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$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

Design Example

Design Example

The innovation of touch-tone telephony revolutionized the telecommunications industry by replacing the traditional rotary dial with a dual-tone multi-frequency (DTMF) signaling system. This system uses a matrix-style keypad with buttons arranged in four rows and three columns, creating 12 distinct signals each assigned to a pair of frequencies. Each button press results in a simultaneous generation of two sinusoidal tones – one from a low-frequency group (697 to 941 Hz) and one from a...

Interference: Path Lengths

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...

Passive Filters

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...

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:

Mesh Analysis for AC Circuits

Mesh Analysis for AC Circuits

In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...

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Updated: Jun 15, 2026

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

Design method for multilayer interference filters.

G Castagno, F Demichelis, E Minetti-Mezzetti

|March 11, 2010

Summary

This summary is machine-generated.

This study presents new expressions for multilayer coatings, enabling precise design of transmittance and reflectance. The findings detail high- and low-transmittance bands and narrowbands in multilayer stacks.

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Area of Science:

Optics and Photonics
Materials Science

Background:

Multilayer optical coatings are crucial components in various photonic devices.
Designing coatings with specific spectral properties, such as tailored transmittance and reflectance, remains a key challenge.

Purpose of the Study:

To present general expressions for calculating the transmittance and reflectance of a spacer system flanked by two multilayer stacks.
To offer a versatile framework for the rational design of multilayer optical coatings.

Main Methods:

Derivation of analytical expressions for transmittance and reflectance.
Analysis of spectral characteristics of multilayer stacks with unequal designed wavelengths.

Main Results:

General expressions for transmittance and reflectance are derived.
Demonstration of high-transmittance bands and low-transmittance bands.
Observation of a narrowband in the transmittance spectrum for stacks with unequal designed wavelengths.

Conclusions:

The presented expressions offer a general and effective approach for multilayer coating design.
The study highlights the ability to engineer specific spectral features, including narrowbands, by controlling layer parameters.