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The Pierce oscillator is a type of electronic oscillator particularly well-suited for use in piezoelectric crystal oscillator circuits. Named for its inventor, George W. Pierce (1872–1956), [ 1 ] [ 2 ] the Pierce oscillator is a derivative of the Colpitts oscillator .
G. W. Pierce had an eye for finding the main sticking point in physical processes. For electronics, he saw that resonance was a key phenomenon. His five-part series "Experiments on resonance in wireless telegraph circuits in Physical Review (1904-7) are evidence of his leadership.
VCOs can be generally categorized into two groups based on the type of waveform produced. [4]Linear or harmonic oscillators generate a sinusoidal waveform. Harmonic oscillators in electronics usually consist of a resonator with an amplifier that replaces the resonator losses (to prevent the amplitude from decaying) and isolates the resonator from the output (so the load does not affect the ...
There is often misunderstanding around Leeson's equation, even in text books. In the 1966 paper, Leeson stated correctly that "P s is the signal level at the oscillator active element input" (often referred to as the power through the resonator now, strictly speaking it is the available power at the amplifier input).
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]
Comparison and Oscillation Theory of Linear Differential Equations. Elsevier. ISBN 978-1-4832-6667-1. Teschl, G. (2012). Ordinary Differential Equations and Dynamical Systems. Providence: American Mathematical Society. ISBN 978-0-8218-8328-0. Weidmann, J. (1987). Spectral Theory of Ordinary Differential Operators. Lecture Notes in Mathematics ...
The above analysis also describes the behavior of the Pierce oscillator. The Pierce oscillator, with two capacitors and one inductor, is equivalent to the Colpitts oscillator. [8] Equivalence can be shown by choosing the junction of the two capacitors as the ground point. An electrical dual of the standard Pierce oscillator using two inductors ...
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point , it is one of the most important model systems in quantum mechanics.