Triple‐band antenna using double periodic CRLH resonator on coplanar waveguide

Arokiaswami Alphones, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. Email: EALPHONES@ntu.edu.sg Abstract The uniplanar implementation of double periodic composite right/left‐handed (DPCRLH) symmetric unit cell is realized using coplanar waveguide and its analysis with parameter extraction are studied. DPCRLH symmetric unit cell is then experimentally validated. The open‐circuited DPCRLH resonator is formed from the DPCRLH unit cell which exhibited five resonance points. The simulated resonant frequencies of the resonator are 1.5494, 2.1968, 3.5072, 5.0438 and 6.089 GHz. A triple‐band antenna is designed from the last three resonant frequencies of the resonator. The antenna is horizontally polarized in all three bands. The measured co‐polarized gain of the antenna at the central frequencies of the three bands are 1.52 dBi (3.59 GHz), 3.67 dBi (5.1694 GHz) and 1.78 dBi (6.0925 GHz), respectively.


| INTRODUCTION
Recently, there has been a rapid development in the future wireless technologies. Because of many specific requirements, the wireless devices need to operate in multiple frequency bands. The multi-band radio frequency circuits including multi-band antennas make the devices compact. Composite right/lefthanded (CRLH) has been used in the design of multi-band components due to its non-linear dispersion characteristics and the resonance characteristics of its resonators [1]. Recently, the double periodic composite right/left-handed transmission line (DPCRLH TL) has been paid attention for multi-band applications [2][3][4][5]. The unit cell of DPCRLH is formed by concatenating two different unit cells of CRLH TL. It was used in the design of leaky wave antennas to get an additional leaky wave band. The symmetric unit cells of DPCRLH were proposed and analysed in [6]. DPCRLH TL has additional left-handed and right-handed regions compared to conventional CRLH TL. The design of open-circuited DPCRLH resonator and the design of triple-band filter using DPCRLH resonator were reported in [7].
The uniplanar implementation of CRLH unit cell using coplanar waveguide (CPW) has been implemented in [8] and its parameter extraction based on effective medium theory was also reported. In [9], the design of CRLH resonator at zerothorder resonance and the design of bandpass filter with spurious suppression were experimentally verified. The design of various filters using CRLH short-circuited stubs was reported in [10][11][12].
Two dual-band antennas using CRLH TL with novel terminations to operate at zeroth-order series and shunt resonances were designed in [13]. Symmetric, asymmetric, and chip-loaded CRLH zeroth-ordered resonant (ZOR) antennas were reported in [14]. A wideband antenna obtained by combining zeroth-order and first-order resonances of CRLH TL in asymmetric CPW was reported in [15]. The same principle was used in the design of epsilon negative wideband antenna in CPW [16]. The epsilon negative dual-band and wideband antennas using ZOR and first-order resonance were designed in [17]. The epsilon negative and double negative meta-structured transmission lines were used to design ZOR antennas in [18]. Both the antennas have the same radiation characteristics. A short-circuited wideband CPW ZOR antenna was reported in [19]. All the above antennas were designed for dual-band or wideband applications. CRLH unit cell was loaded to rectangular loop to form triple-band antenna in [20].
Here the resonant frequencies depend on the length of the rectangular loop. A triple-band antenna using CRLH resonant structures was reported in [21]. There is no description about control of resonant frequencies and bandwidths of the antenna. A triple antenna was designed in [22] using CRLH

| DESIGN OF DPCRLH SYMMETRIC UNIT CELL
The symmetric unit cells of DPCRLH are introduced in [6]. In this paper, the symmetric unit cell shown in Figure 1 is implemented in CPW. The impedance and the admittance parameters of DPCRLH unit cell in Figure 1 are given as follows: The ABCD matrix and the detailed analysis of dispersion diagram of the unit cell in Figure 1 are given in [6], and the parameter values of ABCD matrix are The propagation constant is given as cosh γd ¼ AþD 2 [23]. In the lossless case, within the pass band, the phase constant becomes cos βd ¼ AþD 2 . For the unit cell in Figure 1, the phase constant is given as The dispersion diagram of the DPCRLH is shown in Figure 2. The βd ¼ 0 and βd ¼ π frequency points are plotted in Figure 2. The expressions for these frequency points in the dispersion diagram are found out by substituting βd ¼ 0 and βd ¼ π in Equation (7). At βd ¼ 0, Equation (7) becomes The solutions of Equation (8) are found out as At βd ¼ π, Equation (7) becomes The solutions of Equation (10) are From the ABCD parameters of the unit cell, Y 21 can be found out using the relation given in [23] as From Equation (12), ideally Y 21 becomes infinite at Z 1 ¼ 0 [11]). The parameter Z 21 is obtained from the ABCD parameters by using the relation in [23]. It is given as (11) can be simplified as (14) gives (15) can be written in the form of two equations given as Similarly, another two equations can be obtained from Z 1 Y 2 ¼ À 2 of Equation (11). They are where The interdigital capacitor and short-circuited stub are used to achieve the left-handed properties in the DPCRLH unit cell. The value of L L1 is found out by simulating the short-circuit stub alone and comparing the simulated Z parameters with Z parameters of the equivalent circuit of the short-circuited stub. L L1 can be given as where Z sc 21 is the simulated Z 21 of the short-circuited stub and ω is the frequency at which L L1 is extracted. The other parameters of the DPCRLH unit cell are found out by solving Equations (16)- (19). Based on the above analysis, a DPCRLH unit cell in CPW is designed and it is shown in Figure 3 along with the simulated Y 21 and Z 21 parameters. CST Microwave studio is used for all the simulations in this work. The substrate used is Rogers R04003C with dielectric constant of 3.55, loss tangent of 0.0027, and thickness of 1.524 mm. L L1 is found out by simulating the short-circuited stub separately, and it is found out as 3.197 nH. The frequencies ω π1 -ω π4 are found out from the simulated Y 21 and Z 21 . Substituting ω π1 -ω π4 in Equations (16)- (19) and solving them gives the parameter values of DPCRLH unit cell. The parameter values of DPCRLH unit cell are found out as L R1 ¼ 4 nH, C L1 ¼ 0.72 pF, L L1 ¼ 3.197 nH, C R1 ¼ 0.79 pF, L L2 ¼ 1.04 nH, and C R2 ¼ 1.15 pF. The photograph of the fabricated filter along with the simulated and measured S parameters and dispersion diagram are shown in Figure 4. The simulated and measured Sparameter responses match quite well. The propagation constant extracted from the simulated and measured S parameters are compared with the propagation constant obtained by substituting DPCRLH unit cell parameters in Equation (7) and shown in Figure 4(c).

