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