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Active Filters

Active Filters

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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Interference and Diffraction

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Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...

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Backward wave optical amplification by an asymmetric active interference filter.

¹U.S. Navy Electronics Laboratory, SanDiego, California 92152, USA.

|January 6, 2010

Summary

This study presents equations for active interference filters with unequal mirror reflectances. Asymmetric configurations can achieve higher reflectance gain than transmittance gain with identical bandwidths.

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Area of Science:

Optics and Photonics
Semiconductor Device Physics

Background:

Active interference filters are crucial optical components.
Understanding gain and bandwidth is essential for device optimization.
Previous studies often assumed equal mirror reflectances.

Purpose of the Study:

To derive equations for reflectance, bandwidth, and root gain-bandwidth of active interference filters.
To compare gain for various configurations with constant mirror reflectance product.
To analyze the impact of asymmetric mirror reflectances on device performance.

Main Methods:

Derivation of analytical equations for filter performance metrics.
Comparative analysis of different filter configurations.
Examination of device gain dependence on single-pass gain and mirror reflectances.

Main Results:

Equations for reflectance, bandwidth, and root gain-bandwidth are provided.
Asymmetric configurations demonstrate potential for higher reflectance gain compared to transmittance gain.
Bandwidths remain identical for both gain types in asymmetric configurations.

Conclusions:

Device gain is significantly influenced by single-pass gain and individual mirror reflectances.
Asymmetric mirror reflectances offer a design parameter to enhance reflectance gain.
The findings provide insights for optimizing active interference filter design.