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Standing Waves in a Cavity01:28

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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
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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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Frequency Response of a Circuit01:20

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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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Related Experiment Video

Updated: Jul 29, 2025

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity
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Microwave frequency measurement based on a frequency-to-phase mapping technique.

Chongjia Huang, Erwin H W Chan

    Optics Letters
    |May 23, 2023
    PubMed
    Summary

    A novel frequency-to-phase mapping technique enables instantaneous radio-frequency (RF) signal frequency measurement. This method utilizes low-frequency phase detection for accurate and wide-range RF frequency determination.

    Area of Science:

    • Electrical Engineering and Applied Physics
    • Signal Processing and Communications

    Background:

    • Accurate and instantaneous measurement of radio-frequency (RF) signals is crucial for various applications.
    • Existing methods may face limitations in terms of speed, range, or cost.

    Purpose of the Study:

    • To introduce a new frequency-to-phase mapping technique for RF signal frequency measurement.
    • To enable instantaneous and wide-range frequency determination using low-cost components.

    Main Methods:

    • Generating two low-frequency signals whose phase difference is directly dependent on the input RF signal frequency.
    • Employing a low-cost, low-frequency electronic phase detector to measure the phase difference.
    • Calculating the input RF signal frequency from the measured phase difference.

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    Main Results:

    • Experimental verification of the frequency-to-phase mapping technique.
    • Successful measurement of RF signal frequencies within the 5 to 20 GHz range.
    • Achieved measurement errors of less than ±0.2 GHz.

    Conclusions:

    • The proposed frequency-to-phase mapping technique provides an effective method for instantaneous RF frequency measurement.
    • The system demonstrates a wide frequency measurement range and high accuracy.
    • This technique offers a cost-effective solution for RF frequency measurement applications.