Periodic Solutions of van der Pol's Equations with Large Damping Coefficientlambda = 0 sim 10

Urabe, Minoru

doi:10.1109/tct.1960.1086718

Cited by 26 publications

(20 citation statements)

References 7 publications

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“…The comparison of the waveforms observed in simulations ( Fig. 6) with the published results for van der Pol model [12] shows that this model represents reasonably well the properties of the oscillator described in this paper. Capadtor C, fF…”

Section: Discussionsupporting

confidence: 79%

“…Using the operational condition of steady-state oscillations (2zr l +Cs+(Ls+r)-1 + (2Rr l = 0 (S) (12) we can rewrite (10) for large signal operation as…”

Section: IImentioning

confidence: 99%

“…The normalized equation (17) was well investigated, numerically [12][13] and then analytically [14--1S]. We use below the results of [14], because they require a simple algebra, and cover the range of A sufficient for considered applications.…”

Section: Transition To Van Der Pol Equationmentioning

confidence: 99%

“…More general results can be found in [16]. It was shown in [14] that for 0 <A < 3 the solution of (17) can be expressed as y = A l cos n-r+ A 3 cos3n-r+ � sin3n-r+ As cossn-r + B s sin Sn-r+ A7 cos 7n-r+ B7 sin 7n-r where the amplitudes have two components, namely, A l = A l O+A12;A3 =A 30 +A 32; � =�O+ B 32; The intrinsic oscillation frequency, n, also consists of two (12) components, namely,…”

Section: Transition To Van Der Pol Equationmentioning

confidence: 99%

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Design of a MOS RLC-oscillator with specified total harmonic distortion

Filanovsky

Oliveira

2011

2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS)

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Operation of aMOS RLC-oscillator is considered, and it is shown that it can be described by the van der Pol model. The transformation of time scale to the oscillator intrinsic time allows one to use the previously obtained results for harmonic content of the van der Pol model. One can calculate the total harmonic distortions and use it to design an oscillator with required level of them. The correction of frequency in case of strongly distorted oscillations is also given. The results are verified by design and simulation of an RLC oscillator for realization in 130 nanometer technology for communications in wireless test systems.

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Section: Discussionsupporting

confidence: 79%

“…Using the operational condition of steady-state oscillations (2zr l +Cs+(Ls+r)-1 + (2Rr l = 0 (S) (12) we can rewrite (10) for large signal operation as…”

Section: IImentioning

confidence: 99%

Section: Transition To Van Der Pol Equationmentioning

confidence: 99%

Section: Transition To Van Der Pol Equationmentioning

confidence: 99%

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Design of a MOS RLC-oscillator with specified total harmonic distortion

Filanovsky

Oliveira

2011

2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS)

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“…6, b), 10 nF and c), 1 nF). The calculations of the waveform can be found in [6][7][8], the theory of this paper does not allow doing this. Finally, when C =9.5 pF (the probe only, no external capacitor), the oscillations become relaxation ones (Fig.…”

Section: A 2) Dynamical Root Locusmentioning

confidence: 99%

RLC-oscillator with smooth transition from sinusoidal to relaxation oscillations

Filanovsky

Verhoeven

2013

2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS)

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The paper considers transition from sinusoidal to relaxation oscillations in the RLC-oscillator the frequency of which is tuned by the resonator capacitance. The active element of this oscillator is a transconductance amplifier with limited output current. When the tuning capacitor is large the oscillations are nearly sinusoidal. Diminishing the tuning capacitor value one moves smoothly from sinusoidal to relaxation oscillations, and when this capacitor is reduced to zero value the oscillator becomes an RL-(magnetic) multivibrator. The transition is illustrated using two root loci; the first is called the placement root-locus, and it describes the location of characteristic equation roots when the tuning capacitor changes but the oscillations have not started yet. The second root locus is called the dynamical root locus, and it represents the periodic movement of the root locations within one oscillation period, and the oscillator is in steady-state oscillations. The oscillator was realized using a bipolar transconductance amplifier and then tested, and smooth transition from sinusoidal to relaxation oscillation was confirmed.

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