Calibration of Vector-Summing Type Variable-Gain Phase Shifters using Novel Rectangular Constellation Modeling

This paper presents a novel method for calibrating vector-sum phase shifters (VSPSs) based on rectangular constellation modeling. The proposed method addresses the challenge of excessive measurement time typically associated with calibrating high-resolution VSPSs, while ensuring high accuracy. Formulations are developed to model non-ideal rectangular constellations accurately, and the model is efficiently constructed by measuring a strategically selected subset of constellation states. The method is validated on a 6-bit compact digitally controlled VSPS fabricated in 45 nm silicon-on-insulator CMOS technology. Experimental results validate the proposed method, requiring only 37 measurements to achieve phase and gain root mean square errors (RMSEs) of 0.83° and 0.18 dB, respectively. These values closely match the 0.77° and 0.14 dB of phase and gain RMSEs achieved by the exhaustive search method, while reducing the measurement count by over 100 times.