Design and modeling of 4-bit slow-wave MEMS phase shifters

A true-time-delay multibit microelectromechanical systems (MEMS) phase-shifter topology based on impedance-matched slow-wave coplanar-waveguide sections on a 500-mum-thick quartz substrate is presented. A semilumped model for the unit cell is derived and its equivalent-circuit parameters are extracted from measurement and electromagnetic simulation data. This unit cell model can be cascaded to accurately predict N-section phase-shifter performance. Experimental data for a 4.6-mm-long 4-bit device shows a maximum phase error of 5.5deg and S₁₁ less than -21 dB from 1 to 50 GHz with worst case S₂₁ less than -1.2 dB. In a second design, the slow-wave phase shifter was additionally loaded with MEMS capacitors to result in a phase shift of 257deg/dB at 50 GHz, while keeping S₁₁ below -19 dB (with S₂₁<-1.9 dB). The beams are actuated using high-resistance SiCr bias lines with typical actuation voltage around 30-45 V