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¹H NMR: Complex Splitting

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...

¹H NMR Signal Multiplicity: Splitting Patterns

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...

Phase-lead and Phase-lag Controllers

Phase-lead and Phase-lag Controllers

Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass...

Power Distribution in Three-phase and Single Phase Circuits

Power Distribution in Three-phase and Single Phase Circuits

Power distribution within electrical circuits is a foundational aspect of residential and industrial energy systems. While single-phase power is common in residential settings, three-phase power is the standard for industrial environments with heavy machinery. Each system is different and has advantages, and it's crucial to understand the underlying principles of power distribution and material efficiency.
Single-Phase Power Distribution:
Single-phase circuits are typical in household...

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Related Experiment Video

Updated: Oct 12, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Multipole-phase division multiplexing.

Gianluca Ruffato, Vincenzo Grillo, Filippo Romanato

|November 23, 2021

Summary

This summary is machine-generated.

Researchers introduce a new family of structured light beams with multipole phase properties. This innovation offers a practical method for space division multiplexing, enhancing optical communication and light processing capabilities.

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Last Updated: Oct 12, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

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Published on: March 20, 2017

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

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Published on: January 28, 2019

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Area of Science:

* Physics and Optics
* Information and Communication Technology

Background:

* Control of structured waves is crucial for radiation propagation, advanced imaging, and light-matter interactions.
* Spatial degrees of freedom in information technology offer expanded state space for multiplexing and quantum protocols.
* Orbital angular momentum beams are prominent but spatial decomposition remains challenging.

Purpose of the Study:

* To introduce a novel family of structured-phase beams with multipole phase characteristics.
* To present a framework for controlling, multiplexing, propagating, and demultiplexing these wave fields.
* To demonstrate a practical and compact method for manipulating these beams using conformal optics.

Main Methods:

* Development of a theoretical framework describing wave fields with multipole phase.
* Utilizing conformal optics for practical and compact control of two continuous spatial parameters.
* Integrating multiplexing, propagation, and demultiplexing within a unified description based on conformal mappings.

Main Results:

* Introduction of novel wave fields devoid of phase singularities.
* Demonstration of practical control over beam properties via conformal optics.
* Unified framework for managing wave field evolution and transformation.

Conclusions:

* The new paradigm offers a versatile and easily implementable approach to structured light.
* This framework provides a novel platform for space division multiplexing.
* Potential for unconventional solutions in light processing and free-space optical communications.