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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

Standing Waves in a Cavity

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are 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:

Resonance in an AC Circuit

Resonance in an AC Circuit

The property of an inductor makes it resist any change in the current passing through it, while the property of a capacitor is to build up the charge across its terminals. Hence, if an inductor and capacitor are connected in series, they have opposite effects on the relative phase between current and voltage. The current through the circuit undergoes forced oscillation at the frequency of the source. The resistance term in an R-L-C circuit acts as a damping term because power is dissipated...

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Related Experiment Video

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Fabrication and Testing of Microfluidic Optomechanical Oscillators

Fabrication and Testing of Microfluidic Optomechanical Oscillators

Published on: May 29, 2014

Microcavity laser oscillating in a circuit-based resonator.

Christoph Walther¹, Giacomo Scalari, Maria Ines Amanti

¹Institute for Quantum Electronics, ETH Zurich, Wolfgang-Pauli-Strasse 16, 8093 Zurich, Switzerland. walther@phys.ethz.ch

Science (New York, N.Y.)

|March 20, 2010

Summary

This summary is machine-generated.

Researchers developed an ultrasmall terahertz laser using a subwavelength electronic inductor-capacitor (LC) resonant circuit. This compact, low-power device confines electric fields and offers potential for ultrafast modulation speeds.

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Area of Science:

Photonics
Electrical Engineering
Applied Physics

Background:

Microcavity lasers offer advantages like compactness and low power consumption.
Ultrafast modulation speeds are crucial for advanced communication systems.
Terahertz (THz) frequencies present unique opportunities for spectroscopy and imaging.

Purpose of the Study:

To demonstrate an ultrasmall, electrically injected laser operating in the terahertz range.
To utilize a subwavelength electronic inductor-capacitor (LC) resonant circuit for extreme electric field confinement.
To explore the potential of this design for higher frequencies and other optoelectronic devices.

Main Methods:

Fabrication of an ultrasmall laser device incorporating a subwavelength electronic LC resonant circuit.
Electrical injection for laser operation.
Characterization of the laser's operating frequency and mode volume.

Main Results:

Successful demonstration of an electrically injected laser operating at 1.5 terahertz.
Achieved extreme confinement of the electric field due to the subwavelength LC resonator.
The laser's mode volume was strongly subwavelength, enabling miniaturization.

Conclusions:

The developed ultrasmall LC resonator laser is a significant advancement in terahertz optoelectronics.
The design principle is scalable to higher frequencies and adaptable for detectors and modulators.
This technology holds promise for compact, high-speed THz applications.