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Oscillations In An LC Circuit

Oscillations In An LC Circuit

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

RLC Circuit as a Damped Oscillator

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...

Design Example: Underdamped Parallel RLC Circuit

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...

Characteristics of Series Resonant Circuit

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

Parallel Resonance

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

Sound Waves: Resonance

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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...

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Related Experiment Video

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Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

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Split-mode unstable resonator.

R J Freiberg, D W Fradin, P P Chenausky

|February 20, 2010

Summary

This summary is machine-generated.

Researchers explored unstable resonators with prisms, achieving phase-locked coherent modes. This work advances understanding of laser injection locking for novel optical systems.

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Area of Science:

Optics and Photonics
Laser Physics

Background:

Unstable resonators are critical components in high-power laser systems.
Controlling spatial mode distribution is essential for laser performance.

Purpose of the Study:

To describe a novel class of unstable resonators.
To investigate the phase locking of spatially split beams within a resonator.

Main Methods:

Utilizing an intracavity reflecting prism to split the resonator beam.
Experimental study of phase-locking conditions.
Analysis using laser injection locking principles.

Main Results:

Demonstration of a novel unstable resonator configuration.
Identification of conditions for achieving phase-locked coherent modes from split beams.
Experimental validation of theoretical predictions.

Conclusions:

A new class of unstable resonators with altered spatial mode distribution has been developed.
Phase locking of split beams is achievable, leading to coherent mode formation.
The findings provide insights into laser injection locking mechanisms for unstable resonators.