## Grid Synchronization

PHASE-LOCKED LOOP
� Basic loop configuration
� Operation principle of phase-locked loop
� Loop equations and nonlinear baseband model
� Linear operation of the PLL
� Linear baseband model
� Transfer functions
� PLL with active loop filter (Most commonly used PLL configuration)
� Stability considerations
� An example for PLL application: Coherent FM demodulator
Phase-locked loop is one of the most commonly used circuit in both
telecommunication and measurement engineering. Depending on the operation
principle of loop components we distinguish
� Analog
� Digital
� Hybrid
phase-locked loops. Only the analog phase-locked loop (APLL) is discussed in
this course. For the sake of simplicity, we will call this circuit PLL
ANALOG PHASE-LOCKED LOOP
Circuit configuration:
� Phase detector (PD) is an analog multiplier
� All loop components are analog circuits
Mathematical model:
� Operation of analog phase-locked loop is modeled by an ordinary
differential equation
Conditions:
� For the sake of simplicity, only the noise-free case is studied here
� We assume that the only source of nonlinearity is the phase detector,
the other loop components are assumed to be linear
The PLL is a nonlinear feedback system that tracks the phase of input signal
The basic PLL configuration contains a
� Phase detector (PD)
� Time-invariant linear loop filter and
� Voltage-controlled oscillator (VCO); the oscillator to be synchronized
QUALITATIVE CHARACTERIZATION OF LOOP COMPONENTS
Phase detector (PD):
� Analog multiplier
� PD produces an error signal that is proportional to the phase error,
i.e., to the difference between the phases of input and output signals
of the phase-locked loop
Loop filter:
� Low-pass filter
� It is characterized by its transfer function F(s)
� Low-pass filter suppresses the noise and unwanted PD outputs. It
determines the dynamics of phase-locked loop
Voltage-controlled oscillator (VCO):
� VCO generates a sinusoidal signal
� The instantaneous VCO frequency is controlled by its input voltage