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Parallel Resonance

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:

Characteristics of Series Resonant Circuit

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:

Standing Waves in a Cavity

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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:

Design Example: Underdamped Parallel RLC Circuit

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.
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The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession,...

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An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain.

Sendy Phang^1,2, Ana Vukovic¹, Stephen C Creagh²

¹George Green Institute for Electromagnetics Research, University of Nottingham, Nottingham NG7 2RD, UK.

Scientific Reports

|February 6, 2016

Summary

This study explores Parity Time (PT) symmetric resonator chains, revealing how modulating refractive index affects PT symmetry breaking. Finite chains exhibit early breaking due to edge states, leading to localized lasing and dissipative modes.

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Area of Science:

Photonics
Condensed Matter Physics
Non-Hermitian Systems

Background:

Periodic structures with engineered gain and loss exhibit unique properties.
Parity-Time (PT) symmetry offers a framework for designing such systems.
Understanding PT symmetry breaking is crucial for device applications.

Purpose of the Study:

To analyze finite periodic Parity Time (PT) chains with modulated refractive indices.
To investigate the influence of modulation on PT symmetry breaking thresholds.
To explore the impact of chain finiteness and edge states on PT symmetry.

Main Methods:

Consideration of finite periodic chains of resonant dielectric cylinders.
Modulation of both real and imaginary parts of the refractive index.
Comparison of band structures between finite and infinite PT resonator chains.
Analysis of the interplay between Bloch phase, gain/loss, and PT symmetry.

Main Results:

The type of modulation significantly impacts the PT symmetry breaking threshold.
Lowest thresholds are consistently observed near the Brillouin zone edge.
Finite PT-chains show early symmetry breaking due to localized edge states.
Localized lasing and dissipative modes appear at the chain edges.

Conclusions:

Modulation strategy is key to controlling PT symmetry breaking in resonator chains.
Finite chain effects, particularly edge states, lead to distinct behaviors compared to infinite systems.
The findings provide insights for designing novel optical devices with tailored PT symmetry properties.