The linearized characterization approach used in the phase detector design may have limitations in terms of accuracy, especially when dealing with non-ideal sinusoidal responses in practical circuits. The trade-off of using a linearized approach is that it sacrifices some accuracy for computational speed and reduced complexity. To further improve this approach, advanced calibration techniques could be implemented to account for non-idealities in the circuit response. Additionally, incorporating more sophisticated signal processing algorithms could help mitigate errors introduced by the linear approximation and improve the overall accuracy of the phase detection.