Feedback-induced phase noise in microcantilever-based oscillators

Malo, Javier; Izpura, I.

doi:10.1016/j.sna.2009.08.001

Cited by 6 publications

(12 citation statements)

References 11 publications

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“…when there are other Admittances in parallel), leads to the misconception underlying the aforesaid PI of the pioneering works of Johnson [9] and Nyquist [10]. This error is so deep-rooted in today's research that reviewers of [3] were not ashamed of publishing a piling-up of electrical charge in a resistance devoid of capacitance C, which links electric charge and electric voltage 15 10…”

Section: Reviewing Current Model For Electrical Noise In Resistorsmentioning

confidence: 99%

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A Fluctuation-Dissipation Model for Electrical Noise

Izpura¹,

Malo²

2011

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This paper shows that today's modelling of electrical noise as coming from noisy resistances is a non sense one contradicting their nature as systems bearing an electrical noise. We present a new model for electrical noise that including Johnson and Nyquist work also agrees with the Quantum Mechanical description of noisy systems done by Callen and Welton, where electrical energy fluctuates and is dissipated with time. By the two currents the Admittance function links in frequency domain with their common voltage, this new model shows the connection Cause-Effect that exists between Fluctuation and Dissipation of energy in time domain. In spite of its radical departure from today's belief on electrical noise in resistors, this Complex model for electrical noise is obtained from Nyquist result by basic concepts of Circuit Theory and Thermodynamics that also apply to capacitors and inductors.

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Section: Reviewing Current Model For Electrical Noise In Resistorsmentioning

confidence: 99%

“…To give some figures, the kT/C noise at room T (e.g. the square root of   or With feedback, however, the BW N doubles due to R 2 shunting the same C that this feedback in-phase with the output doesn't vary [15]. From this double BW N with the noise power on R is:…”

Section:  mentioning

confidence: 99%

A Fluctuation-Dissipation Model for Electrical Noise

Izpura¹,

Malo²

2011

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“…The role of this L can be seen as a feedback current that being proportional to the voltage v(t) on C, has -90˚ phase lag under sinusoidal regime (SR). This feedback in quadrature with v(t) that affects f 0 , leads to the feedback-induced phase noise that we showed for oscillators based on resonant microcantilevers in [5]. This Technical phase noise due to a deficient phase control of the feedback adds to the non technical, but Thermodynamical phase noise we will explain for oscillators with perfect loops where current feedback to the resonator is exactly in-phase with its voltage v(t) for Positive Feedback (PF) or exactly at 180˚ for Negative Feedback (NF).…”

Section: Because the Thermal Fluctuation 2 Ktmentioning

confidence: 72%

Thermodynamical Phase Noise in Oscillators Based on L-C Resonators (Foundations)

Izpura

Malo²

2012

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By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resonators. Under this new model that departs markedly from current one based on energy dissipation in Thermal Equilibrium (TE), this dissipation comes from a random series of discrete Dissipations of previous Fluctuations of electrical energy, each linked with a charge noise of one electron in the Capacitance of the resonator. When the resonator out of TE has a voltage between terminals, a discrete Conversion of electrical energy into heat accompanies each Fluctuation to account for Joule effect. This paper shows these Foundations on electrical noise linked with basic skills of electronic Feedback to be used in a subsequent paper where the aforesaid phase noise is explained by the new Admittance-based model for electrical noise

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“…From the above it isn't difficult to realize that a narrow-band CF working synchronously with the carrier at frequency f 0 ≠ 0 will damp well the noise 2FkTR V 2 /Hz it sees in phase, whereas the noise 2FkTR V 2 /Hz it sees with phase error of -90˚ will mislead it so as to create the Pedestal of 2FkTR V 2 /Hz around f 0 shown in [1]. We have to say that this Pedestal of noise that will lead to a feedback-induced Pedestal of phase noise was not considered in [6] because it is not the random modulation of f 0 that we called Technical phase noise in [1].…”

Section: Dissipation and Feedback-induced Noise In An L-c-r Resonatormentioning

confidence: 99%

“…For R FB = R, this PF would compensate exactly the power lost at each instant in R, thus the power lost in R at any f. Although this exact compensation will fail at high f because the finite bandwidth BW FB of the feedback of Figure 4, it will work well at typical oscillation frequencies f 0 , provided a fast enough electronics is used. Given that the effects of any phase error in the loop due to the finite BW FB and its associated phase noise were shown in [6], we will consider this PF as perfectly in-phase at f 0 .…”

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confidence: 99%

Thermodynamical Phase Noise in Oscillators Based on L-C Resonators

Malo

Izpura²

2012

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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

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Feedback-induced phase noise in microcantilever-based oscillators

Cited by 6 publications

References 11 publications

A Fluctuation-Dissipation Model for Electrical Noise

A Fluctuation-Dissipation Model for Electrical Noise

Thermodynamical Phase Noise in Oscillators Based on <i>L-C</i> Resonators (Foundations)

Thermodynamical Phase Noise in Oscillators Based on <i>L-C</i> Resonators

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Feedback-induced phase noise in microcantilever-based oscillators

Cited by 6 publications

References 11 publications

A Fluctuation-Dissipation Model for Electrical Noise

A Fluctuation-Dissipation Model for Electrical Noise

Thermodynamical Phase Noise in Oscillators Based on &lt;i&gt;L-C&lt;/i&gt; Resonators (Foundations)

Thermodynamical Phase Noise in Oscillators Based on &lt;i&gt;L-C&lt;/i&gt; Resonators

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Thermodynamical Phase Noise in Oscillators Based on <i>L-C</i> Resonators (Foundations)

Thermodynamical Phase Noise in Oscillators Based on <i>L-C</i> Resonators