6.5 Two-Bit MEMS DMTL Phase Shifter Designs

A wideband DMTL phase shifter can be designed based on the DMTL structure loaded with MEMS bridges and MIM capacitors as illustrated in Figure 6.6. As stated earlier, the distributed loading can lower an unloaded impedance say from 100 ? to 45 48 ? depending on the loading intensity or the density of the transmission line. The change in line impedance will result in change of phase velocity leading to a phase shift in the CPW line [2]. The phase shift expression can be written as

(6.19)

where

• w is the operating frequency

• c is the velocity of light

• Z _ul and Z _l are the unloaded and loaded impedances of the CPW line

Numerical example for phase shift in a 2-bit, X-band DMTL phase shifter

Assuming a center frequency ( f _o) of 10 GHz, a Bragg frequency ( f _b) of 30 GHz (three times the center frequency to achieve a reflection coefficient better than ?15 dB), number of MEMS bridge section equal to 16, unloaded CPW line impedance of 100 ?, loaded impedance of 53.2 ?, and effective dielectric constant of 2.4 for quartz substrate, and inserting these parameters in Equation 6.19, one get the phase shift ( /cm) as

for phase shifter consisting of 16 MEMS bridge sections with periodic spacing of 906 m, approximately. This phase shift of 163.53 will increase to 183.97 /cm for the phase shifter comprising of...