## 2 Design of the CRLH Resonant Antenna  
The CRLH resonant antenna is designed as shown in Figure 1. Usually, the CRLH structure is designed using an interdigital capacitor and a short-circuited stub. But the metallic vias in the short-circuited stub prevent the radiation in the broadside direction. To obtain patch-like radiation in the broadside direction, the CRLH resonator is formed without metallic vias. The interdigital capacitor with three fingers followed by a stub with length \(l_{1}/2\) forms the first part of the resonator, and this is concatenated with its mirror image to form the CRLH structure. The interdigital capacitor and stub and their \(x\)-axis mirror image are concatenated to form the CRLH resonator, as shown in Figure 1. This creates a virtual zero at the center of the stub of the resonant antenna. So, the metallic vias needed for the short-circuit stub are removed. The electric field pattern of the CRLH resonant antenna, along with the equivalent circuit, is shown in Figure 2. From the electric field pattern, it can be found that the antenna has an electric zero approximately around the center of the antenna and at that point a virtual ground is formed. The interdigital capacitor with its three fingers is represented by \(L_{R_{1}}\) and \(C_{L_{1}}\) in the equivalent circuit shown in Figure 2b. The stub is represented by \(L_{L_{1}}\) and \(C_{R_{1}}\). The mirror image of the interdigital capacitor and short-circuited stubs are also represented as \(L_{R_{1}}\) and \(C_{L_{1}}\) and \(L_{L_{1}}\) and \(C_{R_{1}}\), respectively. The electric zero point between the interdigital capacitor and stub and their mirror image is represented as ground in Figure 2b. Figure 1: Structure of the CRLH antenna with dimensions \(l_{1}=2.46\) mm; \(l_{2}=1\) mm; \(l_{3}=l_{4}=0.4\) mm; \(w_{1}=1.16\) mm; \(w_{2}=0.3\) mm. The width and gap of the interdigital capacitor are 0.2 mm. The two L-shaped structures with two big metallic vias at the sides are for placing the connector. The dispersion diagram is obtained by simulating the CRLH unit cell, as shown in Figure 3. The feed lines are de-embedded to obtain the S-parameter response of the CRLH unit cell, and from the S-parameters, the ABCD parameters are found out. The propagation constant is given as \(\cosh\gamma d=(A+D)/2\)[39]. The dispersion diagram of the CRLH unit cell is shown in Figure 3. The dispersion diagram shows the CRLH unit cell is unbalanced. The left-handed response is below 30 GHz, and the right-handed response is above 40 GHz. The attenuation gap is between 30 GHz and 40 GHz. The shunt resonance is around 30 GHz, and the series resonance is around 40 GHz. So, the open-circuited resonator formed from this unit cell is resonating at around 30 GHz. The antenna is formed from the open-circuit CRLH resonator. The antenna is fabricated on Rogers substrate RO4003c with a dielectric constant of 3.55, a loss tangent of 0.0027, and a thickness of 0.508 mm. The photograph of the fabricated structure is shown in Figure 4. The simulated and measured reflection coefficient (S\({}_{11}\)) responses of the antenna are compared in Figure 5. The simulated and measured S parameter responses match well. There is a slight frequency shift, which is due to the fabrication errors. From the measured response, it can be found that the antenna resonates with a central frequency of around 30.77 GHz, and the measured 10 dB fractional bandwidth is 4.2%. The antenna is free of spurious resonant frequencies over the entire band width of  
Figure 2: (**a**) Electric field distribution of the antenna; (**b**) equivalent circuit of the CRLH antenna. 10 GHz. The normalized simulated and measured radiation patterns of the antenna in the YZ (\(\varphi=90^{\circ}\)) plane are shown in Figure 6. The simulated radiated efficiency of the antenna at the central frequency is approximately 87%. The simulated total gain of the antenna is 5.82 dBi. The measured gain of the antenna is 5.35 dBi.