密码 123456
The Designer s Guide to High-Purity Oscillators
Oscillatory systems exist everywhere, from our planet circulating around the
sun with a period of 365.2422 days in an average tropical year; to a pendulum
in an antique clock ticking every second; to the vibrations of a quartz crystal
in a wrist watch. The study of oscillators was initiated centuries ago in basic
mechanics. Some of the very complicated problems of injection locking in
coupled oscillators were experimentally verified in the century by Huygens.
He used coupled pendulums using elastic threads to move energy from
one pendulum to another. Oscillators belong to a class of systems known as
autonomous systems. As opposed to driven systems, oscillators possess the
unique feature that they do not need a time varying input to produce a time
varying output. The periodicity and amplitude of the produced oscillation are
regulated by the system’s energy balance rather than an external input. This
unique property makes the study of oscillators both complicated and fascinating.
In the field of electrical circuits, the study of oscillators was pioneered by
radio scientists and particularly flourished during World War II. Some ingenious
circuit implementations were devised to produce the best oscillators
possible. Along with the circuit implementations, came the formal mathematical
analysis. One of the earliest models is due to Van Der Pol in the 1920s.
Rigorous nonlinear analysis was carried out throughout the 1920’s until
today.
Despite the long history, most of the literature, until recently, focused on two
questions: ‘what is the precise amplitude of oscillation?’ and ‘what is the
exact period of oscillation?’
