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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>4.5 Resistance to Voltage</TITLE><META NAME="description" CONTENT="4.5 Resistance 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="tex2html258" HREF="node18.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node18.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="tex2html256" 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="tex2html250" HREF="node16.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node16.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="tex2html259" HREF="node18.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node18.html">4.6 Capacitance to Voltage</A><B>Up:</B> <A NAME="tex2html257" HREF="node12.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node12.html">4 Signal Conditioning</A><B> Previous:</B> <A NAME="tex2html251" HREF="node16.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node16.html">4.4 Current to Voltage</A><BR> <P><H2><A NAME="SECTION00045000000000000000">4.5 Resistance to Voltage</A></H2><P><H3><A NAME="SECTION00045100000000000000">4.5.1 Motivation</A></H3><P>Many sensors exhibit a change electrical resistance in response to the quantity that they
are trying to measure. Some examples include force sensing resistors which decrease their
resistance when a force is applied, thermistors which change resistance as a function of the
temperature and carbon microphones which alter their resistance in response to changing
acoustical pressure. In all these cases, one must be able to convert the resistance of the
device into a usable voltage which can be read by the analog to digital converters.
Following are some circuits which perform these measurements along with some examples
of sensors that were described in previous sections.<P><H3><A NAME="SECTION00045200000000000000">4.5.2 Circuits</A></H3><P>There are two ways to convert resistance of a sensor to a voltage. The first, and simplest
way is to apply a voltage to a resistor divider network composed of a reference resistor
and the sensor as shown in Figure <A HREF="node17.html#opamp_RtoV" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#opamp_RtoV">32</A>.<P><P ALIGN=CENTER><A NAME="779"> </A><A NAME="opamp_RtoV"> </A> <IMG WIDTH=203 HEIGHT=159 ALIGN=BOTTOM ALT="figure778" SRC="img84.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img84.gif" > <BR>
</P>
<STRONG>Figure 32:</STRONG> Resistance to Voltage <BR><P><P>The voltage that appears across the sensor (or the reference resistor) is then buffered
before being sent to the ADC. The output voltage is given by:
<P ALIGN=CENTER> <IMG WIDTH=165 HEIGHT=46 ALIGN=BOTTOM ALT="displaymath1978" SRC="img85.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img85.gif" > <P>
</P>
The problem with this method of measuring resistance is that the amplifier is amplifying
the entire voltage measured across the sensor. It would be much better to amplify only the
change in the voltage due to a change in the resistance of the sensor. This can be
accomplished using a bridge as shown in Figure <A HREF="node17.html#opAmp6" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#opAmp6">33</A>.<P><P ALIGN=CENTER><A NAME="786"> </A><A NAME="opAmp6"> </A> <IMG WIDTH=558 HEIGHT=202 ALIGN=BOTTOM ALT="figure785" SRC="img86.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img86.gif" > <BR>
</P>
<STRONG>Figure 33:</STRONG> A Resistance Bridge Connected to an Instrumentation Amplifier (IA) <BR><P><P>If <IMG WIDTH=16 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1980" SRC="img87.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img87.gif" > is set equal to R, then the approximate output of this circuit is:
<IMG WIDTH=76 HEIGHT=21 ALIGN=TOP ALT="tex2html_wrap_inline1982" SRC="img88.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img88.gif" >
Where <I>A</I> is the gain of the IA and <IMG WIDTH=11 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1986" SRC="img89.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img89.gif" > is the change in the resistance of the sensor
corresponding to some physical action. Notice in this equation that the gain can be set
quite high because only the change in voltage caused by a change in the sensor resistance is
being amplified.<P><H3><A NAME="SECTION00045300000000000000">4.5.3 Example</A></H3><P><B>FSR</B><P><P ALIGN=CENTER><A NAME="793"> </A><A NAME="opamp_RtoV1"> </A> <IMG WIDTH=203 HEIGHT=159 ALIGN=BOTTOM ALT="figure792" SRC="img90.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img90.gif" > <BR>
</P>
<STRONG>Figure 34:</STRONG> An FSR in a voltage divider configuration <BR><P><P>The most basic method of interfacing to an FSR is depicted in Figure <A HREF="node17.html#opamp_RtoV1" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#opamp_RtoV1">34</A>. In this
configuration an FSR is used in a voltage divider configuration as described previously. In
this case <IMG WIDTH=18 HEIGHT=18 ALIGN=TOP ALT="tex2html_wrap_inline1994" SRC="img91.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img91.gif" > from Figure <A HREF="node17.html#opamp_RtoV" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#opamp_RtoV">32</A> is the force sensing resistor. An increase in force
results in a decrease in the value of <IMG WIDTH=18 HEIGHT=18 ALIGN=TOP ALT="tex2html_wrap_inline1994" SRC="img91.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img91.gif" > , and hence an increase in the output voltage.
This configuration will not produce a voltage which is a linear function of force. If a
linear characteristic is desired, then one must use a different configuration, or compensate
for the actual response in software once the voltage data is acquired.<P><P ALIGN=CENTER><A NAME="800"> </A><A NAME="rect6a"> </A> <IMG WIDTH=212 HEIGHT=108 ALIGN=BOTTOM ALT="figure799" SRC="img92.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img92.gif" > <BR>
</P>
<STRONG>Figure 35:</STRONG> Measuring the current through an FSR <BR><P><P>An alternative to the above implementation is to measure the current through the device,
and then use an op-amp circuit to convert the current to a voltage. The current through
the FSR is proportional to the conductance which is in turn proportional to the force,
hence current is proportional to force. Moreover, within the appropriate region, this is a
linear relationship. Figure <A HREF="node17.html#rect6a" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#rect6a">35</A> depicts an op-amp in a current to voltage configuration.
