Loop filter approximations for PLLs

Phase Noise Frequency response in a Phase Locked Loop cannot be freely determined, since it is constrained by the Loop structure and the Loop Filter (LF) shape. Therefore, Filter Approximation Theory is of no use in this case. However, we show in this paper that some general relations can be established between the Loop Filter, Loop Gain, and Phase Noise Frequency response, making it possible to apply basic filter theory concepts to PLL design. This approach can be seen as complementary to the conventional way PLLs are analysed.