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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:

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:

Double Resonance Techniques: Overview

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

Sound Waves: Resonance

Sound Waves: Resonance

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...

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

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Related Experiment Video

Updated: May 1, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Published on: August 5, 2013

A multimode electromechanical parametric resonator array.

I Mahboob¹, M Mounaix¹, K Nishiguchi¹

¹NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan.

Scientific Reports

|March 25, 2014

Summary

Researchers developed a novel electromechanical resonator array using higher-order vibration modes. This system enables a mechanical byte memory, shift-register, and controlled-NOT gate, showcasing new possibilities for electromechanical systems.

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Area of Science:

Physics
Electrical Engineering
Materials Science

Background:

Electromechanical resonators are crucial for sensitive detectors and macroscopic quantum mechanics.
Current research focuses on single resonators, with arrays offering expanded potential.
Fabricating electromechanical resonator arrays presents significant experimental challenges.

Purpose of the Study:

To explore the potential of higher-order vibration modes in a single electromechanical resonator.
To demonstrate the feasibility of creating an electromechanical resonator array using these modes.
To showcase the application of such an array in information processing tasks.

Main Methods:

Identification of 75 harmonic vibration modes within a single electromechanical resonator.
Parametric excitation of 7 specific vibration modes.
Utilizing the 2-phase oscillation of parametrically resonating modes to form a binary information array.

Main Results:

Successfully identified and utilized higher-order vibration modes in a single resonator.
Established a functional binary information array from these modes.
Demonstrated a mechanical byte memory, shift-register, and controlled-NOT gate.

Conclusions:

Higher-order vibration modes in a single electromechanical resonator can effectively emulate an array.
This approach overcomes fabrication challenges associated with traditional electromechanical resonator arrays.
The demonstrated functionalities highlight a promising new avenue for electromechanical information processing.