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<P><P ALIGN=CENTER><A NAME="691"> </A><A NAME="rect8"> </A> <IMG WIDTH=403 HEIGHT=203 ALIGN=BOTTOM ALT="figure690" SRC="img55.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img55.gif" > <BR>
</P>
<STRONG>Figure 21:</STRONG> Instrumentation Amplifier<BR><P><P><B>Lowpass and highpass filters</B><P>The non-inverting amplifier configuration can be modified to limit the bandwidth of the
incoming signal. For example, the feedback resistor can be replaced with a
resistor/capacitor combination as shown in Figure <A HREF="node15.html#opAmp8" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opAmp8">22</A> Thus the gain of the circuit is now:
<IMG WIDTH=85 HEIGHT=30 ALIGN=TOP ALT="tex2html_wrap_inline1896" SRC="img56.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img56.gif" >
where:
<P ALIGN=CENTER> <IMG WIDTH=98 HEIGHT=77 ALIGN=BOTTOM ALT="eqnarray692" SRC="img57.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img57.gif" > <P>
</P>
<P><P ALIGN=CENTER><A NAME="700"> </A><A NAME="opAmp8"> </A> <IMG WIDTH=199 HEIGHT=122 ALIGN=BOTTOM ALT="figure699" SRC="img58.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img58.gif" > <BR>
</P>
<STRONG>Figure 22:</STRONG> Single Pole Low-Pass Filter <BR><P><P>A filter ``rolls off'' at 20dB per 10-times increase in frequency (20dB/decade) times the
order of the filter, i.e.:
<IMG WIDTH=283 HEIGHT=19 ALIGN=TOP ALT="tex2html_wrap_inline1898" SRC="img59.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img59.gif" > .
Thus a first order filter ``rolls off'' at 20dB/decade as shown in Figure <A HREF="node15.html#opAmp8resp" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opAmp8resp">23</A>.<P><P ALIGN=CENTER><A NAME="707"> </A><A NAME="opAmp8resp"> </A> <IMG WIDTH=344 HEIGHT=177 ALIGN=BOTTOM ALT="figure706" SRC="img60.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img60.gif" > <BR>
</P>
<STRONG>Figure 23:</STRONG> Frequency Response of Single Pole Lowpass Filter <BR><P><P>The input resistor of the inverting amplifier can also be replaced by a resistor/capacitor
pair to create a high pass filter as shown in Figure <A HREF="node15.html#opAmp9" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opAmp9">24</A> The gain of this filter is given by:
<IMG WIDTH=85 HEIGHT=39 ALIGN=TOP ALT="tex2html_wrap_inline1900" SRC="img61.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img61.gif" >
where:
<P ALIGN=CENTER> <IMG WIDTH=98 HEIGHT=77 ALIGN=BOTTOM ALT="eqnarray708" SRC="img62.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img62.gif" > <P>
</P>
<P><P ALIGN=CENTER><A NAME="716"> </A><A NAME="opAmp9"> </A> <IMG WIDTH=234 HEIGHT=89 ALIGN=BOTTOM ALT="figure715" SRC="img63.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img63.gif" > <BR>
</P>
<STRONG>Figure 24:</STRONG> Single Pole High-Pass Filter <BR><P><P>The frequency response of this filter is shown in Figure <A HREF="node15.html#opAmp9resp" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opAmp9resp">25</A>.<P><P ALIGN=CENTER><A NAME="723"> </A><A NAME="opAmp9resp"> </A> <IMG WIDTH=353 HEIGHT=177 ALIGN=BOTTOM ALT="figure722" SRC="img64.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img64.gif" > <BR>
</P>
<STRONG>Figure 25:</STRONG> Frequency Response of a Single Pole High-Pass Filter <BR><P><P>Higher order filters, which consequently have faster attenuation rates, can be created by
cascading many first-order filters. Alternatively, the filter circuit can include more
resistor/capacitor pairs to increase its order. The technique for doing this can be found in
either of the references given previously. For the HCI designer, however, the two
important steps are to determine the required filter order and to pick a circuit of that order
- making sure that the circuit also meets any of the other previously described
requirements of the signal conditioning circuitry.<P><H3><A NAME="SECTION00043300000000000000">4.3.3 Example: Piezoelectric Sensors</A></H3><P>As mentioned previously, a common implementation practice is to sandwich a
piezoelectric crystal between two metal plates. Figure <A HREF="node15.html#piezoEquiv" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#piezoEquiv">26</A> shows an equivalent electrical
circuit of this arrangement. The voltage source represents the voltage that develops due
to the excess surface charge on the crystal. The capacitor which appears in series is due to
the capacitor formed by the metallic plates of the sensor. An important point to make is
