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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>4.3 Voltage to Voltage</TITLE><META NAME="description" CONTENT="4.3 Voltage 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="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><BR> <P><H2><A NAME="SECTION00043000000000000000">4.3 Voltage to Voltage</A></H2><P><H3><A NAME="SECTION00043100000000000000">4.3.1 Motivation</A></H3><P>Many sensors output a voltage waveform. Thus no signal conditioning circuitry is needed
to perform the conversion to a voltage. However, dynamic range modification, impedance
transformation, and bandwidth reduction may all be necessary in the signal conditioning
system depending on the amplitude and bandwidth of the signal and the impedance of the
sensor. The circuits discussed in this section and in subsequent sections are treated as
building blocks of a human-computer input system. Their defining equations for their
operation are given without proof. For a more detailed description of how they work, see
<B>Design with Operational Amplifiers and Analog Integrated Circuits</B>, Franco 1988 or
<B>The Art of Electronics</B>, Horowitz and Hill 1989. It is especially important to review the
analysis of ideal op-amp circuits.<P><H3><A NAME="SECTION00043200000000000000">4.3.2 Circuits: Amplifiers </A></H3><P><B>Inverting </B><P>The most common circuit used for signal conditioning is the inverting amplifier circuit as
shown in Figure <A HREF="node15.html#opamp1" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opamp1">15</A> This amplifier was first used when op-amps only had one input, the
inverting (-) input. The voltage gain of this amplifier is <IMG WIDTH=26 HEIGHT=24 ALIGN=TOP ALT="tex2html_wrap_inline1856" SRC="img32.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img32.gif" > . Thus the level of
sensor outputs can be matched to the level necessary for the data acquisition system. The
input impedance is approximately <IMG WIDTH=16 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1858" SRC="img33.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img33.gif" > and the output impedance is nearly zero. Thus,
this circuit provides impedance transformation between the sensor and the data acquisition
system.<P><P ALIGN=CENTER><A NAME="650"> </A><A NAME="opamp1"> </A> <IMG WIDTH=191 HEIGHT=98 ALIGN=BOTTOM ALT="figure649" SRC="img34.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img34.gif" > <BR>
</P>
<STRONG>Figure 15:</STRONG> Inverting Amplifier<BR><P><P>It is important to remember that the voltage swing of the output of the amplifier is limited
by the amplifier's power supply as shown in Figure <A HREF="node15.html#rect5" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#rect5">16</A>. In this example, the power supply
is +/- 13V. When the amplifier output exceeds this level, the output is ``clipped''.<P><P ALIGN=CENTER><A NAME="512"> </A><A NAME="rect5"> </A> <IMG WIDTH=644 HEIGHT=442 ALIGN=BOTTOM ALT="figure179" SRC="img35.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img35.gif" > <BR>
</P>
<STRONG>Figure 16:</STRONG> Clipping of an Amplifier's Output<BR><P><P>Just as the dynamic range of the amplifier is limited, so too is the bandwidth. Op-amps
have a fixed gain-bandwidth product which is specified by the manufacturer. If , for
example, the op-amp is specified to have a <IMG WIDTH=37 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1860" SRC="img36.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img36.gif" > gain-bandwidth product, and it is
connected to have a gain of 100, this means that the bandwidth of the amplifier will be
limited to <IMG WIDTH=38 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1862" SRC="img37.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img37.gif" > ( <IMG WIDTH=117 HEIGHT=15 ALIGN=TOP ALT="tex2html_wrap_inline1864" SRC="img38.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img38.gif" > ).
Another important limitation of the amplifier circuit is noise. All op-amps introduce noise
to the signal. The amount and characteristics of the noise are specified by the
manufacturer of the op-amp. Also, the resistors introduce noise. The equation for this
thermal noise is <IMG WIDTH=90 HEIGHT=19 ALIGN=TOP ALT="tex2html_wrap_inline1866" SRC="img39.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img39.gif" > ; where <I>k</I> is Boltzmann's constant, <I>T</I> is the
temperature, <I>B</I> is the bandwidth of the measurement device, and <I>R</I> is the value of the
resistance. The main point to remember, is the larger the resistor values used, the larger
the amount of noise introduced.
One more limitation of the op-amp is offset voltage. All op-amps have a small amount of
voltage present between the inverting and non-inverting terminals. This DC potential is
then amplified just as if it was part of the signal from the sensor.
