Fourth-order PLL loop filter design technique with invariant natural frequency and phase margin

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A new approach to the design of fourth-order PLL loop filters is described. The technique allows the specification of a desired attenuation at a given offset frequency whilst maintaining the same loop natural frequency and phase margin as for a third-order loop filter. The benefit of this approach is that improved attenuation is obtained at wide frequency offsets, without compromising the in-band performance of the loop, in contrast to other approaches. Design equations are presented for this technique, its performance is confirmed by loop-gain trajectory plots and the maximum possible attenuation as a function of the design parameters is established.