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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 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 ...
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 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]
RC oscillators are a type of feedback oscillator; they consist of an amplifying device, a transistor, vacuum tube, or op-amp, with some of its output energy fed back into its input through a network of resistors and capacitors, an RC network, to achieve positive feedback, causing it to generate an oscillating sinusoidal voltage.