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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN"><!--Converted with LaTeX2HTML 96.1 (Feb 5, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>3.3 Accelerometer (Analog Devices ADXL50) </TITLE><META NAME="description" CONTENT="3.3 Accelerometer (Analog Devices ADXL50) "><META NAME="keywords" CONTENT="sensors"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="sensors.css" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/sensors.css"></HEAD><BODY BGCOLOR="#FFFFFF" TEXT="#000000" LANG="EN"> <A NAME="tex2html173" HREF="node10.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node10.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="tex2html171" HREF="node6.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node6.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="tex2html165" HREF="node8.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node8.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="tex2html174" HREF="node10.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node10.html">3.4 Biopotential Sensors </A><B>Up:</B> <A NAME="tex2html172" HREF="node6.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node6.html">3 Sensors </A><B> Previous:</B> <A NAME="tex2html166" HREF="node8.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node8.html">3.2 Force Sensing Resistors </A><BR> <P><H2><A NAME="SECTION00033000000000000000">3.3 Accelerometer (Analog Devices ADXL50) </A></H2><P><P ALIGN=CENTER><A NAME="597">&#160;</A><A NAME="Accelerometer">&#160;</A> <IMG WIDTH=349 HEIGHT=167 ALIGN=BOTTOM ALT="figure596" SRC="img14.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img14.gif"  > <BR>
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<STRONG>Figure 8:</STRONG> Mass-Spring system used for measuring acceleration <BR><P><P>The basic physical principle behind this accelerometer (as well as many others), is that of a simple mass spring system.  Springs (within their linear region) are governed by a physical principle known as Hooke's law.  Hooke's law states that a spring will exhibit a restoring force which is proportional to the 
amount it has been stretched or compressed.  Specifically, <I>F</I>=<I>kx</I>, where <I>k</I> is the constant of proportionality between displacement (<I>x</I>) and force (<I>F</I>).  The other important physical principle is that of Newton's  second law of motion which states that a force operating on a mass which is accelerated will exhibit 
a force with a magnitude <I>F</I>=<I>ma</I>.  Figure&nbsp;<A HREF="node9.html#Accelerometer" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node9.html#Accelerometer">8</A> shows a mass connected to a spring.  If this system undergoes an acceleration, then by Newton's law, there will be a resultant force equal to <I>ma</I>.  This force causes the mass to either compress or expand the spring under the constraint that <I>F</I>=<I>ma</I>=<I>kx</I>.  
Hence an acceleration <I>a</I> will cause the mass to be displaced by  <IMG WIDTH=40 HEIGHT=19 ALIGN=TOP ALT="tex2html_wrap_inline1810" SRC="img15.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img15.gif"  >  or alternatively, if we observe a displacement of <I>x</I>, we know that the mass has undergone an acceleration of  <IMG WIDTH=38 HEIGHT=21 ALIGN=TOP ALT="tex2html_wrap_inline1814" SRC="img16.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img16.gif"  > .  In this way we have turned the problem of measuring acceleration into one of measuring the displacement 
of a mass connected to a spring.  Note that this system only responds to accelerations along the length of the spring.  This is said to be a single axis accelerometer.  In order to measure multiple axes of acceleration, this system needs to be duplicated along each of the required axes.<P><P ALIGN=CENTER><A NAME="604">&#160;</A><A NAME="SiliconAccel1">&#160;</A> <IMG WIDTH=469 HEIGHT=247 ALIGN=BOTTOM ALT="figure603" SRC="img17.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img17.gif"  > <BR>
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<STRONG>Figure 9:</STRONG> Mass-spring system used in the Analog Devices ADXL50 accelerometer <BR><P><P>The Analog Devices ADXL50 is a micro-machined stand-alone accelerometer which consists of a mass spring system as well as a system to measure displacement and the appropriate signal conditioning circuitry (which is the topic of the next section).  The mass spring system used in this device is depicted in 
Figure&nbsp;<A HREF="node9.html#SiliconAccel1" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node9.html#SiliconAccel1">9</A>.  The mass is a bar of silicon, and the spring system is implemented by the 4 tethers which attach to each corner of the mass.  It responds to accelerations that occur in line with the length of the mass.  When an acceleration occurs, the mass moves with respect to the anchored ends of the 
tethers.  Roughly speaking, the amount of acceleration is proportional to the amount of displacement of the mass.  This is not quite true in this case since the spring system is not an <em>ideal</em> spring 
as presented earlier.  This fact is compensated for by some sophisticated signal conditioning circuitry present in the device.<P><P ALIGN=CENTER><A NAME="611">&#160;</A><A NAME="parallelCap">&#160;</A> <IMG WIDTH=212 HEIGHT=94 ALIGN=BOTTOM ALT="figure610" SRC="img18.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img18.gif"  > <BR>
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<STRONG>Figure 10:</STRONG> A simple capacitor <BR><P><P>The next problem which needs to be solved is that of measuring the displacement of the bar.  The principle upon which this is based is that of the electrical property of capacitance.  Capacitors are electrical components which store charge.  A simple capacitors is formed by placing two metal plates in parallel 
with each other as shown in Figure&nbsp;<A HREF="node9.html#parallelCap" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node9.html#parallelCap">10</A>.  The amount of capacitance that a device such as this would exhibit is exhibit is given by  <IMG WIDTH=39 HEIGHT=23 ALIGN=TOP ALT="tex2html_wrap_inline1816" SRC="img19.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img19.gif"  > , where <I>k</I> is a property of the material between 
the two plates.  Using this, if one knew <I>k</I> and could measure capacitance,  they would be able to determine  <IMG WIDTH=16 HEIGHT=13 ALIGN=TOP ALT="tex2html_wrap_inline1822" SRC="img20.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img20.gif"  > , the spacing between the plates.<P><P ALIGN=CENTER><A NAME="618">&#160;</A><A NAME="TriCap">&#160;</A> <IMG WIDTH=201 HEIGHT=234 ALIGN=BOTTOM ALT="figure617" SRC="img21.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img21.gif"  > <BR>
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<STRONG>Figure 11:</STRONG> The dual Capacitor system used to measure displacement in the Analog Devices ADXL50 accelerometer <BR><P><P>The ADXL50 takes this technique one step further and uses two capacitors configured as in Figure&nbsp;<A HREF="node9.html#TriCap" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node9.html#TriCap">11</A>.  If the device is at rest, and the spacing between each of the plates is  <IMG WIDTH=16 HEIGHT=13 ALIGN=TOP ALT="tex2html_wrap_inline1822" SRC="img20.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img20.gif"  > , then each of the 
capacitors exhibits a capacitance of  <IMG WIDTH=39 HEIGHT=23 ALIGN=TOP ALT="tex2html_wrap_inline1816" SRC="img19.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img19.gif"  > .  If the middle plate is moved by a distance <I>x</I>, then this results in:
<P ALIGN=CENTER> <IMG WIDTH=100 HEIGHT=77 ALIGN=BOTTOM ALT="eqnarray619" SRC="img22.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img22.gif"  > <P>

