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Related Concept Videos

Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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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.
Starting with a fixed...
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Capacitor With A Dielectric01:18

Capacitor With A Dielectric

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Parallel plate capacitors consist of two conducting plates separated by a certain distance. However, it is mechanically difficult to hold the large plates parallel to each other without actual contact. Hence, a dielectric layer is commonly placed between the plates, which provides an easy solution for holding the plates together with a small gap and increases the capacitance of the capacitor.
Dielectrics are non-conducting materials with no free or loosely bound electrons. When a dielectric is...
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Characteristics of Series Resonant Circuit01:24

Characteristics of Series Resonant Circuit

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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:
806
Parallel Resonance01:23

Parallel Resonance

743
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:
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Series Resonance01:17

Series Resonance

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The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...
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Resonance in an AC Circuit01:26

Resonance in an AC Circuit

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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...
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Fabrication and Characterization of Superconducting Resonators
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Metallically coated dielectric rectangle resonator.

Shuai Liu, Kai-Jun Che, Chang-Lei Guo

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    |September 15, 2015
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    Summary
    This summary is machine-generated.

    The double transfer matrix method (DTMM) accurately calculates resonant modes in dielectric resonators. Modifications are needed for TM modes due to surface plasma polaritons, improving accuracy with geometric deformation.

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    Area of Science:

    • Electromagnetics
    • Optical physics
    • Materials science

    Background:

    • Metallic dielectric resonators exhibit unique optical properties.
    • The double transfer matrix method (DTMM) is a theoretical tool for analyzing resonant modes.
    • Understanding resonant modes is crucial for optical device design.

    Purpose of the Study:

    • To propose the DTMM for calculating resonant mode eigenvalues in metallic dielectric rectangle resonators.
    • To investigate the optical influences of planar structure parameters on these resonators.
    • To address the deviations in TM mode resonances caused by surface plasma polaritons (SPPs).

    Main Methods:

    • Two-dimensional electromagnetic analyses were performed.
    • The double transfer matrix method (DTMM) was employed.
    • Geometric deformation (circular boundaries) was introduced to account for SPPs.

    Main Results:

    • A highest Q-factor resonance was theoretically found for both TE and TM modes at specific resonator dimensions.
    • TM mode resonances deviated from the analytical model due to unconsidered SPPs.
    • Geometric deformation corrected SPP-influenced mode behaviors to standing waves.

    Conclusions:

    • The DTMM provides a basis for analyzing resonant modes in dielectric resonators.
    • SPPs significantly impact TM mode resonances, necessitating model adjustments.
    • Geometric modifications can reconcile theoretical models with observed SPP effects.