Analysis of Input Voltage-Output Frequency Relationship in VCOs Using a Linear Time-Varying Model

This paper delves into the dynamic behavior and control complexities of voltage-controlled oscillators (VCOs) within high-speed data transmission systems. We conduct an in-depth analysis of the intricate dynamics inherent to VCOs, recognizing their nonlinear nature. To accurately capture these nonlinearities and dynamic characteristics, we meticulously develop a comprehensive state-space model. Furthermore, we investigate the evolution of the linear time-varying (LTV) model from nonlinear models, particularly concerning specific voltage inputs. Our study also proposes a frequency calculation formula for computing the LTV model of the VCO, facilitating the design of control inputs. These advancements hold significant potential to enhance VCO performance in high-speed data transmission applications, offering valuable insights for further research and practical implementation.