# A VHF Band Small CRLH Antenna Using Double-Sided Meander Lines
## 2 Design of the CRLH Unit Cell and Antenna  
Figure 1 shows the equivalent circuit of the CRLH TL [4]. The LH component consists of a series capacitor and a parallel inductor, and the RH component can be implemented with a series inductor and a parallel capacitor. The CRLH TL antenna was implemented by designing unit cells which combine the RH and LH components and which are periodically arranged. Although the miniaturized unit cells (\(\ll\)\(\lambda\)/4) are periodically arranged, the zeroth-order resonant frequency does not change significantly. Therefore, it was an important step to design the CRLH unit cell and determine the zeroth-order resonant frequency to design the antenna. As mentioned in the introduction, the antenna has an open-ended and a short-ended structure, and the zeroth-order resonant frequency can be calculated from the propagation constant of the unit cell [4]. In the open-ended structure, the zeroth-order resonant frequency is determined by the parallel element, as shown in Equation (1). \(C_{R}\) is the capacitance formed between the top and bottom conductors and corresponds to a parasitic component. \(L_{L}\) is implemented as a meander line or spiral inductor, and a greater parallel inductance is required to design an antenna operating at a low frequency. This can be achieved by increasing the length of the inductor or by using thinner meander lines. \[\omega_{sh}=\frac{1}{\sqrt{L_{L}C_{R}}} \tag{1}\]  
Figure 2a shows a CRLH TL unit cell structure with full ground at the bottom like a conventional CRLH TL unit cell, and Figure 2b shows a new unit cell structure proposed in this paper. The proposed unit cell was designed to operate at a low frequency by adding a meander line at the bottom in addition to the one at top to have a greater parallel inductance. The zeroth-order resonant frequencies of the two structures was confirmed using a dispersion diagram obtained by setting ports at both ends of a unit cell; moreover, the dispersion diagram was calculated from Equation (2) using the s  
parameter characteristics [16; 17]. In Equation (2), \(p\) represents the period of the unit cell, and the frequency at which the propagation constant (\(\beta\)) becomes 0 is a zeroth-order resonant frequency. \[\beta=cos^{-1}\left(\frac{1-S_{11}S_{22}+S_{12}S_{21}}{2S_{21}}\right) \tag{2}\]  
Figure 3a shows the dispersion diagram of Figure 2a, which confirms that the zeroth-order resonant of the unit cell is 131.6 MHz (\(\beta\) = 0 at 131.6 MHz). Figure 3b shows the dispersion diagram of Figure 2b, which shows that the zeroth-order resonant of the unit cell is 90.2 MHz (\(\beta\) = 0 at 90.2 MHz). In addition, the parallel element values of the two structures are shown in Table 1, and the parallel inductance is higher in the case where there is a meander line at the bottom of the unit cell than in the case where there is no meander line. A structure with a meander line only at the top also operates at low frequencies, but the length of the meander line must be increased to obtain a zeroth-order resonant frequency below 100 MHz. This means an increase in the physical size of the antenna. Moreover, it is difficult to increase parallel inductance simply by using thin lines because there is a manufacturing limit on planar antennas. Thus, the proposed unit cell is an advantageous structure for designing miniaturized antennas operating at low frequencies. The proposed CRLH unit cell used a Tsconic TLY-5 (\(\varepsilon_{r}\) = 2.2) with a thickness of 40 mil. The unit cell size is 0.01\(\lambda\)\(\times\) 0.017\(\lambda\)\(\times\) 0.0003\(\lambda\) (37 \(\times\) 58.65 \(\times\) 1 mm\({}^{3}\)), and each  
Figure 1: Equivalent circuit of CRLH transmission line. Figure 2: CRLH TL unit cell structure: (**a**) CRLH TL unit cell with full ground at the bottom; (**b**) CRLH TL unit cell with meander line at the bottom.