Phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator

Abstract

Phase feedback is commonly utilized to set up a synchronized MEMS oscillator for high performance sensor applications. It's a consensus that the synchronization region varies with phase delay with a 'Anti-U' mode within 0 to π and phase delay is typically fixed on π/2 to achieve maximum synchronization range and best frequency stability. In this paper, phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical os-*Corresponding author

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators

“…Defining the frequency difference between the synchronization lower bound Ω 1 and the center frequency Ω 0 as the lower half bandwidth (∆Ω 1 = Ω 0 − Ω 1 ), and the frequency difference between the synchronization upper bound Ω 2 and the center frequency Ω 0 as the upper half bandwidth (∆Ω 2 = Ω 2 − Ω 0 ), we plotted the upper and lower bounds of the synchronization region, varied with the phase delay and observed in Figure 2e, which revealed noteworthy trends. Notably, a monotonic decrease in synchronization bandwidth with phase delay is evident, particularly when employing a small feedback strength (V f = 10 mV), reaching its minimum at ϕ 0 = π/2, as previously verified in [26,27]. Importantly, throughout the entire range of phase delay variations, the lower half bandwidth ∆Ω 1 and upper half bandwidth ∆Ω 2 consistently maintained equal magnitudes (Figure 2f), signifying the symmetry of the synchronization region under linear conditions.…”

“…Yet, due to the amplitude-frequency effect [24] induced by nonlinearity, synchronization regions can exhibit asymmetry [31]. Such results have been shown in the experimental measured synchronization region in [26,27]; however, the asymmetry of synchronization has been largely unexplored regarding the intrinsic mechanism of nonlinearity's influence. Asymmetric synchronization in systems such as communication networks or electronic circuits can result in decreased efficiency and predictability during data transmission or signal processing, and it may exert notable effects on the stability and overall performance of engineering [32] and physical systems [33].…”

“…By manipulating the oscillator's operating point, achieving a zero-dispersion state enhances frequency stability significantly. Most notably, nonlinearities can substantially broaden synchronization bandwidth compared to linear oscillators by orders of magnitude [25][26][27]. Manipulating feedback, phase delay, coupling, and perturbation strengths significantly affects synchronization behavior.…”

Overmodulation causes a variation in the number of jumps in the Duffing system

“…In addition, Wang et al [41] used the Melnikov method to study fast-slow dynamics under amplitude modulation, uncovering hybrid relaxation oscillation patterns. Besides, Shi et al [42] proposed a method to predict synchronization bandwidth and frequency stability through phase delay, thereby enabling oscillators to maintain optimal performance. Moreover, Song et al [43,44] and Han et al [45] investigated modulation effects on relaxation oscillations in Duffing and forced van der Pol systems, respectively.…”