Transient response of Colpitts-VCO and its effect on performance of PLL system

In this paper, we investigate the frequency step response of the Colpitts-voltage-controlled oscillator (VCO) by solving its third-order circuit state equation. The result shows that after the capacitance change, its oscillation frequency changes to its steady state value with vibration. We also establish a more accurate transfer function of the Colpitts-VCO by considering its transient response with the assumption that the change of the capacitance is small. Moreover, we also introduce the idea of VCO time constants which represent a degree of the transient response of the VCO. Finally, to evaluate how the transient response of VCO influences on performance of phase-locked loops (PLL´s), we investigate acquisition processes of PLL model using our new transfer function. In the high-speed PLL, transient response of the VCO affects acquisition performance. There might be the case where response of the acquisition changes to its steady state with vibration, even in case where there is only overshoot in conventional analysis with conventional idealized VCO model