## 4 Applications
### Wideband Bandpass Filters and Dual-band Components based on OSRRs and OCSRRs  
OSRRs and OCSRRs can be combined in order to implement artificial transmission lines exhibiting left handed wave propagation at low frequencies and right handed wave propagation at high frequencies. The typical layout of these structures is depicted in Figure 16.  
Figure 16: Topology of the unit cell of a CPW composite right/left handed transmission line based on a combination of series connected open split ring resonators in the external stages and a pair of shunt connected open complementary split ring resonators in the central stage. The considered substrate is the _Rogers RO3010_ with thickness \(h=1.27\) mm and dielectric constant \(\varepsilon_{r}=10.2\). Dimensions are: \(l=12.3\) mm, \(W=5\) mm, \(G=1.28\) mm. For the open complementary split ring resonator: \(r_{ext}\)= 2.9 mm, \(c=0.5\) mm, \(d=1.2\) mm. For the open split ring resonators: \(r_{ext}=2\) mm, \(c=d=0.2\) mm. Figure 15: Typical layout of a SIR-loaded CPW (**a**) and equivalent circuit model (**b**). Figure 17 shows the frequency response, as well as the characteristic impedance and dispersion. Clearly, the structure exhibits a composite right/left handed behavior. It is interesting to mention that the equivalent circuit model of the structure (consisting of the cascade of the circuits shown in Figures 13 and 14 for each OSRR and OCSRR section) provides a good estimation of the characteristics of the artificial transmission line up to frequencies that extend beyond the allowed transmission band. If parasitics in the models of Figures 13 and 14 are removed, the equivalent circuit  
Figure 17: (**a**) Frequency response of the circuit of Figure 16. (**b**) Characteristic impedance. (**c**) Dispersion diagram. The element values of the circuit model are (in reference of Figure 13(c) and Figure 14(c)): \(L^{{}^{\prime}}s\) = 6.94 nH, \(C_{s}\)= 0.85 pF, \(C\)= 0.28 pF, \(L\)= 0.76 nH, \(L^{{}^{\prime}}p\) = 1.95 nH and \(C^{{}^{\prime}}p\) = 2.43 pF. From [43]; copyright © 2009, IEEE; reprinted with permission. Figure 18: Fabricated wideband bandpass filter and frequency response. The substrate is the _Rogers RO3010_ with thickness \(h\)= 0.254 mm and measured dielectric constant \(\varepsilon_{r}\)= 11.2. Dimensions are: \(l\) = 12.32 mm, \(W\)= 5.6 mm, \(G\)= 0.574 mm. For the OCSRR: \(r_{ext}\)=2.1 mm, \(c\) = 0.5 mm, \(d\) = 0.16 mm. For the OSRR: \(r_{ext}\)= 1.9 mm, \(c\) = 0.3 mm, \(d\) = 0.16 mm. The element values of the circuit model are (in reference of Figure 13c and Figure 14c): \(C^{{}^{\prime}}p\) = 1.779 pF, \(L^{{}^{\prime}}p\) = 3.216 nH, \(C_{s}\)= 1.08 pF, \(L_{s}\)= 4.89 nH, \(L\) = 0.384 nH, \(C\) = 0.182 pF and \(L_{hs}\)= 0.2 nH, where an additional shunt inductance \(L_{hs}\) in series with the OCSRR tank has been considered to take into account the shunt inductive effect of the narrow strip connection between the main line and the OCSRR (this being needed to predict the broadband response of the OCSRR). From [44]; copyright © 2011, Elsevier; reprinted with permission. that is obtained by cascading those models of such figures is the model of a canonical composite right left/handed line, which is also the equivalent circuit model of a band pass filter [43,44]. Therefore, combined OSRR and OCSRR structures are useful for the implementation of band pass filters and metamaterial-based microwave components. The key aspect is the fact that the wide bands can be obtained. Hence, these structures are specially suited for the design of wideband filters. An illustrative example is shown in Figure 18, where the agreement between the simulated and measured frequency responses is very reasonable [44]. Another possible application of OSRR and OCSRR-based lines is the design of dual-band components. As compared to dual-band components based on CSRRs [45], a wider band for the first frequency is obtained by using artificial lines based on open particles. Figure 19 depicts a fabricated dual-band power splitter and its frequency response.