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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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Time and frequency -Domain Interpretation of PI Control01:27

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Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
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Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Time and frequency -Domain Interpretation of Phase-lag Control01:21

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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
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Related Experiment Video

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Fast Grid Preparation for Time-Resolved Cryo-Electron Microscopy
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Time-resolved terahertz time-domain near-field microscopy.

N J J van Hoof, S E T Ter Huurne, J Gómez Rivas

    Optics Express
    |January 18, 2019
    PubMed
    Summary

    Researchers developed a new near-field microscope to measure terahertz (THz) photoconductivity in semiconductors. This technique achieves sub-diffraction-limit resolution for studying ultrafast carrier dynamics.

    Area of Science:

    • Optics and Photonics
    • Condensed Matter Physics
    • Semiconductor Science and Technology

    Background:

    • Terahertz (THz) spectroscopy is crucial for characterizing semiconductor properties.
    • Measuring nanoscale photoconductivity at THz frequencies is challenging due to the diffraction limit.

    Purpose of the Study:

    • To demonstrate a novel near-field microscopy technique for measuring THz photoconductivity.
    • To achieve sub-diffraction-limit spatial resolution for THz spectroscopic measurements.
    • To investigate ultrafast photoexcited carrier dynamics in semiconductors.

    Main Methods:

    • Utilized a near-field microscope to measure THz pulse transmission through photoexcited semiconductors.
    • Employed back-excitation with a Dove prism and a dual lock-in detection scheme.

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  • Performed time-resolved THz time-domain spectroscopy with nanoscale resolution.

    • Main Results:

    • Successfully mapped the complex photoconductivity of a gallium arsenide thin film.
    • Resolved sub-picosecond dynamics of photoexcited carriers.
    • Achieved a spatial resolution of λ/10 at 0.5 THz.

    Conclusions:

    • The developed near-field microscope enables nanoscale THz photoconductivity measurements.
    • This method provides a flexible platform for studying ultrafast carrier dynamics in semiconductors.
    • The technique offers significant advancements for semiconductor characterization at THz frequencies.