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📁 Input/Data Acquisition System Design for Human Computer Interfacing
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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>4.6 Capacitance to Voltage</TITLE><META NAME="description" CONTENT="4.6 Capacitance to Voltage"><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="tex2html268" HREF="node19.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node19.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="tex2html266" 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="tex2html260" HREF="node17.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.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="tex2html269" HREF="node19.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node19.html">4.7 Additional Signal Conditioning </A><B>Up:</B> <A NAME="tex2html267" HREF="node12.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node12.html">4 Signal Conditioning</A><B> Previous:</B> <A NAME="tex2html261" HREF="node17.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html">4.5 Resistance to Voltage</A><BR> <P><H2><A NAME="SECTION00046000000000000000">4.6 Capacitance to Voltage</A></H2><P><H3><A NAME="SECTION00046100000000000000">4.6.1 Motivation</A></H3><P>We have seen that the electrical property of capacitance has been the main physical 
principle behind many of the sensors that we have discussed.  The main reason why it is so 
useful is that it is a property which varies directly proportional to the distance between the 
metal plates.  This has made it a useful tool in measuring small vibrations.  Capacitance 
can also be used to measure much greater distances than we have seen so far.  The Radio-
Baton is an example of a system which uses capacitance to measure distances on the order 
of 1 meter.<P>Another useful property of capacitors is that they are sensitive to the material that resides 
between their metal plates.  Specifically, it is the dielectric constant associated with the 
material that results in a change in capacitance.  One example which makes use of this 
principle is that capacitors can be used as sensors which can detect the presence of an 
object between their plates.  This principle can be used as a detector to determine when 
someone enters a space.
In the case of the piezoelectric sensor, we used the fact that the voltage of a charged 
capacitor will vary inversely proportional to its capacitance.  An op-amp circuit could then 
be used to amplify the voltage to a useable level.  Since voltage and capacitance are 
inversely proportional, this is useful when small values of capacitance are to be measured.  
When one is dealing with larger values of capacitance the voltages resultant from a 
practical amount of charge are too small to be useful, and hence other methods must be 
used.<P><H3><A NAME="SECTION00046200000000000000">4.6.2 Circuits</A></H3><P>Capacitance can be measured in the same two ways discussed previously for measuring 
resistance - a voltage divider or a bridge circuit. Instead of using resistors, capacitors are 
used. There is only one critical difference:   <IMG WIDTH=24 HEIGHT=18 ALIGN=TOP ALT="tex2html_wrap_inline2018" SRC="img101.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img101.gif"  >  must be a sinusoidal signal since the 
capacitor blocks DC.  Since the impedance of a capacitor is inversely proportional to 
frequency, the HCI designer should choose a frequency for  <IMG WIDTH=24 HEIGHT=18 ALIGN=TOP ALT="tex2html_wrap_inline2018" SRC="img101.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img101.gif"  >  that creates a 
voltage across the capacitor that is appropriate for amplification (i.e, too small a frequency 
will cause too high of an impedance of the sensor which will cause too much noise from 
the sensor; too high of a frequency will cause too low of an impedance of the sensor which 
will cause other circuit noise to swamp out the voltage across the sensor).<P><H3><A NAME="SECTION00046300000000000000">4.6.3 Examples</A></H3><P><B>ADXL50 Accelerometer</B><P>The ADXL50 accelerometer provides as its output a voltage level which varies in 
proportion to the amount of acceleration experienced along its sensitive axis.  It is 
calibrated such that under no acceleration the output will be 1.8 volts.  Furthermore, an 
acceleration of 50g (where 1g is the acceleration due to gravity) will cause a voltage 
swing of 1volt (ie. an acceleration of 50g would result in an output of either 2.8volts, or .8 
volts depending upon the direction).  In many cases this voltage swing would not be 
appropriate for a specific application, hence one must use a circuit which converts the 
output voltage into a more useful voltage range.  For example, one might desire a more 
sensitive device which varied 1volt for every g of acceleration.
Figure&nbsp;<A HREF="node18.html#amp1" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node18.html#amp1">39</A> depicts a circuit which accomplishes this task.<P><P ALIGN=CENTER><A NAME="828">&#160;</A><A NAME="amp1">&#160;</A> <IMG WIDTH=172 HEIGHT=148 ALIGN=BOTTOM ALT="figure827" SRC="img102.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img102.gif"  > <BR>
</P>
<STRONG>Figure 39:</STRONG> Schematic of an op-amp circuit which converts the output voltage of the ADXL-50 to a range which is suitable for analog-digital conversion.  <BR><P><P>The output voltage of this 
circuit is given by:<P><P ALIGN=CENTER> <IMG WIDTH=215 HEIGHT=38 ALIGN=BOTTOM ALT="displaymath2022" SRC="img103.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img103.gif"  > <P>
</P>
<P>When no acceleration is applied to the device, the output voltage will be 1.8volts which 
makes the second term will be zero, and the output will be   <IMG WIDTH=63 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline2024" SRC="img104.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img104.gif"  > , 
the new zero-g output.  The output voltage can be written as:<P><P ALIGN=CENTER> <IMG WIDTH=200 HEIGHT=38 ALIGN=BOTTOM ALT="displaymath2026" SRC="img105.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img105.gif"  > <P>
</P>
<P>where  <IMG WIDTH=26 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline2028" SRC="img106.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img106.gif"  >  is the deviation of the output voltage from 1.8 volts.  A 
50g acceleration will result in  <IMG WIDTH=29 HEIGHT=18 ALIGN=TOP ALT="tex2html_wrap_inline2030" SRC="img107.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img107.gif"  >  of 1volt, which will be scaled by 
 <IMG WIDTH=16 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline2032" SRC="img108.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img108.gif"  > .  In this way, we see that  <IMG WIDTH=16 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline2032" SRC="img108.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img108.gif"  >  determines the 
sensitivity of the output, while the new zero-g output is determined by 
 <IMG WIDTH=63 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline2024" SRC="img104.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img104.gif"  > .<P><HR><A NAME="tex2html268" HREF="node19.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node19.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="tex2html266" 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="tex2html260" HREF="node17.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.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="tex2html269" HREF="node19.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node19.html">4.7 Additional Signal Conditioning </A><B>Up:</B> <A NAME="tex2html267" HREF="node12.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node12.html">4 Signal Conditioning</A><B> Previous:</B> <A NAME="tex2html261" HREF="node17.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html">4.5 Resistance to Voltage</A><P><ADDRESS><I>Tim Stilson <BR>Thu Oct 17 16:32:33 PDT 1996</I></ADDRESS></BODY></HTML>
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