Theory of the Pierce Oscillator
The simplest possible oscillator uses a single active device to generate the required negative resistance. If no inductance is available, the only possibility is the 3-point oscillator developed in 1923 by G. W. Pierce [2, 3]. The principle of this oscillator is depicted in Fig. 4.1. The active device is assumed to be a MOS transistor, but it could be a bipolar transistor as well. The source of the MOS transistor is connected to its substrate, to make it a 3-terminal device. The bias circuitry needed to activate the transistor is omitted here. Capacitors C 1 and C 2 connected between gate and source, respectively drain and source, are functional: they must have finite values in order to obtain a negative resistance across the motional impedance of the resonator.
KeywordsPhase Noise Gate Voltage Bias Current Negative Resistance Strong Inversion
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- 2.G. W. Pierce, “Piezoelectric Crystal Resonators and Crystal Oscillators Applied to the Precise Calibration of Wavemeters”, Proc. American Academy of Arts and Sciences, vol. 59, October 1923, pp. 81-106.Google Scholar
- 3.G. W. Pierce, “Electrical System”, US patent 2,133,642, filed Febr. 25, 1924, issued Oct. 18, 1938.Google Scholar