76 Phase-Locked Loop 76.1 Introduction 76.2 Loop Filter 76.3 Noise 76.4 PLL Design Proced Steven L. Maddy 76.5 Components 76.6 Applications 76.1 Introduction a phase-locked loop(PLL)is a system that uses feedback to maintain an output signal in a specific phase relationship with a reference signal. PLLs are used in many areas of electronics to control the frequency and/or phase of a signal. These applications include frequency synthesizers, analog and digital modulators and demod- ulators, and clock recovery circuits. Figure 76.1 shows the block diagram of a basic PLL system. The phase etector consists of a device that produces an output voltage proportional to the phase difference of the two input signals. The VCO (voltage-controlled oscillator) is a circuit that produces an ac output signal whose frequency is proportional to the input control voltage. The divide by n is a device that produces an output ignal whose frequency is an integer(denoted by n) division of the input signal frequency. The loop filter is a circuit that is used to control the Pll dynamics and therefore the performance of the system. The Rs)term is used to denote the Laplace transfer function of this filter. Servo theory can now be used to derive the equations for the output signal phase relative to the reference input signal phase. Because the VCO control voltage sets the frequency of the oscillation(rather than the phase) this will produce a pure integration when writing this expression. Several of the components of the PLl have a fixed gain associated with them. These are the VCo control voltage to output frequency conversion gain(k), he phase detector input signal phase difference to output voltage conversion gain(K,), and the feedback division ratio (N). These gains can be combined into a single factor called the loop gain(k). This loop gain is calculated using Eq (76. 1)and is then used in the following equations to calculate the loop transfer function (76.1) The closed-loop transfer function [H(s)] can now be written and is shown in Eq (76.2). This function is typically used to examine the frequency or time-domain response of a PLL and defines the relationship of the phase of the VCO output signal (0) to the phase of the reference input(0 ) It also describes the relationship of a change in the output frequency to a change in the input frequency. This function is low-pass in nature. H(s)= 0(s) KF(s) (76.2) (s) s+ kF(s) c 2000 by CRC Press LLC© 2000 by CRC Press LLC 76 Phase-Locked Loop 76.1 Introduction 76.2 Loop Filter 76.3 Noise 76.4 PLL Design Procedures 76.5 Components 76.6 Applications 76.1 Introduction A phase-locked loop (PLL) is a system that uses feedback to maintain an output signal in a specific phase relationship with a reference signal. PLLs are used in many areas of electronics to control the frequency and/or phase of a signal. These applications include frequency synthesizers, analog and digital modulators and demod￾ulators, and clock recovery circuits. Figure 76.1 shows the block diagram of a basic PLL system. The phase detector consists of a device that produces an output voltage proportional to the phase difference of the two input signals. The VCO (voltage-controlled oscillator) is a circuit that produces an ac output signal whose frequency is proportional to the input control voltage. The divide by N is a device that produces an output signal whose frequency is an integer (denoted by N) division of the input signal frequency. The loop filter is a circuit that is used to control the PLL dynamics and therefore the performance of the system. The F(s) term is used to denote the Laplace transfer function of this filter. Servo theory can now be used to derive the equations for the output signal phase relative to the reference input signal phase. Because the VCO control voltage sets the frequency of the oscillation (rather than the phase), this will produce a pure integration when writing this expression. Several of the components of the PLL have a fixed gain associated with them. These are the VCO control voltage to output frequency conversion gain (Kv), the phase detector input signal phase difference to output voltage conversion gain (Kf), and the feedback division ratio (N). These gains can be combined into a single factor called the loop gain (K). This loop gain is calculated using Eq. (76.1) and is then used in the following equations to calculate the loop transfer function. (76.1) The closed-loop transfer function [H(s)] can now be written and is shown in Eq. (76.2). This function is typically used to examine the frequency or time-domain response of a PLL and defines the relationship of the phase of the VCO output signal (uo) to the phase of the reference input (ui ). It also describes the relationship of a change in the output frequency to a change in the input frequency. This function is low-pass in nature. (76.2) K K K N v = f ¥ H s s s KF s s KF s o i ( ) ( ) ( ) ( ) ( ) = = + q q Steven L. Maddy RLM Research