Thermodynamical Phase Noise in Oscillators Based on L-C Resonators

Javier Malo, Jose-Ignacio Izpura

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DOI: 10.4236/cs.2012.31009                

Abstract

Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show that Fluctuations produce the Line Broadening of their output spectrum around its mean frequency f₀ and that the Pedestal of phase noise far from f₀ comes from Dissipations modified by the feedback electronics. The charge noise power 4FkT/R C²/s that disturbs the otherwise periodic fluctuation of charge these oscillators aim to sustain in their L-C-R resonator, is what creates their phase noise proportional to Leeson’s noise figure F and to the charge noise power 4kT/R C²/s of their capacitance C that today’s modelling would consider as the current noise density in A²/Hz of their resistance R. Linked with this (A²/Hz?C²/s) equivalence, R becomes a random series in time of discrete chances to Dissipate energy in Thermal Equilibrium (TE) giving a similar series of discrete Conversions of electrical energy into heat when the resonator is out of TE due to the Signal power it handles. Therefore, phase noise reflects the way oscillators sense thermal exchanges of energy with their environment.

Keywords

Phase Noise; Admittance-Based Noise Model; Fluctuation; Dissipation; Conversion into Heat

Conflicts of Interest

The authors declare no conflicts of interest.

References

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