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Oscillations In An LC Circuit

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An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

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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Aging

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Current Growth And Decay In RL Circuits

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Related Experiment Video

Updated: Jul 7, 2026

Quantifying Yeast Chronological Life Span by Outgrowth of Aged Cells

Quantifying Yeast Chronological Life Span by Outgrowth of Aged Cells

Published on: May 6, 2009

Long-term aging of oscillators.

R L Filler¹, J R Vig

¹US Army Res. Lab., Fort Monmouth, NJ.

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|January 1, 1993

Summary

This study presents aging data for over 40 crystal oscillators, including temperature-compensated (TCXO) and oven-controlled (OCXO) types, over 1-10 years. Ruggedized TCXOs show excellent aging performance (<2x10(-10)/d), while OCXOs achieve a few parts in 10(12)/d.

Area of Science:

Electrical Engineering
Materials Science
Physics

Background:

Crystal oscillators are critical frequency-determining components in electronic systems.
Long-term aging is a key parameter affecting oscillator performance and system reliability.
Understanding oscillator aging is crucial for applications requiring high frequency stability.

Purpose of the Study:

To report and analyze aging data for a diverse set of crystal oscillators.
To evaluate the aging performance of temperature-compensated crystal oscillators (TCXOs) and oven-controlled crystal oscillators (OCXOs).
To assess the impact of ruggedization on TCXO aging for demanding applications.

Main Methods:

Accumulation of aging data using an automated aging facility.

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Testing of over 40 oscillators from various sources over periods of 1 to over 10 years.

Controlled temperature environment maintenance for TCXOs.

Main Results:

Aging data collected for TCXOs and OCXOs over extended periods.
Ruggedized TCXOs designed for high-shock environments demonstrated surprisingly good aging (<2x10(-10)/d).
Superior OCXO models exhibited long-term aging rates of a few parts in 10(12)/d.

Conclusions:

Crystal oscillators, particularly OCXOs and specialized TCXOs, can achieve excellent long-term aging performance.
Ruggedized TCXOs are suitable for applications with extreme environmental demands without significant aging degradation.
The study provides valuable data for selecting and utilizing oscillators in high-stability and harsh-environment applications.