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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
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Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.
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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Updated: Apr 15, 2026

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
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Analytical modeling and tolerance analysis of a linear variable filter for spectral order sorting.

Cheng-Hao Ko, Kuei-Ying Chang, You-Min Huang

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    This study introduces a novel method using a commercial coater and local mask for fabricating linear variable filters (LVFs) faster. An analytical model accurately predicts filter profiles, improving production rates and precision.

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    Area of Science:

    • Optical Engineering
    • Thin Film Technology
    • Materials Science

    Background:

    • Current linear variable filter (LVF) fabrication methods suffer from low production rates.
    • Precisely controlling thin film thickness across a substrate is challenging for LVF manufacturing.

    Purpose of the Study:

    • To propose and validate an innovative method for increasing the production rate of linear variable filters (LVFs).
    • To develop an analytical thin film thickness model for accurate LVF profile prediction.
    • To analyze the impact of fabrication parameters on LVF performance.

    Main Methods:

    • Integration of a commercial coater with a local mask on a substrate.
    • Development of an analytical thin film thickness model based on coater geometry.
    • Analysis of thickness tolerance, zone width, layer structure, and transmission spectra.
    • Evaluation of critical parameter variations in the coater.

    Main Results:

    • The proposed method significantly enhances the production rate of LVFs.
    • The analytical model accurately predicts LVF thickness profiles.
    • Local mask theory demonstrates high accuracy in predicting evaporation profiles.
    • Parameter variations were analyzed for their effects on LVF characteristics.

    Conclusions:

    • The combined use of a commercial coater and local mask offers an efficient LVF fabrication solution.
    • The developed analytical model provides a powerful tool for designing and optimizing LVFs.
    • This approach overcomes previous limitations in LVF production speed and accuracy.