that piezo sensors cannot be used to measure a constant force, but rather is only useful for
dynamic forces. If one is familiar with basic circuit theory, it should be clear that the
capacitor blocks the direct current (the constant voltage resulting from a constant force).<P><P ALIGN=CENTER><A NAME="730"> </A><A NAME="piezoEquiv"> </A> <IMG WIDTH=200 HEIGHT=70 ALIGN=BOTTOM ALT="figure729" SRC="img65.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img65.gif" > <BR>
</P>
<STRONG>Figure 26:</STRONG> A piezoelectric sensor with a load resistance <BR><P><P>In order to measure the force, one must measure the voltage which appears across the
terminals of the sensor. It is impossible to measure voltage without drawing at least a
little electrical current. This situation is summed up in
Figure <A HREF="node15.html#piezoEquiv" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#piezoEquiv">26</A> where <IMG WIDTH=18 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1926" SRC="img66.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img66.gif" > represents the load impedance inherent in the measuring
device. Figure <A HREF="node15.html#piezoResp" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#piezoResp">27</A> shows a typical response which might arise if a constant force is
applied to the piezo. In the absence of a load resistance, a force applied to the crystal will
develop a charge which will remain as long as the force is present. In the case where the
load resistor is present, an electrical path is formed which serves to allow the charge to
dissipate, which in turn reduces the voltage. The higher the value of the resistance, the
longer it will take for the charge to dissipate. The <em>time-constant</em> of the system is
defined as the time it takes the charge (or voltage) to decrease to approximately 37its original value. The time constant <IMG WIDTH=10 HEIGHT=12 ALIGN=TOP ALT="tex2html_wrap_inline1928" SRC="img67.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img67.gif" > is give by <IMG WIDTH=41 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1930" SRC="img68.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img68.gif" > . Typical values for
common piezo sensors is about <IMG WIDTH=35 HEIGHT=14 ALIGN=BOTTOM ALT="tex2html_wrap_inline1932" SRC="img69.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img69.gif" > ( nano-farads), and typical input impedances
for measuring devices is on the order of <IMG WIDTH=38 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1934" SRC="img70.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img70.gif" > ( mega-ohms). These values
result in a <IMG WIDTH=10 HEIGHT=12 ALIGN=TOP ALT="tex2html_wrap_inline1928" SRC="img67.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img67.gif" > of <IMG WIDTH=44 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1938" SRC="img71.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img71.gif" > . Roughly speaking, this means that forces that are
constant, or vary slowely will suffer from the fact that the voltage across the sensor will
tend to decrease in amplitude, and the overall amplitude of the measure voltage will be
reduced. Alternatively, forces which vary rapidly will not be subject to much if any
decrease in amplitude.<P><P ALIGN=CENTER><A NAME="737"> </A><A NAME="piezoResp"> </A> <IMG WIDTH=351 HEIGHT=303 ALIGN=BOTTOM ALT="figure736" SRC="img72.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img72.gif" > <BR>
</P>
<STRONG>Figure 27:</STRONG> Time domain response of the output of a piezo sensor subject to a constant force <BR><P><P><P ALIGN=CENTER><A NAME="744"> </A><A NAME="piezoResp2"> </A> <IMG WIDTH=387 HEIGHT=152 ALIGN=BOTTOM ALT="figure743" SRC="img73.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img73.gif" > <BR>
</P>
<STRONG>Figure 28:</STRONG> Frequency response of a piezo sensor <BR><P><P>This situation can also be described in the <em>frequency domain</em>. In the time domain,
the system is characterized by its time constant whereas in the frequency domain it is
characterized by its cutoff frequency <IMG WIDTH=38 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline1940" SRC="img74.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img74.gif" > . A plot of the
frequency response of piezo sensor along with a load resistance is shown in Figure <A HREF="node15.html#piezoResp2" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#piezoResp2">28</A>.
