An overview of the phase-locked loop (PLL)

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INTRODUCTION
The basic phase-locked loop (PLL) concept has been known and
widely utilized since first being proposed in 1922. Since that time,
PLLs have been used in instrumentation, space telemetry, and many
other applications requiring a high degree of noise immunity and
narrow bandwidth. Techniques and systems involved in these
applications frequently are quite complex, requiring a high degree of
sophistication. Many of the PLL applications have been at
microwave frequencies and employ complex phase shifters, signal
splitters, modulation, and demodulation schemes such as bi-phase
and quadra-phase. Because of the high frequencies involved in
microwave applications, most all components of these PLL systems
are made from discrete as opposed to integrated circuits. However,
in other communication system applications such as FSK and FM
and AM demodulation where frequencies are below approximately
100MHz, monolithic PLLs have found wide application because of
their low cost versus high performance.



A MECHANICAL ANALOG TO THE PLL
To better visualize the frequency and phase relationships in a PLL,
consider the mechanical system shown in Figure 2 which is a dual
to the electronic PLL. This mechanical system has two identical,
heavy disks with two separate center shafts attached to each disk.
Each shaft is presumed to be mounted on a bearing that allows
each massive disk to be rotated in either direction when some
external force is applied. The shafts are coupled together by a
spring whose end points are fixed to each shaft. This spring can be
twisted in either direction, depending upon the relative positions of
the shafts. The spring cannot ”kink up” due to the shafts passing
through the center of the spring.



EXAMPLES OF PLL APPLICATIONS
Now consider the action of the voltagecontrolled oscillator, phase
comparator and low pass filter in the PLL. The VCO generates a
signal that is periodic. Normally, the rate or frequency of the VCO is
primarily determined by the value of a capacitance connected to this
oscillator. This action of starting the VCO running by itself is
analogous to disconnecting the spring from one of the shafts in the
mechanical system and starting the output disk rotating at a
constant rate through some external means such as a motor. In the
PLL system this frequency is called the oscillator’s free running
frequency, (fO’), because it occurs when the system is unlocked and
there is no coupling between input and output frequencies



TYPES OF PLLS
Generally speaking, the monolithic PLLs can be classified into two
groups — digital and analog. While both perform as PLLs, the digital
circuits are more suitable for synchronization of digital signals, clock
recovery from encoded digital data streams, and other digital
applications. Analog monolithic PLLs are used quite extensively in
communication systems since they maintain linear relationships
between input and output quantities.


PLL TERMINOLOGY
The following is a brief glossary of frequently encountered terms in
PLL literature.

Free-running Frequency (fO’, wO’) — Also called the center
frequency, this is the frequency at which the loop VCO operates
when not locked to an input signal. The ”prime” superscripts are
used to distinguish the free-running frequency from fO and wO which
are used for the general oscillator frequency. (Many references use
fO and wO for both the free-running and general oscillator frequency
and leave the proper choice for the reader to infer from the context.)
The appropriate units for fO’ and wO’ are Hz and radians per second,
respectively.

Lock Range (2fL, 2wL)* — The range of frequencies over which the
loop will remain in lock. Normally the lock range is centered at the
free-running frequency, unless there is some nonlinearity in the
system which limits the frequency deviation on one side of fO’. The
deviations from fO’ are referred to as the Tracking Range or Hold-in
Range. (See Figure 6). The tracking range is therefore one-half of
the lock range.