A tri-band branch-line coupler design using double-Lorentz transmission line Metamaterial

A branch-line coupler (BLC) working at three arbitrary frequencies using double-Lorentz (DL) transmission line (TL) Metamaterial is presented. A DL has sufficient degrees of freedom to realize tri-band microwave devices. We demonstrate that the three operating frequencies can be obtained by tuning the phase slope of the line section. Then, the design equations are extracted and validated for the first time to the best of our knowledge. Moreover, a tri-band BLC is introduced for the application of GSM-UMTS services. Such prototype is demonstrated by simulation at 900 MHz, 1800 MHz, and 2100 MHz. This coupler exhibits transmission of 3±0.5dB, return losses more than 14dB, isolations larger than 14dB, and a phase difference of 90±3.5 degrees.