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Dual-frequency antennas play strong roles in many wireless products. These antennas can reduce the number of antennas needed in a portable wireless design, such as for personal communications systems (PCS) and wireless-local-area-network (WLAN) systems, while reducing the size and weight of a handheld device. A number of approaches have already been developed for producing dual-frequency antennas for such applications.1-3 For example, fractal antennas ave shown promise as compact multiband planar antennas.4 Based on conventional transmission lines (TLs), they typically include a single branch dispersion curve to form multiple paths with different resonant lengths at one-half or one-quarter-wavelength modes to obtain the multiple resonances needed for multiple-frequency operation. Other design approaches are also being explored, as the use of metamaterials based on periodic unit-cell structures for high-frequency antennas application has grown rapidly with the verification of left-handed (LH) metamaterials.5-11

Antennas fed by means of coplanar waveguide (CPW) can be easily incorporated with microwave integrated circuits (MICs) and monolithic microwave integrated circuits ((MMICs).12 In addition to the design freedoms they offer, CPW TLs suffer lower radiation loss and less dispersion than microstrip TLs. The use of a viahole-free structure and signal-layer process can yield a simpler fabrication process compared to many approaches used for producing metamaterial-based resonant antennas.6,7 By creating a structure with CPW feed and composite left/right hand transmission lines (CRLH TLs), it is possible to form compact antennas capable of dual-frequency operation. The design approach will be analyzed by means of computer-aided-engineering (CAE) software and verified by means of high-frequency measurements of key parameters, such as gain, impedance, and radiation pattern.

Figure 1 shows a CPW unit cell for a CRLH TL. To realize the left-handed inductance and capacitance, the meander lines are connected between the top patch and the CPW ground plane as the shorted stub and an interdigital line between the two top patches. The meander lines of the dual-frequency antenna are symmetrically aligned on both sides of the CPW ground. The CPW-fed dual-frequency antenna was designed as one unit cell and fabricated on low-cost P4BM-2 substrate material, available from a number of suppliers including Altechna. The P4BM-2 material, with circuit-board thickness of 1 mm, exhibits a dielectric constant of 2.2.

1. This diagram shows the basic structure of the CPW CRLH TL unit cell.

By applying the periodic boundary condition related with the Bloch-Floquet theorem to the unit cell, the dispersion can be obtained by means of Eq. 1:

In practice, the dispersion curves cannot be calculated directly; the Z-parameters must be transformed from the S-parameters by using relationships such as Eqs. 2(a)-(d):

Since the CRLH TL unit cell is a symmetrical structure, the circuit model for a lossless (R = 0 and G = 0) symetrical structure can be based on the structure of Fig. 1. The characteristic resistance of the structure, Zc1, is equal to Zc2, while the S-parameters, S11 is equal to S22 and S12 is equal to forward transmission, S21. As a result, simplified equations for the relationships of Eq. 2 can be expressed as Eqs. 3(a) and 3(b):

2. The CPW CRLH TL unit cell can be shown as a T-shaped equivalent network.

The structure can then be fashioned in the form of a T-shaped network (Fig. 2), using Eqs. 4(a) and 4(b):

Therefore, the relationship of Eq. 5 can be applied:

3. These are the simulated S-parameters of the CPW CRLH TL unit cell.

4. These are the dispersion curves of the CPW CRLH TL.

Figure 3 shows the full-wave S-parameters for the CPW CRLH TL unit, while Fig. 4 depicts the dispersion relationships calculated by Eqs. 3 through 5. For a balanced condition, where ωse = ωsh, the dispersion takes place in the LH and RH regions. When the length of the resonator is equivalent to a negative, zero, and positive resonant number times one-half wavelength, the resonances of an open-ended artificial CRLH TL resonator are achieved. This means that the propagation constants for an artificial CRLH TL for resonant mode (n) should be satisfied by Eq. 6:


l = the physical length of the resonator;

n = the mode number of the resonator; and

N = the number of unit cells.          

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