# An Optimization Design of Bi-log Hybrid Antenna with Taguchi's Method for EMI Measurements
## 3 Antenna Optimization using Taguchi's Method
### Optimization of Antenna Design  
The Bi-log hybrid antenna has been presented and optimized, which is made up of a combination of bowtie and LPDA antenna parts. Using proper geometry, the bowtie part of the proposed antenna achieves small dimensions at lower frequencies. The LPDA part determines the antenna properties at higher frequencies, typically over 200 MHz. To optimize the design of an LPDA part, attention must be paid to the directivity of radiation patterns and the impedance characteristics within the operating frequency ranges. The LPDA part of this antenna, in physical size and gain, are defined by the constants \(\tau\) and \(\sigma\). Larger values result in longer antennas with more elements and gain. The optimization focuses on impedance matching, stable gain, continuity of the AF, and incorporation of miniaturized elements. The optimal design was determined with a series \(\tau\) of the key parameters and in the frequency range from 30 MHz to 6 GHz. The analysis uses [PERSON]'s method with an OA to obtain results from simulations using NEC2 and CST software. The established frequency response conditions of the cost function \(\mathrm{X_{i}}\) and SNR are nominal-the-best as VSWR \(<\) 2, which are obtained from the formula represented in Equations (1) and (2). It also iteratively reduces the search range and repeats the simulations to achieve convergence. Simulation results are used to determine optimal matching parameters for the proposed antenna configuration. \[\mathrm{S/N~{}Ratio}=\frac{1}{n}\sum_{i=1}^{n}\mathrm{X_{i}} \tag{1}\]  
\[\mathrm{X_{i}}= \begin{cases}0&,\ \mathrm{VSWR}\leq 2\\ \mathrm{VSWR}-2&,\ \mathrm{VSWR}>2\end{cases}  \tag{2}\]  
The numerical model of a Bi-log hybrid antenna used in the NEC2 simulation is shown in Figure 3. The initial parameters for the dipole elements and their spacing in the proposed optimal antenna design are obtained through the use of NEC2 simulation. The characteristic impedance of the dipole element can be adjusted by changing its length and width. This model is composed of 267 segments, and the elements of the antenna are connected to each other by transmission lines. Following the optimization of the Taguchi method and a standard OA table, the details of the antenna element are presented in Table 3. The LPDA antenna has 21 sets of broadband antenna units, which consist of 11 planar plates (2000-6000 MHz) and 10 cylindrical dipoles (200-2000 MHz). Both types of LPDA elements were under the same procedure with optimal design, respectively. The spacing factor \(\sigma\) of LPDA elements is 0.06 compared to the relative spacing of each element. The \(\tau\) values of the planar plate dipole of LPDA elements are 0.796, 0.806, 0.798, 0.792, 0.803, 0.800, and 0.825. The scale factor \(\tau\) of the cylindrical dipole of LPDA elements are 0.770, 0.787, 0.792, 0.759, 0.803, 0.798, 0.792, 0.800, and 0.840. Achieving an optimal performance for the proposed antenna depends on the meticulous design of its LPDA elements, which has been elaborated upon earlier. The antenna booms are parallel two-wire transmission lines that affect the length of each element for impedance matching. Therefore, the relationship among the input impedance (R\({}_{0}\)) of 50 ohms, the average characteristic impedance of the dipole element (\(Z_{\mathrm{a}}\)), and the impedance of the transmission line (\(Z_{0}\)) has been investigated. The nominal input impedance of the proposed antenna is 50 ohms. A constant radius of dipole element has been utilized to make construction easier. The characteristic impedance of \(Z_{0}\) is fixed at 120 ohms for planar plate elements on a 10 mm square aluminum tube and 150 ohms for cylindrical dipole elements on a 19 mm square aluminum tube, respectively. To achieve practical antenna designs, dipole diameters of cylindrical elements are grouped into four categories of 4 mm, 5 mm, 7 mm, and 9 mm, while planar plate elements with widths of 1-5 mm.