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Related Concept Videos

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...
Series RLC Circuit without Source01:21

Series RLC Circuit without Source

Within the field of electrical circuits, source-free RLC circuits present an intriguing domain. These circuits comprise a series arrangement of a resistor, inductor, and capacitor, operating independently of external energy sources. Their initiation hinges upon utilizing the initial energy stored within the capacitor and inductor to instigate their functionality. Their mathematical equation, a second-order differential equation, sets these circuits apart. This equation captures how the...
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
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:
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:
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.

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Related Experiment Video

Updated: Jun 14, 2026

Fabrication and Characterization of Superconducting Resonators
10:26

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

Extracting coupling and loss coefficients from a ring resonator.

W R McKinnon1, D X Xu, C Storey

  • 1Institute for Microstructural Sciences, National Research Council of Canada, 1200 Montreal Road, Ottawa, Ontario, Canada. ross.mckinnon@nrc-cnrc.gc.ca

Optics Express
|April 8, 2010
PubMed
Summary
This summary is machine-generated.

A new method extracts coupling and loss coefficients from single ring resonators. These optical coefficients can be distinguished by analyzing their changes with wavelength or device parameters.

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Area of Science:

  • Photonics and Optical Engineering
  • Integrated Optics
  • Resonator Devices

Background:

  • Ring resonators are fundamental components in integrated photonics.
  • Accurate characterization of coupling and loss coefficients is crucial for device design and performance optimization.
  • Existing methods may require multiple resonators or complex setups.

Purpose of the Study:

  • To develop a novel method for extracting optical coupling and loss coefficients from a single ring resonator.
  • To provide a simplified approach for characterizing resonator performance.
  • To enable disentanglement of coupling and loss parameters from resonance spectra.

Main Methods:

  • Analysis of resonance peak widths, depths, and spacings within a single ring resonator.
  • Application of derived formulas to extract characteristic coefficients.
  • Investigation of the wavelength and device parameter dependence of the coefficients to distinguish between coupling and loss.

Main Results:

  • Successfully extracted coupling and loss coefficients from single resonator spectra.
  • Demonstrated a method to differentiate between coupling and loss coefficients.
  • Validated the technique's reliance on spectral variations with wavelength or device parameters.

Conclusions:

  • The developed method offers an efficient way to determine critical optical parameters of ring resonators.
  • This technique simplifies the characterization process, requiring only a single resonator.
  • Understanding the disentanglement based on spectral variations is key for accurate coefficient assignment.