# An Optimization Design of Bi-log Hybrid Antenna with Taguchi's Method for EMI Measurements
## 3 Antenna Optimization using Taguchi's Method
### Concepts of Taguchi's Method  
In general, the concept of optimization of antenna design procedures includes several steps such as determining the parameters and frequency ranges of the proposed antenna, using [PERSON]'s method with an OA for simulations, establishing the frequency response condition, reducing the searching range iteratively, and repeating the simulations to achieve convergence. The [PERSON] method yields better antenna parameters of impedance match, and the desired directive pattern is compared with traditional trial and error approaches.  
To achieve a better combination of parameter values, it is necessary to utilize the benefits of OAs. As mentioned earlier, it offers an efficient method for identifying the optimal parameters of a general optimization problem. The notation OA(N,k,s,t) is usually  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Refs.** & **Antenna Type** & \begin{tabular}{c} **Operation** \\ **Frequency (MHz)** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Element** \\ \end{tabular} & \begin{tabular}{c} **Scaling Factor** \\ **(r)** \\ \end{tabular} & \
\begin{tabular}{c} **FBW** \\ \end{tabular} &
\begin{tabular}{c} **Gain (dBi)** \\ \end{tabular} \\ \hline This work & Bi-log & 30–6000 & 21 & 0.802 & 198\% & 5–7 \\ \hline
[2,3,8] & Bi-log & 30–1000 & 15 & 0.855 & 188\% & 3–7 \\ \hline
[4] & Bi-log & 30–1000 & 17 & 0.865 & 188\% & - \\ \hline
[5] & LPDA & 500–6000 & 12 & 0.860 & 170\% & 4.6–7 \\ \hline
[6] & LPDA & 500–6000 & 12 & 0.852 & 170\% & 5.1–6.4 \\ \hline
[8] & LPDA & 500–10,000 & 25 & 0.916 & 181\% & 3–6.01 \\ \hline
[9] & LPDA & 550–9000 & 50 & 0.942 & 177\% & 2.48–7.89 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the published antennas.  
Figure 2: Benchmark performance of the proposed antenna: (**a**) VSWR, (**b**) antenna factor, and (**c**) antenna symmetry.  
used to represent an OA of N rows and k columns (for k parameters) with s levels and strength t. In Table 2, the OA table (L27 310) determines varying \(\tau\) values as 10 control factors, with three levels, only 27 experiments are needed to find a better combination of parameter values. In 27 runs of the experiment, which are dramatically less than 310, a full factorial strategy is used instead. The established frequency response condition of the cost function \(X_{i}\) is nominal-the-best. The value was calculated from experimental data using the simulation result, which satisfies the good impedance matching condition as VSWR \(<\) 2. The signal-to-noise ratio (SNR) is also obtained from the average of the cost function value (calculated).  
Footnote 10: The \(\tau\) values are calculated from the \(\tau\) values.  
The higher number of antenna elements required in the whole band depends on the physical dimensions of the antenna and the greater values of \(\tau\). The ratio of the longest element length to the second longest element length is called \(\tau\)1. \(\tau\)2, \(\tau\)3, \(\tau\)4, and so on, and they are  
because each level of a factor is represented an equal number of times, and if one factor is held constant, the other factors' levels are also equally represented. This promotes fairness and objectivity in evaluating the frequency response of each factor level. Therefore, the obtained antenna parameter achieves the desired frequency response with fewer iterations to reach the optimum solutions in an equally distributed fractional factorial experiment.