Related Experiment Video
Updated: Jul 7, 2026
08:21
Sample Preparation in Quartz Crystal Microbalance Measurements of Protein Adsorption and Polymer Mechanics
Published on: January 22, 2020
First-order sensitivity analysis of quartz crystal resonator model parameters
1Dept. of Electr. Eng., Univ. of Central Florida, Orlando, FL.
Summary
This study analyzes measurement sensitivity in quartz resonators, predicting motional arm resistance variations. Results from theory, simulation, and experiments show good agreement, validating the analysis method.
Area of Science:
- Electrical Engineering
- Materials Science
- Physics
Background:
- Quartz resonator devices are critical components in electronic circuits.
- Accurate modeling of resonator behavior is essential for reliable performance.
- Understanding sensitivity to measurement errors is key for device characterization.
Purpose of the Study:
- To perform a first-order measurement sensitivity analysis on a single-mode quartz resonator device model.
- To predict variations in motional arm resistance relative to the resonance S-parameter due to measurement errors.
- To validate the sensitivity analysis through computer simulation and experimental verification.
Main Methods:
- Developed a first-order sensitivity analysis for a quartz resonator model.
- Extracted model parameters according to the EIA-512 standard.
- Verified the analysis using computer simulations and experimental measurements.
Main Results:
- The analysis accurately predicts variations in motional arm resistance versus the resonance S-parameter.
- Theoretical predictions, simulation outcomes, and experimental data demonstrate strong agreement.
- The EIA-512 standard provided a reliable method for parameter extraction.
Conclusions:
- The first-order measurement sensitivity analysis is a valid and accurate method for quartz resonators.
- The study confirms good agreement between theoretical analysis, simulation, and experimental results.
- This work contributes to the precise characterization and modeling of quartz resonator devices.
Related Concept Videos
01:17Design 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...
Starting with a fixed...
01:24Characteristics 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:
01:23Parallel 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:
01:17Second-Order Circuits
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
01:11Types 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.
01:21Series 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...