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Discrete Fourier Transform Using Capacitive Cantileavers

IP.com Disclosure Number: IPCOM000118981D
Original Publication Date: 1997-Oct-01
Included in the Prior Art Database: 2005-Apr-01
Document File: 4 page(s) / 127K

Publishing Venue

IBM

Related People

Due rig, U: AUTHOR [+3]

Abstract

Figure a) Sketch of a micro-machined capacitive resonator. b) Circuit diagram of the interface electronics. The bias potential 'V' sub b ' bias', typically of order V, must be substantially larger than the input voltage for linear operation. The response of the resonator is sensed by means of an I/V converter. The response function of the resonator can be modified, e.g., for adjustment of the Q-factor, by means of optional electronic feedback (shown dashed). c) Sketch of a linear capacitive resonator array consisting of 100 channels spanning the frequency range from 100 Hz to 10 kHz. The input, bias, and feedback signals are simultaneously applied to all resonators in parallel via the substrate.

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Discrete Fourier Transform Using Capacitive Cantileavers

Figure a) Sketch of a micro-machined capacitive resonator.  b)
Circuit diagram of the interface electronics.  The bias potential 'V'
sub b ' bias', typically of order V, must be substantially larger
than the input voltage for linear operation.  The response of the
resonator is sensed by means of an I/V converter.  The response
function of the resonator can be modified, e.g., for adjustment of
the Q-factor, by means of optional electronic feedback (shown
dashed).  c) Sketch of a linear capacitive resonator array consisting
of 100 channels spanning the frequency range from 100 Hz to 10 kHz.
The input, bias, and feedback signals are simultaneously applied to
all resonators in parallel via the substrate.  The response of the
resonators, reflecting the frequency spectrum of the input signal, is
sensed individually by means of I/V converters integrated onto the Si
substrate.  Note that the entire device can be integrated on a chip
area of the order of 1.5 cm *1 cm.

      An electro-mechanical system based on mechanical resonators
provides a frequency spectral analysis of an electrical or acoustical
signal.  Frequency spectral analysis is one of the key processing
steps in speech recognition.  The standard approach is to use signal
processors to perform a Fast Fourier Transformation (FFT) of the
input signal.  The problem with FFT, however, is that it is not well
adapted to the logarithmic perception in natural hearing and owing to
the vast amount of high speed computation that is performed, FFT is
rather power consuming.  The latter issue is particularly critical in
portable devices.

      As an alternative, the spectral analysis can be effectively
performed by means of a mechanical resonator array.  Such a resonator
array can be manufactured using Si based micro-machining technology
(1).  The great advantage of using discrete resonators is that the
frequency raster can easily be made logarithmic with each resonator
sensing a frequency interval given by its resonance frequency divided
by the Q-factor.  To match the spectral analysis to the frequency
resolving capabilities of the human ear, approximately 50 resonators
per decade are required.  Neighboring resonators must have a slightly
overlapping response interval which is achieved with a Q-factor of
the order of 50/ln(10) &app. 20.

      Suppose that the resonators consist of Si cantilever beams
which are attached to a substrate at one end (Figure).  The resonance
frequency for such levers is f sub 0 &app.  1500 Hz m * t/l2  where
t and l denote the thickness and the length of the levers,
respectively.  For speech recognition, it is sufficient to cover only
a restricted frequency span, say from 100 Hz to 10 kHz corresponding
to 100 channels (note that an FFT analysis would require roughly 2200
channels to cover the same frequency span).  Assuming a fixed
thickness t=10 &mu.m, the length of the levers range...