Analysis of PLL frequency synthesizer considering transient response of the VCO represented as Van der Pol equation

With the increasing demand for high speed technology in modern communication systems, PLL frequency synthesizers with a faster acquisition speed have been required. In the past, many analyses of PLLs have been carried out with the assumption that there is no delay between the input voltage and the output frequency in the VCO. However, when the PLLs with high speed acquisition are considered, one must know more accurately the VCO transfer function. The paper shows a more accurate VCO transfer function by solving the circuit state equations of the VCO, and investigates the effect of the VCO transient response on the frequency switching performance of the PLL frequency synthesizer