Theory of the Pierce Oscillator

  • Eric VittozEmail author
Part of the Integrated Circuits and Systems book series (ICIR, volume 0)


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.


Phase Noise Gate Voltage Bias Current Negative Resistance Strong Inversion 
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  1. 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
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    G. W. Pierce, “Electrical System”, US patent 2,133,642, filed Febr. 25, 1924, issued Oct. 18, 1938.Google Scholar
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    M.R. Spiegel, Complex Variables, Schaum Publishing Co, New York, 1964.zbMATHGoogle Scholar
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    C. Enz and E. Vittoz, Charge-Based MOS Transistor Modeling, John Wiley and Sons, Chichester, 2006.CrossRefGoogle Scholar
  5. 20.
    J. K. Clapp, “An inductive-Capacitive Oscillator of Unusual Frequency Stability”, Proc. IRE, vol. 36, 1948, pp. 356-358.CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Ecole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland

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