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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:

Series Resonance

Series Resonance

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...

Concept of Resonance and its Characteristics

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...

Double Resonance Techniques: Overview

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved 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.
Starting with a fixed...

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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

High performance Vernier racetrack resonators.

Robert Boeck¹, Jonas Flueckiger, Han Yun

¹Department of Electrical and Computer Engineering, University of British Columbia, 2332 Main Mall, Vancouver, British Columbia V6T 1Z4, Canada. rboeck@ieee.org

|December 22, 2012

Summary

This summary is machine-generated.

We achieved record performance in silicon racetrack resonators using the Vernier effect, significantly improving interstitial peak suppression (IPS) by 14.5 dB. Increasing the gap distance enhances IPS but reduces 3 dB bandwidth (BW).

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Area of Science:

Photonics and optical engineering
Integrated optics
Semiconductor device physics

Background:

Silicon racetrack resonators are key components in photonic integrated circuits.
The Vernier effect enables enhanced optical filtering.
Improving interstitial peak suppression (IPS) is crucial for device performance.

Purpose of the Study:

To demonstrate record performance of series-coupled silicon racetrack resonators exhibiting the Vernier effect.
To investigate the relationship between inter-ring gap distance, IPS, and 3 dB bandwidth (BW).

Main Methods:

Fabrication of series-coupled silicon racetrack resonators.
Experimental characterization of device performance, including IPS and BW.
Theoretical modeling of the inter-ring gap distance effects.

Main Results:

Achieved a record interstitial peak suppression (IPS) of 25.5 dB, exceeding previous results by 14.5 dB.
Demonstrated experimentally and theoretically that increasing inter-ring gap distance improves IPS.
Showed that increasing inter-ring gap distance leads to a decrease in 3 dB bandwidth (BW).

Conclusions:

Series-coupled silicon racetrack resonators with the Vernier effect offer a pathway to high-performance optical filters.
Device performance, specifically IPS and BW, can be precisely tuned by controlling the inter-ring gap distance.
The findings provide valuable insights for the design and optimization of silicon photonic devices.