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Related Concept Videos

RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
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...
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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.
Starting with a fixed...
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
Second-order Op Amp Circuits01:19

Second-order Op Amp Circuits

Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.
The analysis of such circuits follows a systematic approach, similar to the second-order RLC circuits. In practical scenarios, bulky inductors are rarely employed due to their size and weight. This means...

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Related Experiment Video

Updated: Jun 10, 2026

Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators
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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

Published on: August 8, 2025

Analytic eigenmode solution for the self-filtering unstable resonator.

W P Latham, M L Tilton, T R Ferguson

    Applied Optics
    |August 20, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents an analytic solution for unstable resonator eigenmodes using prolate functions. The method accurately represents cavity modes with minimal terms, offering an efficient computational approach.

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    Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
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    Last Updated: Jun 10, 2026

    Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators
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    Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

    Published on: August 8, 2025

    Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
    15:25

    Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

    Published on: February 4, 2018

    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Computational Electromagnetics

    Background:

    • Unstable resonators are crucial for high-power lasers.
    • Nonsymmetric and self-filtering designs present unique challenges for mode analysis.
    • Accurate calculation of cavity eigenmodes is essential for resonator design and performance prediction.

    Purpose of the Study:

    • To develop an analytic solution for the bare cavity eigenmodes of nonsymmetric self-filtering unstable resonators.
    • To demonstrate the efficacy of modal expansion in prolate functions for this problem.
    • To present an efficient computational methodology.

    Main Methods:

    • Modal expansion using prolate functions, a complete and orthogonal set.
    • Representation of resonator modes within the aperture.
    • Application of Gaussian quadrature for numerical calculations.

    Main Results:

    • An analytic solution for the bare cavity eigenmodes was obtained.
    • Accurate representation of modes within the aperture requires only three terms of the expansion.
    • The use of Gaussian quadrature proved efficient for calculations.

    Conclusions:

    • The modal expansion in prolate functions provides an effective analytic solution for nonsymmetric self-filtering unstable resonators.
    • The method offers high accuracy with a reduced number of terms.
    • This approach facilitates efficient computational analysis of complex laser resonator systems.