Structural Health Monitoring Using Smart Sensors - ideals ...

order of the filter design, or number of poles, is also a filter parameter. High-order filters,
in general, have more freedom in filter design, giving better magnitude characteristics at
the expense of design difficulty (Skolnick & Levine, 1997) and larger time lag; the slope
of a filter’s transfer function phase is the time lag.
If an 8-pole, elliptic-type AA filter along with 16-bit ADC is employed as in many
applications in civil engineering, the attenuation, A s is about -96 dB ( = ),
and f sb
is 1.28 times f c
. Therefore, the sampling frequency is set about 2.56 times the
highest frequency signal of interest. The combination of another type of AA filter and
ADC with different resolution gives different values for the attenuation and the stopband
cutoff frequency.
A 4-pole, Butterworth low-pass filter with a cutoff frequency of 50 Hz was selected
as the AA filter for the Berkeley Mote platform. The filter order and cutoff frequency were
set in order to investigate concurrently the ‘Tadeo’ acceleration sensor board developed
by Ruiz-Sandoval (2004) and the strain sensor board characteristics over a wide frequency
range (i.e., 0-50 Hz), and to limit the associated time lag. A small time lag is important for
applications with real-time response requirements, such as structural control and
triggering smart sensor tasks based on the measurement; high filter order and a low cutoff
frequency result in large deterministic time lags. From the AA perspective, this 4-pole
filter cannot completely eliminate aliasing for Mica2’s 10-bit ADC when sampled at 100
or 250 Hz. f sb
for a 10-bit ADC is around 230 Hz. The noise is, however, unlikely to have
an amplitude as large as the ADC’s input range. Small noise components below f sb
and all
of the components above are completely eliminated by this filter.
f sb
There are three major designs to implement the AA filter as an electrical circuit: (a)
passive filter, (b) active filter, and (c) switched capacitor filter designs (National
Semiconductor, 1991). A passive filter is made up of passive components without
amplifiers, i.e., resistors, capacitors, and inductors. Though having a small noise level,
being free from power supply, and having the capability to deal with a large voltage and
current are advantages of this filter design, inflexibility in the design of the filter is
detrimental. Active filter designs employ operational amplifiers, eliminating the need for
the hard-to-handle inductors, and have more flexibility in design. The noise level is higher
than that of the passive design, but it is still moderate. Switched-capacitor filters are
clocked, sampled-data systems widely available in monolithic form. The cutoff frequency
is typically set by an external clock frequency. This filter has design flexibility, a variable
cutoff frequency, and insensitivity to temperature change. Poor DC precision and high
noise level, however, need to be addressed by additional external circuits, according to
application requirements. Frequency components higher than half the clock frequency
cannot be eliminated by this filter; they need to be eliminated with passive or active filters.
In this research, an active design was employed because of its design flexibility, moderate
noise level, and good DC precision.
A 4-pole Butterworth filter was realized by the Sallen-Key active filter design (Sallen
& Key, 1955), as shown in Figure 4.5. Rail-to-rail input/output amplifiers, MAX4132
(Maxim Integrated Products, Inc., 2007), give the filter a rail-to-rail input/output property,
which results in the efficient use of the input/output voltage range. The cutoff frequency
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