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