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A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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A Nonlinear Pulse Shaping Method Using Resonant Piezoelectric MEMS Devices.

Mathieu Gratuze, Abdul-Hafiz Alameh, Alexandre Robichaud

    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
    |February 1, 2022
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    This study introduces pulse shaping to enhance nonlinear resonator performance. This method significantly boosts membrane displacement and allows dynamic frequency tuning, improving device applications.

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    Area of Science:

    • Microelectromechanical Systems (MEMS)
    • Nonlinear Dynamics
    • Acoustic Transducers

    Background:

    • Nonlinear resonators are crucial for advanced applications but often limited by membrane displacement.
    • Enhancing displacement and tuning resonant frequency are key challenges in MEMS transducer design.

    Purpose of the Study:

    • To present a novel pulse shaping methodology for increasing membrane displacement in nonlinear transducers.
    • To demonstrate the benefits of frequency modulation for amplitude modulation of resonator displacement.
    • To verify the effectiveness of pulse shaping through simulations and experimental validation.

    Main Methods:

    • Utilizing frequency modulation of the excitation signal to achieve amplitude modulation of resonator displacement.
    • Implementing pulse shaping techniques on nonlinear resonators (3.9 and 7.9 kHz).
    • Conducting simulations and experiments on softening type resonators (STR) and hardening type resonators (HTR).

    Main Results:

    • Pulse shaping increased membrane velocity by up to 191% for STR and 348% for HTR.
    • Dynamic frequency tuning enabled operation over bandwidths of 280 Hz (STR) and 115 Hz (HTR).
    • The methodology offers control over resonator decay time and improved velocity compared to non-optimized signals.

    Conclusions:

    • The presented pulse shaping methodology effectively enhances membrane displacement and enables dynamic frequency tuning in nonlinear resonators.
    • This technique offers significant improvements in velocity and operational bandwidth for both STR and HTR.
    • The findings suggest broader applicability of this method to various nonlinear resonator systems, potentially increasing their use in diverse applications.