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Related Concept Videos

Active Filters01:25

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:
Passive Filters01:27

Passive Filters

Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...

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Extended active optical lattice filters: filter synthesis.

Mieczyslaw Dabkowski1, Amr El Nagdi, Louis R Hunt

  • 1Department of Mathematical Sciences, University of Texas at Dallas, P.O. Box 830688,Richardson, Texas 75083, USA.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 3, 2010
PubMed
Summary

This study details creating stable optical lattice filters using semiconductor optical amplifiers. Researchers determined conditions for achieving asymptotic stability and explored placing transmission zeros alongside poles.

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Area of Science:

  • Photonics
  • Optical Engineering
  • Filter Design

Background:

  • Two-dimensional tunable lattice filter architectures are crucial for advanced optical signal processing.
  • Semiconductor optical amplifiers (SOAs) integrated into waveguide structures offer tunable gain.
  • Asymptotic stability is a key performance metric for such filters.

Purpose of the Study:

  • To investigate the synthesis of asymptotically stable filters from a unit cell of a 2D tunable lattice filter.
  • To determine upper bounds on the number of gains required for prescribed poles.
  • To explore conditions for achieving asymptotic stability with real-valued gains and discuss pole-zero placement.

Main Methods:

  • Analysis of a unit cell comprising four four-port couplers and four waveguides with SOAs.
  • Derivation of upper bounds for gain parameters.
  • Development of sufficient conditions based on reflection-type coefficients of the couplers.
  • Theoretical exploration of transmission zeros.

Main Results:

  • Established upper bounds on the number of gains for achieving specific pole placements.
  • Identified sufficient conditions on coupler coefficients for asymptotic stability using real gains [0,1].
  • Motivated the concept of transmission zeros in this filter architecture.

Conclusions:

  • The synthesis of asymptotically stable filters is feasible within the studied 2D tunable lattice architecture.
  • Gain and coupler characteristics can be engineered to ensure filter stability.
  • Simultaneous placement of poles and transmission zeros is a potential area for future research.