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This can then be written as:
<P ALIGN=CENTER> <IMG WIDTH=109 HEIGHT=70 ALIGN=BOTTOM ALT="eqnarray621" SRC="img23.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img23.gif"  > <P>
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<P>The ADXL50 measures the difference between the two capacitors which is given by:
<P ALIGN=CENTER> <IMG WIDTH=304 HEIGHT=42 ALIGN=BOTTOM ALT="displaymath1790" SRC="img24.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img24.gif"  > <P>

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For small values of displacement <I>x</I>, the above expression reduces to:
<P ALIGN=CENTER> <IMG WIDTH=63 HEIGHT=41 ALIGN=BOTTOM ALT="displaymath1791" SRC="img25.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img25.gif"  > <P>

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Hence the difference in capacitance is proportional to <I>x</I>, but only for small values of displacement.  The ADXL50 uses a negative feedback control loop to make sure that the movement of the mass is kept small so that the above expression remains correct.  Figure&nbsp;<A HREF="node9.html#AccelFeedback" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node9.html#AccelFeedback">12</A> shows a block diagram of the entire system.<P><P ALIGN=CENTER><A NAME="629">&#160;</A><A NAME="AccelFeedback">&#160;</A> <IMG WIDTH=617 HEIGHT=216 ALIGN=BOTTOM ALT="figure628" SRC="img26.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img26.gif"  > <BR>
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<STRONG>Figure 12:</STRONG> Block diagram of the Analog Devices ADXL50 accelerometer <BR><P><HR><A NAME="tex2html173" HREF="node10.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node10.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="tex2html171" HREF="node6.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node6.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="tex2html165" HREF="node8.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node8.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="tex2html174" HREF="node10.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node10.html">3.4 Biopotential Sensors </A><B>Up:</B> <A NAME="tex2html172" HREF="node6.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node6.html">3 Sensors </A><B> Previous:</B> <A NAME="tex2html166" HREF="node8.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node8.html">3.2 Force Sensing Resistors </A><P><ADDRESS><I>Tim Stilson <BR>Thu Oct 17 16:32:33 PDT 1996</I></ADDRESS></BODY></HTML>
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