Characterization of Limit Cycle Oscillations Induced by Fixed Threshold Samplers

This chapter offers a comprehensive examination of limit cycle oscillations induced by samplers with multilevel fixed thresholds. These Fixed Threshold Samplers (FTS) are defined by various parameters that, when appropriately chosen, yield common forms of quantization. Due to certain characteristics inherent to these samplers, resulting limit cycle oscillations may exhibit bias. To characterize these oscillations, the Dual Input Describing Function (DIDF) method is employed. Analysis of the obtained DIDF unveils insightful properties that streamline robustness analysis. Guidelines for conducting robustness analysis are provided, demonstrated through several case studies.