Vector-Sum Phase Shifter Using a Tunable Active g m -C Polyphase Filter

Abstract

We have proposed a vector-sum phase shifter (VSPS) with a low phase shift error using a tunable active $g_{m}{\text {-}}{C}$ polyphase filter (PPF). The proposed VSPS realizes high insertion gain and a low phase shift error because the tunable active ${g}_{m}{\text {-}}{C}$ PPF exhibits insertion gain and low I/Q imbalance by easily controlling the transconductance of transistors. This study provides a general formula and design method based on the design equations of the tunable active ${g}_{m}{\text {-}}{C}$ PPF for VSPS. The analysis shows the limitation of the tunable frequency range of I/Q balance and the condition of the maximum insertion gain. The results also clarify that the relative bandwidth of the tunable active ${g}_{m}{\text {-}}{C}$ PPF is equivalent to that of the single-stage or multistage RC -PPF. The ${S}$ -band VSPS with the two-stage active ${g}_{m}{\text {-}}{C}$ PPF fabricated by the design method demonstrates improvement in phase shift errors lower than 0.52° rms in the 500-MHz bandwidth and high insertion gain of 13.4 dB with a frequency range of 2.2–3.2 GHz.