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Related Concept Videos

Sound Waves: Resonance01:14

Sound Waves: Resonance

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
Parallel Resonance01:23

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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.
Starting with a fixed...
Concept of Resonance and its Characteristics01:19

Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...
Resonance in an AC Circuit01:26

Resonance in an AC Circuit

The property of an inductor makes it resist any change in the current passing through it, while the property of a capacitor is to build up the charge across its terminals. Hence, if an inductor and capacitor are connected in series, they have opposite effects on the relative phase between current and voltage. The current through the circuit undergoes forced oscillation at the frequency of the source. The resistance term in an R-L-C circuit acts as a damping term because power is dissipated...
Characteristics of Series Resonant Circuit01:24

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

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Perturbed open resonators.

S R Barone

    Applied Optics
    |January 23, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study analyzes open resonators with non-ideal mirror shapes, calculating resonant frequencies and diffraction losses using perturbation methods for various configurations.

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    Area of Science:

    • Physics
    • Electromagnetism
    • Optical Engineering

    Background:

    • Open resonators are crucial in various optical and microwave applications.
    • Deviations from ideal configurations can significantly impact resonator performance.
    • Accurate modeling of non-ideal resonators is essential for device optimization.

    Purpose of the Study:

    • To evaluate the resonant frequencies and diffraction losses of two-mirror open resonators with non-ideal configurations.
    • To develop a perturbative technique for analyzing these complex systems.
    • To provide detailed results for specific non-ideal mirror geometries.

    Main Methods:

    • A perturbative technique is employed to analyze the resonant frequencies and diffraction losses.
    • The method is applied to two-mirror open resonator systems.
    • Mathematical derivations are performed for specific non-ideal configurations.

    Main Results:

    • Detailed results for resonant frequencies and diffraction losses are derived.
    • Analysis includes flat mirrors with rectangular or circular apertures and parabolic phase perturbations.
    • Results are also presented for flat-roof and conical systems with large apex angles.

    Conclusions:

    • The perturbative technique provides an effective method for evaluating non-ideal open resonators.
    • Understanding the impact of mirror geometry on resonator performance is crucial.
    • The derived results offer valuable data for designing and optimizing optical and microwave devices.