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Design Example: Underdamped Parallel RLC Circuit

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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.
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Related Experiment Video

Updated: Jun 15, 2026

Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

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Published on: August 8, 2025

Modal analysis of practical quartz resonators using finite element method.

Liu Yang¹, Nikolay Vitchev, Zhiping Yu

¹Institute of Microelectronics, Tsinghua University, Beijng, China. yangliu@mails.thu.edu.cn

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|February 25, 2010

Summary

This summary is machine-generated.

Precise finite element simulations accurately predicted the performance of real quartz crystal resonators, matching experimental data. This method allows studying how practical factors influence device behavior.

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Area of Science:

Physics
Electrical Engineering
Materials Science

Background:

Finite element simulation is a key tool for analyzing piezoelectric devices.
Experimental validation is crucial for ensuring simulation accuracy in real-world applications.

Purpose of the Study:

To develop and validate a precise 3-D finite element simulator for realistic quartz crystal resonators.
To investigate the impact of practical design factors on resonator performance.

Main Methods:

Generated precise geometry models of quartz resonators from direct measurements.
Included realistic components like quartz blanks, electrodes, and mountings in the models.
Developed a 3-D finite element simulator for modal analysis and temperature property simulation.

Main Results:

Simulation results for modal analysis and temperature properties showed strong consistency with experimental measurements.
The study successfully simulated real quartz crystal resonators using the developed model and simulator.
Dependencies of device performance on practical factors were effectively analyzed.

Conclusions:

The developed finite element simulation method provides accurate predictions for real quartz crystal resonators.
This approach enables a deeper understanding of how practical factors influence piezoelectric device performance.
The validated simulator is a valuable tool for the design and optimization of crystal resonators.