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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...

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

Parallel Resonance

Parallel 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:

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...

Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Discrete-Time Fourier Series

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...

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Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

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Tunable spatial demultiplexer based on the Fabry-Perot filter.

Xuezheng Sun, Peifu Gu, Mingyu Li

|June 17, 2009

Summary

The superprism effect in thin film stacks enables tunable wavelength demultiplexing. A low-cost Fabry-Perot filter demonstrates this, offering multiple channels with varying incident angles.

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Area of Science:

Optics and Photonics
Materials Science

Background:

The superprism effect arises from abnormal dispersion and anisotropy in thin film stacks near the bandgap.
Fabry-Perot filters (FPFs) are optical devices with potential for exploiting such effects.

Purpose of the Study:

To design and fabricate a thin film Fabry-Perot filter exhibiting the superprism effect.
To investigate the use of FPFs as tunable demultiplexing devices for polychromatic light.

Main Methods:

Fabrication of a thin film Fabry-Perot filter.
Application of polychromatic light at various incident angles.
Utilizing the transfer matrix method (TMM) combined with the Gaussian angular spectrum method for analysis.

Main Results:

Demonstration of the superprism effect in the fabricated FPF.
Achieved tunable demultiplexing with multiple channels across different wavelength ranges.
Accurate calculation of spatial shifts and analysis of beam splitting phenomena.

Conclusions:

Thin film FPFs can be fabricated simply and cost-effectively.
FPFs serve as tunable demultiplexing devices by leveraging the superprism effect.
The TMM with the Gaussian angular spectrum method provides accurate analysis for FPFs.