3 t+ iN .0 tNin 20.0 Frequency(Hz) FIGURE 76.4 Closed-loop second-order type-2 PLL error response for various damping factors. For the active loop filter case Eqs. (76. 8)and (76. 10)are solved and yield the synthesis equations shown in Eqs.(76.14)and(76. 15). It can be seen that no constraints on the loop damping factor exist in this case. K RI 0-C A typical design procedure for these loop filters would be, first, to select the loop damping factor ar frequency based on the system requirements. Next, all the loop gain parameters are determined. A capacitor value may then be selected. The remaining resistors can now be computed from the synthesis Figure 76.4 shows the closed-loop frequency response of a PLL with an active loop filter [Eq.76.10)]for various values of damping factor. The loop natural frequency has been normalized to 1 Hz for all cases. Substituting Eq (76.6)into(76. 3)will give the loop error response in terms of damping factor. This function is shown plotted in Fig. 76.5. These plots may be used to select the Pll performance parameters that will give a desired frequency response shap The time response of a PLL with an active loop filter to a step in input phase was also computed and is shown plotted in Fig. 76.6 76.3 noise An impe aspect of a PlL is the noise content of the output. The dominant resultant noise will appear as Gitter)on the output signal from the VCO. Due to the dynamics of the Pll these noise sources will be filtered by the loop transfer function [Eq (76.2)] that is a low-pass characteristic. e 2000 by CRC Press LLC© 2000 by CRC Press LLC For the active loop filter case Eqs. (76.8) and (76.10) are solved and yield the synthesis equations shown in Eqs. (76.14) and (76.15). It can be seen that no constraints on the loop damping factor exist in this case. (76.14) (76.15) A typical design procedure for these loop filters would be, first, to select the loop damping factor and natural frequency based on the system requirements. Next, all the loop gain parameters are determined. A convenient capacitor value may then be selected. The remaining resistors can now be computed from the synthesis equations presented above. Figure 76.4 shows the closed-loop frequency response of a PLL with an active loop filter [Eq. (76.10)] for various values of damping factor. The loop natural frequency has been normalized to 1 Hz for all cases. Substituting Eq. (76.6) into (76.3) will give the loop error response in terms of damping factor. This function is shown plotted in Fig. 76.5. These plots may be used to select the PLL performance parameters that will give a desired frequency response shape. The time response of a PLL with an active loop filter to a step in input phase was also computed and is shown plotted in Fig. 76.6. 76.3 Noise An important design aspect of a PLL is the noise content of the output. The dominant resultant noise will appear as phase noise (jitter) on the output signal from the VCO. Due to the dynamics of the PLL some of these noise sources will be filtered by the loop transfer function [Eq. (76.2)] that is a low-pass characteristic. FIGURE 76.4 Closed-loop second-order type-2 PLL error response for various damping factors. R K nC 1 2 = w R nC 2 = 2z w