What is shown here is simply the output of the FSR connected to the inverting input of the
inverting amplifier described previously. The output voltage, <IMG WIDTH=28 HEIGHT=17 ALIGN=TOP ALT="tex2html_wrap_inline1998" SRC="img93.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img93.gif" > is given
by:<P><P ALIGN=CENTER> <IMG WIDTH=111 HEIGHT=38 ALIGN=BOTTOM ALT="displaymath1992" SRC="img94.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img94.gif" > <P>
</P>
<P>Since <IMG WIDTH=37 HEIGHT=21 ALIGN=TOP ALT="tex2html_wrap_inline2000" SRC="img95.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img95.gif" > , <IMG WIDTH=28 HEIGHT=17 ALIGN=TOP ALT="tex2html_wrap_inline1998" SRC="img93.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img93.gif" > is linearly proportional to force.
Since the non-inverting terminal of the op-amp is grounded, the inverting terminal is
effectively at ground, hence the current through the FSR is given by <IMG WIDTH=25 HEIGHT=29 ALIGN=TOP ALT="tex2html_wrap_inline2004" SRC="img96.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img96.gif" > , hence the above expression can be written as
<IMG WIDTH=65 HEIGHT=17 ALIGN=TOP ALT="tex2html_wrap_inline2006" SRC="img97.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img97.gif" > .<P><P ALIGN=CENTER><A NAME="807"> </A><A NAME="fsr2"> </A> <IMG WIDTH=437 HEIGHT=275 ALIGN=BOTTOM ALT="figure806" SRC="img98.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img98.gif" > <BR>
</P>
<STRONG>Figure 36:</STRONG> Linear potentiometer configuration of an FSR capable of measuring both force and position. <BR><P><P>Standard FSRs are two terminal devices which measure force. Another configuration
offered by Interlink is a three terminal linear potentiometer. Depending upon the circuitry
it is hooked up to, this device can be used to measure either force or position. The physical
layout of the device and a schematic representation of the device are given in Figure <A HREF="node17.html#fsr2" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#fsr2">36</A>.<P>In order to understand how it measures the position of contact, first imagine that the force
sensing resistive element is simply a wire. When pressure is exerted somewhere along the
length of the device, contact is made. By measuring the amount of the resistance from
either of the ends to one of the terminals one can determine the location at which the
potentiometer has been pressed. One way to do this is to apply a voltage across the
potentiometer. When the device is pressed, a connection is established which effectively
creates a voltage divider. The voltage which appears at this terminal will be proportional
to the position of contact. In our case, we do not have a wire, but rather a resistor, hence
any current flowing through the resistor will cause a voltage drop. Furthermore, we
cannot know the amount of the voltage drop since the resistance is unknown. One way
around this dilemma is to sense the voltage while drawing as little current as possible. In
order to do this, a buffer circuit, like the one described previously, is employed. This is
summarized in Figure <A HREF="node17.html#fsr_position" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#fsr_position">37</A>.<P><P ALIGN=CENTER><A NAME="814"> </A><A NAME="fsr_position"> </A> <IMG WIDTH=267 HEIGHT=224 ALIGN=BOTTOM ALT="figure813" SRC="img99.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img99.gif" > <BR>
</P>
<STRONG>Figure 37:</STRONG> High input impedance measuring system used to measure position. <BR><P><P>One way to measure the applied force is to apply a voltage to only one end of the
potentiometer while leaving the other end open. Using the voltage divider circuit
discussed earlier, one can measure the series combination of the force sensing resistive
element and an unknown amount of resistance due to the section of the linear
potentiometer. This circuit is shown in Figure <A HREF="node17.html#fsr_force" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node17.html#fsr_force">38</A>. The amount of uncertainty can be
reduced by tying both ends to the voltage supply. A more sophisticated approach is to
implement a circuit that can switch between the two measurements schemes just
discussed. Furthermore, if this is done fast enough, one can obtain both measurements
almost simultaneously, and use the position measurement to compensate for the unknown
resistance in the above scheme.<P><P ALIGN=CENTER><A NAME="821"> </A><A NAME="fsr_force"> </A> <IMG WIDTH=404 HEIGHT=279 ALIGN=BOTTOM ALT="figure820" SRC="img100.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img100.gif" > <BR>
</P>
<STRONG>Figure 38:</STRONG> Circuit used to measure force with a linear FSR potentiometer. <BR><P><HR><A NAME="tex2html258" HREF="node18.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node18.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="tex2html256" 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="tex2html250" HREF="node16.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node16.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="tex2html259" HREF="node18.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node18.html">4.6 Capacitance to Voltage</A><B>Up:</B> <A NAME="tex2html257" HREF="node12.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node12.html">4 Signal Conditioning</A><B> Previous:</B> <A NAME="tex2html251" HREF="node16.html" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node16.html">4.4 Current to Voltage</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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