Design Method for the Fastest Settling Type 2 Phase Lock Loop: Part 2
Akmarul Ariffin Bin Salleh
I started the analysis of 4th order with the loop filter. Basically, additional pole due to Rp2 and Rp2 are added at the output of the op amp increase the order from 3rd to 4th. After some lengthy analysis, which will not be shown here, I found out that it is impossible to match the denominator of the CL(s) to the Gaussian LPF since this require the pole due to Rp2 and Rp2, to be the complex conjugate of the pole due Rz, Cp and Cz as in (30). Both of these pole can only be real so this loop filter topology will not work. To solve this problem, the loop filter topology shown in Figure 10 needs to be used. By using this topology, the two poles created by Lp and Cp will definitely be complex conjugate of each other, and Rp can be used to further define the placement of the complex pole.
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