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Series Resonance

Series Resonance

The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...

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...

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:

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

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...

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Related Experiment Video

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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

Published on: August 8, 2025

ZnO-on-Si mode conversion resonator.

S S Schwartz¹, S J Martin, S Datta

¹Sandia Nat. Lab., Albuquerque, NM.

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|January 1, 1989

Summary

This summary is machine-generated.

This study introduces a new model for surface-acoustic-wave (SAW) mode conversion resonators, detailing transducer coupling and wave propagation. The model accurately predicts resonator behavior and optimizes device design for maximum coupling.

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Area of Science:

Acoustics and Materials Science
Electrical Engineering and Applied Physics

Background:

Surface-acoustic-wave (SAW) devices are crucial for signal processing.
Understanding mode conversion in SAW resonators is key to improving device performance.
Existing models may not fully capture the complexities of simultaneous wave propagation.

Purpose of the Study:

To develop a comprehensive two-port admittance matrix model for SAW mode conversion resonators.
To uniquely address transducer coupling within the context of mode conversion.
To enable the prediction of optimal design parameters for resonance and maximum coupling.

Main Methods:

Formulation of a two-port admittance matrix model.
Inclusion of simultaneous Rayleigh and Sezawa wave propagation.
Construction of an equivalent circuit model for resonator behavior.
Analysis of reflector array separation and interdigital transducer placement.

Main Results:

The model successfully describes SAW mode conversion resonator operation.
It accounts for the simultaneous presence of Rayleigh and Sezawa waves.
The model allows for the determination of optimal design parameters for resonance and maximum coupling.
Experimental results validate the developed theoretical model.

Conclusions:

The presented admittance matrix model provides a robust framework for analyzing SAW mode conversion resonators.
The model facilitates the design optimization of these devices for enhanced performance.
Experimental validation confirms the accuracy and utility of the theoretical approach.