Investigation of transient processes in a digital phase locked loop by the state-space method

The state-space method is used to examine transient processes in a second-order digital phased locked loop (DPLL) with an analog-digital converter inside the loop and a digital frequency synthesizer in the form of a discrete phase shifter. It is shown that this precise method can be used for the effective analysis of DPLLs of higher orders of astatism. Results obtained with the state-space method are compared with those obtained by the approximate quasi-continuous method, and it is found that this latter method assures a sufficient accuracy for cases of practical interest.