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Design Example: Underdamped Parallel RLC Circuit01:17

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Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
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In an NMR sample, precise measurement of the absolute absorption frequencies of nuclei is difficult. A standard internal reference compound is added, and the frequency difference between the reference signal and sample signals is measured.
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Related Experiment Video

Updated: Jul 8, 2025

Fabrication and Characterization of Superconducting Resonators
10:26

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

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Optical frequency reference based on a cryogenic silicon resonator.

Eugen Wiens, Chang Jian Kwong, Timo Müller

    Optics Express
    |December 13, 2023
    PubMed
    Summary
    This summary is machine-generated.

    We developed a cryogenic optical reference laser for precise frequency measurements. This system achieves high stability, showing potential for advanced timing applications.

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    Area of Science:

    • Physics
    • Metrology
    • Optical Engineering

    Background:

    • Optical atomic clocks require highly stable laser sources.
    • Cryogenic operation of optical resonators can reduce thermal noise and improve stability.
    • Vibrations and temperature fluctuations are key challenges in achieving high-performance optical references.

    Purpose of the Study:

    • To develop and characterize a 1.5 μm laser stabilized to a cryogenic silicon optical resonator.
    • To investigate the frequency instability and drift of the cryogenic optical reference.
    • To identify sources of noise and limitations in the current system.

    Main Methods:

    • Stabilization of a 1.5 μm laser to a silicon optical resonator.
    • Operation of the resonator within a closed-cycle cryostat at 1.7 K with passive vibration isolation.
    • Frequency instability measurements over various integration times (1 s to 6000 s).

    Main Results:

    • Achieved frequency instability of 2 × 10⁻¹⁴ at 1 s integration time, limited by residual vibrations.
    • Demonstrated frequency instability of 6.2 × 10⁻¹⁵ at 100 s and 3.5 × 10⁻¹⁶ at 6000 s.
    • Measured a mean fractional frequency drift rate of -3.7 × 10⁻²⁰/s over 190 days.

    Conclusions:

    • The cryogenic optical reference shows promising performance for high-accuracy optical frequency dissemination.
    • Residual vibrations and laboratory temperature variations significantly impact short-to-medium term stability.
    • Further mitigation of environmental factors could enable reaching the thermal-noise-limited performance of the resonator.