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Related Concept Videos

Calculations of Electric Potential I01:15

Calculations of Electric Potential I

Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of λRdθ.
Gravitational Potential Energy for Extended Objects01:07

Gravitational Potential Energy for Extended Objects

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:
The Ideal Transformer01:26

The Ideal Transformer

In single-phase two-winding transformers, two windings are coiled around a magnetic core characterized by cross-sectional area A and magnetic permeability μ. A phasor current i1 enters the left winding while i2 exits the right winding, establishing the fundamental working of the transformer through electromagnetic principles.
Ampere's Law forms the basis of understanding the magnetic field within the transformer. It states that the integral of the magnetic field intensity's tangential component...
Equivalent Circuits for Practical Transformers01:28

Equivalent Circuits for Practical Transformers

The practical equivalent circuits of single-phase two-winding transformers exhibit significant deviations from their idealized versions due to the inherent properties of winding resistance and finite core permeability. These properties result in real and reactive power losses, affecting the transformer's performance. Understanding these deviations is crucial for designing more efficient transformers.
In a practical transformer, each winding exhibits resistance and leakage reactance. The winding...
Three-Winding Transformers01:19

Three-Winding Transformers

Three identical single-phase transformers can be configured to form a three-phase transformer connection, which involves high-voltage and low-voltage windings. The high-voltage windings are denoted by capital letters A-B-C, while the low-voltage windings are labeled with lowercase letters a-b-c, representing their respective phases. This notation helps distinguish between the high and low voltage sides of the transformer.
In the per-unit equivalent circuit of a grounded Y-Y three-phase...
Transformers with Off-Nominal Turns Ratios01:25

Transformers with Off-Nominal Turns Ratios

In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the rated...

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Related Experiment Video

Updated: May 26, 2026

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
07:44

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

Published on: April 27, 2016

Finite element analysis on piezoelectric ring transformer.

Hing Leung Li1, Jun Hui Hu, Helen Lai Wah Chan

  • 1Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China.

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|November 24, 2004
PubMed
Summary

This study explores piezoelectric ring transformers operating at high-order modes. Optimized designs show good agreement between simulations and experiments, indicating potential for low-cost, small-size transformers.

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Area of Science:

  • Materials Science
  • Electrical Engineering
  • Acoustics

Background:

  • Piezoelectric transformers (PTs) offer efficient energy conversion.
  • High-order modes in PTs can enhance performance but require careful design.
  • Ring-shaped piezoelectric devices present unique structural and operational characteristics.

Purpose of the Study:

  • To investigate the feasibility and performance of piezoelectric ring transformers operating at high-order extensional modes.
  • To analyze the vibration characteristics and optimize the dimensions of these ring PTs.
  • To compare simulation results with experimental data for validation.

Main Methods:

  • Fabrication of piezoelectric ceramic ring prototypes using Lead Zirconate Titanate (PZT).
  • Development and application of 3-D finite element models (FEM) to simulate vibration characteristics.
  • Experimental characterization of PT prototypes operating at mode orders three and four.
  • Optimization of ring dimensions using FEM to enhance performance and avoid mode coupling.

Main Results:

  • Simulations and experimental measurements showed good agreement for resonant frequencies, mode shapes, and open-circuit characteristics.
  • Optimized dimensions were determined for PTs utilizing higher-order symmetric extensional modes.
  • A critical ring thickness (≤0.6 mm) was identified to prevent undesirable coupling with the thickness mode.
  • The fabricated PTs operated effectively at mode orders three and four.

Conclusions:

  • Piezoelectric ring transformers can be effectively designed to operate at high-order extensional modes.
  • FEM is a reliable tool for analyzing and optimizing the performance of these devices.
  • The ring PT design offers advantages in terms of simple structure, small size, and potential for low-cost manufacturing.
  • These devices show promise for low-voltage power applications.