## 2 A Near Isotropic Planar Antenna
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Antenna Design** & **Dimensions (\(\lambda\))** & **Bandwidth** & **Gain Variation** & **Efficiency** \\ \hline Printed Arc antenna & 0.203 \(\times\) 0.25 & 4\% & \(\leq\)0.5 dB & 86\% \\ Patch antenna [10] & 0.22 \(\times\) 0.22 \(\times\) 0.044 & 0.61\% & 0.91 dB & 90\% \\ Spherical antenna [11] & 0.15 \(\times\) 0.15 \(\times\) 0.125 & 2.2\% & 3 dB & 98.5\% \\ Single feed antenna [12] & 0.17 \(\times\) 0.3 \(\times\) 0.06 & - & 9.46 dB & - \\ L-shaped monopole [15] & 0.37 \(\times\) 0.37 \(\times\) 0.0066 & 20.82\% & 5.75 dB & 80\% \\ Linear slot antenna [16] & 0.5 \(\times\) 0.02 \(\times\) 0.001 & - & 2.1 dB & - \\ Dipole loop-loaded [17] & 0.102 \(\times\) 0.102 \(\times\) 0.005 & 0.5\% & 3.8 dB & 30.4\% \\ Dielectric antenna [18] & 0.027 \(\times\) 0.027 \(\times\) 0.0045 & 6.9\% & 3 dB & 90\% \\ Crossed dipoles [19] & 0.26 \(\times\) 0.26 \(\times\) 0.008 & 3.3\% & 3.7 dB & 97\% \\
3D slot antenna [20] & 0.09 \(\times\) 0.018 \(\times\) 0.018 & 11.25\% & 3 dB & - \\ Inverted-F antenna [1] & 1.8 \(\times\) 1.3 \(\times\) 0.06 & 15\% & 10.78 dB & - \\ Dual Band 3-D antenna [23] & 0.67 \(\times\) 0.67 \(\times\) 0.67 & 8.9\% & 0.9 dB & - \\ Planar Quasi-isotropic antenna [25] & 0.47 \(\times\) 0.47 & 1.2\% & 3.01 dB & 82.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A comparison of simulation performance of proposed antenna with simulation results of existing antenna designs. Figure 1: Initial design simulated using MATLAB. After arriving at initial design by use of Equation (1), a single antenna was modeled in NEC. However, the linear slope segment was replaced with a curved arc shaped segment for smoother as well as lesser gain variation. The geometrical parameters of the arc would control the current distribution and thus can be used to achieve isotropy [27]. Lengths of all three segments were fine tuned to further improve the achievable isotropy. The final design is shown in Figure 2. The red dot in the centre shows the feed point. It is shown in [27] that a full parametric sweep of arc radius from minimum to maximum value does not render equal magnitude of vertical (along \(z\)-axis) and horizontal (along \(x\)-axis) components and the former always remains dominant. Therefore, an equivalent contribution from both gain components was required to achieve lesser variation in total gain and better isotropy, which was achieved by using a larger horizontal segment. A parametric study was carried out to study the effects on isotropy due to the variation in arc radius, vertical arm's length, and horizontal arm's length in order to find the optimum dimensions of the antenna. The most important parameter is arc radius, because it contributes in both horizontal and vertical gains, as already stated. Figure 3 shows the 3D plots by only varying the horizontal arm's length while keeping other parameters constant. The horizontal arm dimensions were reduced and increased and we found that as we go away from the optimum point, the total gain variation increases. Figure 2(a) shows a variation of 7.4 dB in total gain when the horizontal arm's length is decreased by 27% of optimum dimensions. Similarly, Figure 2(b) shows the results when the dimensions are decreased by 13% of optimum length. Figure 2(c),d show the results when the dimensions are increased by 13% and 27% that of optimum dimensions. As we go near the optimum length, the isotropy increases or the total gain variation reaches the lowest value. Figure 2: Structure of proposed Isotropic antenna at 1 GHz. Similar results were found for the variations in dimensions of the vertical arm, while keeping the arc radius and horizontal arm's length constant at the optimum point. As we go, go farther from the optimum length, either increasing side or decreasing side, the variation in total gain increases. Figure 3(a),b show the 3D total gain plots when the vertical arm's length is decreased by 80% and 50%, while Figure 3(c),d show the results when it is increased by 93% and 187%, respectively.