Even-odd mode of a double-Lorentz metamaterial and its application to a tri-band branch-line coupler

The theoretical approach of a double-Lorentz (DL) transmission line (TL) metamaterial using even-odd mode analysis is presented for the application to a tri-band Branch-Line Coupler (BLC). This BLC is based on double-Lorentz (DL) transmission line (TL) metamaterial to achieve the tri-band property. The tri-band operation is achieved by the flexibility in the phase response characteristic of such transmission line. Since metamaterials are in symmetric form, this analysis utilizes superposition and circuit symmetry to solve for the structure's scattering parameters. A design example of a triple band quarter wavelength DL TL suitable for GSM-UMTS applications is designed and evaluated by simulation using even-odd mode analysis to validate the proposed methodology at circuit level. Then, this simulated DLTL is used in the design of a tri-band BLC which is also being analyzed using even-odd mode analysis. This coupler exhibits transmission of 3 +/- 0.5 degrees dB, return losses and isolations larger than 14 dB, and a phase difference of +/- 90 +/- 3.5 degrees.