For the sensor mentioned earlier with an internal capacitance of <IMG WIDTH=35 HEIGHT=14 ALIGN=BOTTOM ALT="tex2html_wrap_inline1942" SRC="img75.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img75.gif" > and a
load resistance of <IMG WIDTH=38 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1934" SRC="img70.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img70.gif" > , the cutoff frequency is equal to <IMG WIDTH=36 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1946" SRC="img76.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img76.gif" > .
Specifically, this means that a force varying at a frequency of <IMG WIDTH=36 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1946" SRC="img76.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img76.gif" > will result in a
measured voltage which is <IMG WIDTH=25 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1950" SRC="img77.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img77.gif" > less than a more rapidly varying force with the same
amplitude. In many applications it is important to make the <IMG WIDTH=25 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1950" SRC="img77.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img77.gif" > frequency as low as
possible. In order to do this one must make the input impedance of their measuring circuit
as high as possible. Thus a non-inverting amplifier is connected to the piezo output as
shown in Figure <A HREF="node15.html#piezoAmp" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#piezoAmp">29</A>.<P><P ALIGN=CENTER><A NAME="757"> </A><A NAME="piezoAmp"> </A> <IMG WIDTH=210 HEIGHT=109 ALIGN=BOTTOM ALT="figure756" SRC="img78.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img78.gif" > <BR>
</P>
<STRONG>Figure 29:</STRONG> Amplified piezo sensor <BR><P><P>Hence the circuit amplifies the voltage by the factor <IMG WIDTH=36 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline1954" SRC="img40.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img40.gif" > . The <IMG WIDTH=25 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1950" SRC="img77.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img77.gif" >
cutoff frequency of this circuit is <IMG WIDTH=67 HEIGHT=21 ALIGN=TOP ALT="tex2html_wrap_inline1958" SRC="img79.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img79.gif" > , where <I>C</I> is
the internal capacitance of the sensor. It is clear that an increase in the value of the input
resistor will result in a decrease in the cutoff frequency.<P><P ALIGN=CENTER><A NAME="765"> </A><A NAME="AccelP1"> </A> <IMG WIDTH=323 HEIGHT=195 ALIGN=BOTTOM ALT="figure764" SRC="img80.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img80.gif" > <BR>
</P>
<STRONG>Figure 30:</STRONG> Using a piezoelectric sensor as an accelerometer <BR><P><P>As mentioned several times, piezo sensors find many applications. Figure <A HREF="node15.html#AccelP1" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#AccelP1">30</A> shows a
mechanical system which implements an accelerometer. In this system, a mass is placed
on the tip of a piezo sensor forming a cantilever beam. When the mass undergoes an
acceleration, a resultant force will cause the piezo film to bend, which will result in a
voltage. Remember that the piezo sensor cannot measure a constant force, so this device
can only measure dynamic acceleration, and cannot be used for applications such as tilt
sensors.<P><HR><A NAME="tex2html238" HREF="node16.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node16.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif" tppabs="http://ccrma.stanford.edu/Images//next_motif.gif"></A> <A NAME="tex2html236" HREF="node12.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node12.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif" tppabs="http://ccrma.stanford.edu/Images//up_motif.gif"></A> <A NAME="tex2html230" HREF="node14.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node14.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif" tppabs="http://ccrma.stanford.edu/Images//previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html239" HREF="node16.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node16.html">4.4 Current to Voltage</A><B>Up:</B> <A NAME="tex2html237" HREF="node12.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node12.html">4 Signal Conditioning</A><B> Previous:</B> <A NAME="tex2html231" HREF="node14.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node14.html">4.2 Additional Requirements for </A><P><ADDRESS><I>Tim Stilson <BR>Thu Oct 17 16:32:33 PDT 1996</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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