FIGURE 76.1 PLL block diagram. The loop error function, shown in Eq (76.3), describes the difference between the vco phase and the reference phase and is typically used to examine the performance of PLls that are modulated. This function 6(s)-6(s)6(s) (76.3) 6;(s) 6;(s)+KF(s) The open-loop transfer function [G(s)] is shown in Eq (76.4). This function describes the operation of the loop before the feedback path gn of the system in determining the and phase margin of the PLL. These are indications of the stability of a PlL when the feedback loop is connected. KF(s) (76.4) These functions describe the performance of the basic PLL and can The synthesis equations will be used to calculate circuit components that will give a desired performance characteristic. These characteristics usually involve the low-pass corner frequency and shape of the closed-loop response characteristic [Eq (76.2)] and determine such things as the loop lock-up time, the ability to track the input signal, and the output signal noise characteristics. 76.2 Loop Filter The loop filter is used to shape the overall response of the Pll to meet the design goals of the system. There re two implementations of the loop filter that are used in the vast majority of PLLs: the passive lag circuit shown in Fig. 76.2 and the active circuit shown in Fig. 76.3. These two circuits both produce a PLL with a second-order response characteristic. The transfer functions of these loop filter circuits may now be derived and are shown in Eqs. (76.5)for the ssive circuit(Fig. 76.2)and(76.6)for the active circuit(Fig. 76.3) F(S= SCiR,+ 1 (76.5) s(R1+R2C1+1 FIGURE 76.2 Passive loop filter. FIGURE 76.3 Active loop filter. e 2000 by CRC Press LLC© 2000 by CRC Press LLC The loop error function, shown in Eq. (76.3), describes the difference between the VCO phase and the reference phase and is typically used to examine the performance of PLLs that are modulated. This function is high-pass in nature. (76.3) The open-loop transfer function [G(s)] is shown in Eq. (76.4). This function describes the operation of the loop before the feedback path is completed. It is useful during the design of the system in determining the gain and phase margin of the PLL. These are indications of the stability of a PLL when the feedback loop is connected. (76.4) These functions describe the performance of the basic PLL and can now be used to derive synthesis equations. The synthesis equations will be used to calculate circuit components that will give a desired performance characteristic. These characteristics usually involve the low-pass corner frequency and shape of the closed-loop response characteristic [Eq. (76.2)] and determine such things as the loop lock-up time, the ability to track the input signal, and the output signal noise characteristics. 76.2 Loop Filter The loop filter is used to shape the overall response of the PLL to meet the design goals of the system. There are two implementations of the loop filter that are used in the vast majority of PLLs: the passive lag circuit shown in Fig. 76.2 and the active circuit shown in Fig. 76.3. These two circuits both produce a PLL with a second-order response characteristic. The transfer functions of these loop filter circuits may now be derived and are shown in Eqs. (76.5) for the passive circuit (Fig. 76.2) and (76.6) for the active circuit (Fig. 76.3). (76.5) FIGURE 76.1 PLL block diagram. FIGURE 76.2 Passive loop filter. FIGURE 76.3 Active loop filter. q q q q q i o i e i s s s s s s s KF s ( ) ( ) ( ) ( ) ( ) ( ) - = = + G s KF s s ( ) ( ) = F s sC R s R R C p ( ) ( ) = + + + 1 2 1 2 1 1 1