## 3 Design of CRLH Transmission Line Antenna  
In our previous work [9], we proposed a CRLH TL-based VHF antenna with operating-frequencies from 159.6 to 164.4 MHz. In this paper, we designed and optimized another CRLH TL-based VHF antenna with the operating frequencies from 249.2-268.2 MHz. Figure 7 illustrates an equivalent circuit of a general CRLH TL unit cell, which is decomposed into a left-handed circuit and right-handed one. The left-handed circuit technically consists of a series capacitance (\(\mathrm{C_{L}}\)) and a shunt inductance (\(\mathrm{L_{L}}\)). However, it should be noted that the pure LH circuit does not exist because of the properties of the transmission line, i.e., the parasitic series inductance (\(\mathrm{L_{R}}\)) and the shunt capacitance (\(\mathrm{C_{R}}\)). The parasitic capacitance is induced due to voltage gradients between the metal patterns and the ground plane. In CRLH TL, a magnetic field occurs when a current flows along a series capacitance [26]. CRLH TL has a zeroth-order resonant frequency in which the propagation number becomes zero. Below the zeroth-order resonant frequency, CRLH TL has LH TL characteristics and above zeroth-order resonant frequency, CRLH TL has RH TL characteristics. At the zeroth-order frequency, the resonant frequency is independent from physical size of the antenna, so the antenna can be miniaturized. The zeroth-order resonant frequency is determined by the shunt resonant frequency in the case of open termination [26]. \[\omega_{sh}=\frac{1}{\sqrt{\mathrm{C_{R}}\mathrm{L_{L}}}} \tag{1}\]  
By Equation (1), the zeroth-order resonant frequency can be adjusted by shunt capacitance and inductors, which means that the zeroth-order frequency can be adjusted by the unit cell parameter of CRLH TL. Figure 8 shows the design procedure for CRLH TL antenna. First, we designed a basic model of a CRLH TL unit cell. We optimized the zeroth-order resonant frequency to target frequency with optimizing parameters of the CRLH TL unit cell. After optimization, we arranged three CRLH TL unit cells to obtain CRLH TL characteristics. To enhance CRLH TL characteristics, CRLH TL had to have more than two unit cells [26]. It should be noted that the input impedance of CRLH TL was changed when the unit cells were arranged. Because of this characteristic, we matched the input impedance of the CRLH TL. Figure 9 shows a unit cell of the designed CRLH TL. We implemented an interdigital capacitor (IDC) to realize series capacitance (\(\mathrm{C_{L}}\)). Using IDC, we could obtain large capacitance by adjusting the number of fingers and parameters of the IDC and implementing series capacitance. In addition, we implemented a spiral inductor which was connected to the ground to realize shunt inductance (\(\mathrm{L_{L}}\)). Using the spiral inductor, we could obtain large inductance while minimizing the inductor area. The \(\mathrm{C_{L}}\) and the \(\mathrm{L_{L}}\) were artificially implemented with a designing structure, and then the values of \(\mathrm{C_{L}}\) and \(\mathrm{L_{L}}\) were adjusted by changing the parameters of the unit cell. The extracted parameters of the CRLH TL unit cell using a pseudo-inverse technique are shown in Table 2[27]. In the simulation,  
Figure 7: Equivalent circuit of composite right/left-handed (CRLH) transmission line. The size of the antenna was \(0.025\times 0.014\times 0.0008\)\(\lambda\) (\(51.4\times 30\times 1.6\) mm). Because the input impedance of the antenna should be close to about 30-70 \(\Omega\) for the impedance matching between the antenna and the non-Foster circuit, a 50-\(\Omega\) chip resistor was implemented to the antenna feeding part. As the frequency of the CRLH TL antenna decreased, the input reactance became negative due to the series capacitance. The non-Foster circuit could broaden the antenna operating bandwidth by canceling