Novel dissipative Lagrange-Hamilton formalism for LC/van der pol oscillator with new implication on phase noise dependency on quality factor

Leung, Bosco

doi:10.1109/mwscas.2014.6908463

Cited by 1 publication

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“…With V'= ε**V, (59) has similar form as (53)+(52) from the oscillator. 1) transform L diss (P, V') → L ( P , ' V ), which has no "dissipation term" via non-canonical transformation [31] , [32]. Thus P, V →…”

Section: Figure 15mentioning

confidence: 99%

“…Thus T is practically constant (≅,T c ), and g is given by the reduced equation of state function (evaluated at the critical point T c ) . In step 1, when we do the non-canonical transformation following [32], called rectification, we rely on assumption of local rectification i.e. T (and hence P, V') does not change much.…”

Section: Figure 15mentioning

confidence: 99%

“…T (and hence P, V') does not change much. As a side note, not only does[32] rely on P, V' not changing much, the equation there assume g is only a function of x, y, but not t. In the present case, the rectification method can be extended to varying t(or T) by using the non-autonomous extension[33] 13. Note (61) is "deterministic" only in the sense that average value of P, V (in the trajectories) are taken.…”

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Noise Spike Model in Relaxation Oscillators Based on Physical Phase Change

Leung

2016

IEEE Trans. Circuits Syst. I

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A new approach to investigate noise spikes due to regeneration in a relaxation oscillator is proposed. Noise spikes have not been satisfactorily accounted for in traditional phase noise models. This paper attempts to explain noise spikes/jump phenomenon by viewing it as phase change in the thermodynamic system(for example, from gas to liquid or magnetization of ferromagnet). Both are due to regeneration (positive feedback in oscillator as well as alignment of spin due to positive feedback in ferromagnet). The mathematical tool used is the partition function in thermodynamics, and the results mapped between thermodynamic system and relaxation oscillator. Theory is developed and formula derived to predict the magnitude of the jump, as a function of design parameter such as regeneration parameter or loop gain. Formulas show that noise increases sharply as regeneration parameter/loop gain approaches one, in much the same way when temperature approaches critical temperature in phase change. Simulations on circuits (Eldo) using CMOS as well as Monte Carlo simulations (Metropolis) on ferromagnet (Ising model) were performed and both show jump behaviour consistent with formula. Measurements on relaxation oscillators fabricated in 0.13um CMOS technology verify such behaviour, where the sharp increase in noise when regeneration parameter/loop gain is close to one, matches closely with the theoretical formula. Using the formula the designer can quantify the variation of noise spikes dependency on design parameters such as g m (device transconductance), R, I 0 , via their influence on regeneration parameter/loop gain.I.

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confidence: 99%

Section: Figure 15mentioning

confidence: 99%

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