**4. Conclusion**

272 Trends in Electromagnetism – From Fundamentals to Applications

In comparison with the conventional forward CLCs, the electrical length of the proposed CLC is more compact than CLCs presented in (Chang et al., 2001; Deng et al., 2002; Lauro et al., 2009). For instance, the coupled-line electrical length of the coupler is shortened to 50% of the conventional CLC electrical length reported in (Deng et al., 2002). Moreover, the bandwidth of the proposed CLC is wider than forward CLCs presented in (Deng et al., 2002; Lauro et al., 2009; Chang et al., 2001; Sen-Kuei & Tzong-Lin, 2010). For example, compared with the forward couplers reported in (Deng et al., 2002) and (Lauro et al., 2009), the proposed structure is capable of producing 65% bandwidth enhancement for the amplitude and a 0-dB coupling level with a smaller coupled-line length. Moreover, the proposed structure exhibits broader bandwidth than couplers presented in (Chang et al., 2001; Huang & Chu, 2010; Ikalainen & Matthaei, 1987; Sen-Kuei & Tzong-Lin, 2010; Lauro et al., 2009). Fig. 23 shows the even- and odd-mode characteristic impedances computed using full-wave simulation. This result indicates that the proposed structure is matched to 50 Ω port impedance over the operating bandwidth, such that the additional tapered structure at each port for impedance matching can be eliminated. Hence, the proposed forward coupler would be more compact in size. As it was mentioned, for the proposed forward CLC, the coupler area is approximately constant. It means that reduction of the structure length

results width increasing, proportionally (Fig. 20).

*<sup>r</sup>* = 4.6, *h* = 1.6 *mm* ) (Keshavarz et al., 2010).

(ε

Fig. 21. Proposed forward symmetrical coupler which realized on FR-4 substrate

(a)

In this chapter, some new techniques for realizing compact and tight coupling microstrip backward and forward CLCs with obtainable dimension, broad bandwidth and smaller size than the most conventional microstrip and CRLH couplers have been introduced. We presented three CLCs based on the concept of CRLH CLCs; a symmetrical backward CLC, an asymmetrical backward CLC and a symmetrical forward CLC.

New symmetrical backward coupler structure consists of only one interdigital capacitor in each coupled TL without shorted stubs as the CRLH TL. Designed and fabricated 3-dB microstrip coupler at center frequency about = 3.2 *cf* GHz exhibits a matching (10-dB) bandwidth of over 2 GHz, a phase-balance (*±*10º) bandwidth of 1.3 GHz and at least 20-dB isolation between adjacent ports. The coupled-line length and the width of the proposed

Coupled-Line Couplers Based on the Composite Right/Left-Handed (CRLH) Transmission Lines 275

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Fujii, T. & Ohta, I. (2005). Size-Reduction of Coupled-Microstrip 3-dB Forward Couplers by

Garcia-Perez, O., Garcia Munoz, L. E., Segovia-Vargas, D., & Gonzalez-Posadas, V. (2010).

Hirota, A., Tahara, Y., & Yoneda, N. (2009). A compact coupled-line forward coupler using

Hirota, A., Tahara, Y., & Yoneda, N. (2011). A wide band forward coupler with balanced

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Islam, R. & Eleftheriades, G. V. (2006). Printed high-directivity metamaterial MS/NRI

Islam, R., Elek, F., & Eleftheriades, G. V. (2004). Coupled line metamaterial coupler having

Joon-Bum K., Chul-Soo K., Kwan-Sun C., Jun-Seok P., & Dal A. (2001). A design mapping

Keshavarz, R., Movahhedi, M., Hakimi, A., & Abdipour, A. (2011). A novel broad

Keshavarz, R., Movahhedi, M., Hakimi, A., & Abdipour, A. (2011). A broadband and

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compact asymmetrical backward coupled-line coupler with high coupling level.

structure are approximately*¸* 4 λ*<sup>g</sup>* and 36 λ*<sup>g</sup>* , respectively. Also, this coupler exhibits higher design simplicity than the existing CRLH CLCs.

Moreover, a new type of backward CLC composed of two different coupled lines, i.e. interdigital and conventional microstrip TLs has been proposed, fabricated, and investigated theoretically and experimentally. In this structure, an interdigital capacitor with only one finger is used as interdigital TL. This interdigital TL is coupled with a conventional microstrip TL and achieves an asymmetrical backward CLC. The proposed backward-wave coupler with 0.2 mm spacing between two coupled lines exhibits the amplitude balance of *±*2 dB from 2.2 GHz to 4.2 GHz and the phase balance of 90º*±*10º from 2.2 GHz to 3.5 GHz.

Finally, a forward CLC composed of two identical microstrip TLs and periodic shunt stubs between them has been proposed and investigated experimentally and theoretically. Using loaded stubs between two microstrip coupled-lines forms the proposed 0-dB forward CLC which exhibits the amplitude balance of *±*2 dB around center frequency of 3 GHz from 2 GHz to 4 GHz (66% bandwidth). A matching (| <sup>11</sup> S |<15-dB) bandwidth of over 4 GHz (1-5 GHz) bandwidth and at least 15 dB isolation between adjacent ports have been seen in measurement results. In this forward-wave CLC, by increasing the length of the stubs, the coupler length decreases, proportionally.