There are many other limitations of the amplifier circuit that are important for the HCI
designer to be aware. Too many, in fact, to describe in detail here (refer to the previously
mentioned references.)<P><B>Non-Inverting</B><P>Another commonly used amplifier configuration is shown in Figure <A HREF="node15.html#opamp3" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opamp3">17</A>. The gain of this
circuit is given as <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 input impedance is nearly infinite (limited
only by the op-amp's input impedance) and the output impedance is nearly zero. The
circuit is ideal for sensors that have a high source impedance and thus would be affected
by the current draw of the data acquisition system.<P><P ALIGN=CENTER><A NAME="661"> </A><A NAME="opamp3"> </A> <IMG WIDTH=168 HEIGHT=122 ALIGN=BOTTOM ALT="figure660" SRC="img41.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img41.gif" > <BR>
</P>
<STRONG>Figure 17:</STRONG> Non-Inverting Amplifier<BR><P><P>If <IMG WIDTH=40 HEIGHT=17 ALIGN=TOP ALT="tex2html_wrap_inline1878" SRC="img42.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img42.gif" > and <IMG WIDTH=17 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1880" SRC="img43.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img43.gif" > is open (removed), then the gain of the non-inverting amplifier is
unity. This circuit, as shown in Figure <A HREF="node15.html#opampbuf" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opampbuf">18</A> is commonly referred to as a unity-gain buffer
or simply a buffer.<P><P ALIGN=CENTER><A NAME="668"> </A><A NAME="opampbuf"> </A> <IMG WIDTH=128 HEIGHT=66 ALIGN=BOTTOM ALT="figure667" SRC="img44.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img44.gif" > <BR>
</P>
<STRONG>Figure 18:</STRONG> Unity-Gain Buffer<BR><P><P><B>Summing and Subtracting </B><P>The op-amp can be used to add two or more signals together as shown in Figure <A HREF="node15.html#opamp12" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opamp12">19</A>.<P><P ALIGN=CENTER><A NAME="675"> </A><A NAME="opamp12"> </A> <IMG WIDTH=224 HEIGHT=164 ALIGN=BOTTOM ALT="figure674" SRC="img45.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img45.gif" > <BR>
</P>
<STRONG>Figure 19:</STRONG> The Summing Amplifier<BR><P><P>The output of this circuit is <IMG WIDTH=176 HEIGHT=24 ALIGN=TOP ALT="tex2html_wrap_inline1882" SRC="img46.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img46.gif" > . This circuit can be used to combine the outputs of many sensors
such as a microphone array.
The op-amp can also be used to subtract two signals as shown in Figure <A HREF="node15.html#opAmp123" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#opAmp123">20</A> This circuit is
commonly used to remove unwanted DC offset. It can also be used to remove differences
in the ground potential of the sensor and the ground potential of the data acquisition
circuitry (so-called ground loops).<P><P ALIGN=CENTER><A NAME="682"> </A><A NAME="opAmp123"> </A> <IMG WIDTH=196 HEIGHT=133 ALIGN=BOTTOM ALT="figure681" SRC="img47.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img47.gif" > <BR>
</P>
<STRONG>Figure 20:</STRONG> Difference Amplifier<BR><P><P>The output of this circuit is given as <IMG WIDTH=109 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline1884" SRC="img48.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img48.gif" > . Thus
<IMG WIDTH=15 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1886" SRC="img49.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img49.gif" > can be the output of the sensor and <IMG WIDTH=14 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1888" SRC="img50.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img50.gif" > can be the signal that is to be removed.<P><B>Instrumentation amplifier</B><P>Possibly the most important circuit configuration for amplifying sensor output is the
instrumentation amplifier (IA). Franco defines the requirements for an IA as follows:
<OL><LI> Finite, accurate and stable gain, usually between 1 and 1000.<LI> Extremely high input impedance.<LI> Extremely low output impedance<LI> Extremely high CMRR.
</OL><P>CMRR (common mode rejection ratio) is defined as:<P> <P> <IMG WIDTH=89 HEIGHT=38 ALIGN=BOTTOM ALT="displaymath1890" SRC="img51.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img51.gif" > <P>
Where:
<P> <IMG WIDTH=278 HEIGHT=81 ALIGN=BOTTOM ALT="eqnarray683" SRC="img52.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img52.gif" > <P>
That is, CMRR is the ratio of the gain of the amplifier for differential-mode signals
(signals that are different between the two inputs) to the gain of the amplifier for
common-mode signals (signals that are the same at both inputs).
The difference amplifier described above, clearly does not satisfy the second requirement
of high input impedance. To solve this problem, a non-inverting amplifier is placed at each
one of the inputs to the difference amplifier as shown in Figure <A HREF="node15.html#rect8" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/node15.html#rect8">21</A>. Remember that a
non-inverting amplifier has a nearly infinite input impedance. Notice that instead of
grounding the resistors, the two resistors are connected together to create one common
resistor, <IMG WIDTH=19 HEIGHT=16 ALIGN=TOP ALT="tex2html_wrap_inline1892" SRC="img53.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img53.gif" > . The overall differential gain of the circuit is:
<IMG WIDTH=114 HEIGHT=25 ALIGN=TOP ALT="tex2html_wrap_inline1894" SRC="img54.gif" tppabs="http://ccrma.stanford.edu/CCRMA/Courses/252/sensors/img54.gif" > ⌨️ 快捷键说明
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