| DPCRLH RESONATOR
After analysing the unit cell, DPCRLH resonator is formed by introducing open circuits at both ends of the resonator. The input impedance of the open-circuited DPCRLH resonator is given in [6] as At resonance, DPCRLH unit cell parameters L R1 ¼ 4 nH, C L1 ¼ 0.72 pF, L L1 ¼ 3.197 nH, C R1 ¼ 0.79 pF, L L2 ¼ 1.04 nH, and C R2 ¼ 1.15 pF are substituted in Equation (21), and the resonance frequencies are 1.54, 2.28, 4.02, 5.98, and 6.97 GHz. The DPCRLH open-circuited resonator is shown in Figure 5 along with the simulated S parameters. The simulated resonance frequencies are 1.5494, 2.1968, 3.5072, 5.0438, and 6.089 GHz.
If the resonator is assumed to be lossless, then the external quality factor is given as [24,25]

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where G is the shunt conductance at the terminal of the resonator and B is the susceptance of the resonator. The quality factor at resonant frequency points is important. The susceptance of the resonator is given as From Equation (24), ∂B ∂ω at (Z 1 Y 2 þ 2) ¼ 0 resonant points can be found out as where Y 2 ′ and Z 1 ′ are the derivatives of Y 2 and Z 1 . The external quality factor at (Z 1 Y 2 þ 2) ¼ 0 resonant points is found out from Equations (23) and (25) as From Equation (26), it can be concluded that, if the values of L R1 and C R2 are decreased and the values of C L1 and L L2 are increased, the bandwidth will increase at the two resonant points given by ( where Y 2 ′ , Z 1 ′ ; and Y 1 ′ are the derivatives of Y 2 , Z 1 , and Y 2 . The external quality factor at the remaining three (23) and (27) as From Equation (28), it can be found out, if the values of L R1 , C R1 , and C R2 are decreased and the values of C L1 ,L L1 , and L L2 are increased, the bandwidth will increase at three resonant points given by ðY 1 þ Y 2 þ Z 1 Y 1 Y 2 2 Þ ¼ 0. Also, comparing Equations (26) and (28), Equation (28) has one extra term, so bandwidth at (Z 1 Y 2 þ 2) ¼ 0 resonant point is always higher than bandwidth at

| DESIGN OF TRIPLE BAND ANTENNA
The triple-band antenna is formed from the last three resonant frequencies of the DPCRLH open-circuited resonator. The antenna is matched at the three frequencies by introducing the discontinuities in the feed line. The ground planes on both sides of CPW are extended up to 22.37 mm. The structure of the antenna and its photograph and the simulated and measured S-parameter responses are shown in Figure 6. The reason for the frequency shift between the simulated and measured results is due to the fabrications errors. The measured central frequencies of the antenna are 3.59, 5.1694, and 6.0925 GHz, whereas the simulated central frequencies are     Also, the connector increased the cross-polarization component to a small amount around 270°in the measured radiation patterns. The variation of simulated and measured total realized gains and radiation efficiencies with respect to the frequency are shown in Figure 8. The comparison of the designed triple-band antenna with other CPW-based metamaterial antennas is given in Table 1.

| CONCLUSION
The uniplanar DPCRLH symmetric unit cell has been implemented in CPW. The parametric extraction and the analysis of the DPCRLH unit cell have been studied first and is experimentally validated. The design of the open-circuited DPCRLH resonator from the DPCRLH unit cell is discussed. DPCRLH resonator has five resonance points. The triple-band antenna is formed by the last three resonant frequencies of DPCRLH resonator. The triple-band antenna has the measured co-polarization gain in the three bands as 1.52 dBi (3.59 GHz), 3.67 dBi (5.1694 GHz), and 1.78 dBi (6.0925 GHz). Thus, uniplanar DPCRLH unit cell can be implemented and its resonator can be used in the design of multi-band components.