 10 pF for the upper monopole. All of the component values are represented by 8 bits in GA optimization. Hence, the location of each load for the lower monopole and the upper monopole is specified by 6 bits and 4 bits, respectively, in GA optimization. The goal of optimization was satisfied when both antennas were optimized at the same time. The optimized value of the loaded elements as well as the locations of the loads are presented in Table 1 for the lower monopole and in Table 2 for the upper monopole. The location of the load circuits corresponds to their distances to the feed point. \begin{table}
\begin{tabular}{c c c c} \hline
**Load Position (cm)** & **Resistance (ohm)** & **Inductance (nH)** & **Capacitance (pF)** \\ \hline
25 & 1600 & 11 & 2.2 \\ \hline
30 & 1800 & 8 & 2 \\ \hline
40 & 500 & 50 & 6.5 \\ \hline
65 & 1300 & 60 & 4.5 \\ \hline
100 & 100 & 375 & 51 \\ \hline
155 & 300 & 210 & 5 \\ \hline
170 & 200 & 375 & 5 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of optimized load of lower monopole. Figure 5: Attenuation of lower monopole by \(\pi\)-type resistive circuit composed partly of ferrite beads. The optimized gain of the lower monopole is shown in Figure 6, and the optimized gain is above \(-4\) dB below \(200\) MHz and above \(0\) dB above \(200\) MHz. For comparison, the gain of an unloaded monopole with the same dimension is also depicted in Figure 6. The optimized loaded monopole avoids gain dips in all directions that appear naturally in the unloaded monopole due to pattern split. Figure 6 also plots the gain of the loaded monopole with the same load parameters in Table 1 but with a constant value. In the case of constant load, the gain deviates from the expected level far away across a wide band. However, the gain of the loaded monopole with the component of the approximate model appears well in the concerned band. Figure 7 shows the optimized gain of the upper monopole, and the optimized gain is above \(0\) dB from \(800\) to \(3000\) MHz. For comparison, the gain of an unloaded monopole with the same dimension is also depicted in Figure 7, and the dip of the gain in the concerned band is also removed in the load version. As shown in Figure 7, the constant load also deviates from the expected level, even though the BWR of the upper monopole is not great compared to the lower monopole. Both loaded monopoles sharing some common structures are optimized with satisfactory gain in all directions at the same time.