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Related Concept Videos

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:
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Double Resonance Techniques: Overview01:12

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...
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:
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
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...

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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators
09:46

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Published on: August 8, 2025

Nonlinear properties of split-ring resonators.

Bingnan Wang1, Jiangfeng Zhou, Thomas Koschny

  • 1Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA.

Optics Express
|October 1, 2008
PubMed
Summary
This summary is machine-generated.

Nonlinear split-ring resonators (SRRs) with varactors show tunable resonance frequencies dependent on incident power. This leads to bistable metamaterials and hysteresis effects, with potential for tunable microwave devices.

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Fabrication and Characterization of Superconducting Resonators
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Area of Science:

  • Metamaterials and Nanophotonics
  • Electromagnetics and Microwave Engineering
  • Nonlinear Optics and Devices

Background:

  • Split-ring resonators (SRRs) are fundamental building blocks for metamaterials.
  • Incorporating nonlinear components like varactors introduces power-dependent electromagnetic properties.
  • Understanding nonlinear SRR behavior is crucial for advanced tunable devices.

Purpose of the Study:

  • To theoretically analyze and experimentally measure the properties of nonlinear SRRs.
  • To investigate the influence of incident power on the resonance frequency of SRRs loaded with varactors.
  • To explore phenomena such as bistability, hysteresis, and coupling in nonlinear metamaterials.

Main Methods:

  • Theoretical analysis of nonlinear SRR properties.
  • Experimental measurements of SRRs loaded with high-Q capacitors and nonlinear varactors.
  • Investigation of varying incident power levels and varactor configurations (single and back-to-back).

Main Results:

  • Resonance frequency (f(m)) of nonlinear SRRs is tunable with incident power.
  • f(m) shifts to lower frequencies with one varactor and higher frequencies with two back-to-back varactors.
  • Bistable tunable metamaterials and hysteresis effects are observed at high incident powers.
  • Coupling effects between two nonlinear SRRs are discussed.

Conclusions:

  • Nonlinear SRRs offer a pathway to power-tunable metamaterial properties.
  • The configuration of varactors significantly impacts the frequency tuning direction.
  • Observed bistability and hysteresis open possibilities for novel nonlinear electromagnetic devices.