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<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="new34">
  <name>Transistor I-V Characteristics</name>
  <metadata>
  <md:version>2.15</md:version>
  <md:created>2000/08/04</md:created>
  <md:revised>2007/08/22 09:59:57.289 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="wlw">
      <md:firstname>Bill</md:firstname>
      
      <md:surname>Wilson</md:surname>
      <md:email>wlw@madriver.net</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="wlw">
      <md:firstname>Bill</md:firstname>
      
      <md:surname>Wilson</md:surname>
      <md:email>wlw@madriver.net</md:email>
    </md:maintainer>
    <md:maintainer id="lizzardg">
      <md:firstname>Elizabeth</md:firstname>
      
      <md:surname>Gregory</md:surname>
      <md:email>elizabeth.gregory@gmail.com</md:email>
    </md:maintainer>
    <md:maintainer id="jsilv">
      <md:firstname>Jeffrey</md:firstname>
      <md:othername>M</md:othername>
      <md:surname>Silverman</md:surname>
      <md:email>JSilverman@astro.berkeley.edu</md:email>
    </md:maintainer>
    <md:maintainer id="gerardw">
      <md:firstname>Gerard</md:firstname>
      
      <md:surname>Wysocki</md:surname>
      <md:email>gerardw@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>characteristics</md:keyword>
    <md:keyword>transistor</md:keyword>
  </md:keywordlist>

  <md:abstract>Transistor I-V Characteristics
</md:abstract>
</metadata>

  <content>
    <para id="para1">Let's now take a look at some current voltage relationships for
      the bipolar transistor.  In the absence of any voltage or
      current on the emitter-base junction, if we were to make a plot
      of
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:mi>C</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      as a function of
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>V</m:mi>
				<m:mi>CB</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      it would look something like <cnxn target="fig04"/>.  Check back
      with the voltage convention in the figures on <cnxn document="m1014" target="fig1">the structure </cnxn> and <cnxn document="m1014" target="fig2">forward active biasing</cnxn> of a bipolar transistor to make sure you agree with what I drew.  All
      we've got here is a pn junction or diode.  It just happens to be
      biased in a reverse direction, so it conducts when
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>V</m:mi>
				<m:mi>CB</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      is negative and not when
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>V</m:mi>
				<m:mi>CB</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      is positive.  Thus, all we need to do is draw a diode curve, but
      upside down!
    </para>

    <figure id="fig04">
      <media type="image/png" src="3_4.png"/>
      <caption>
	I-V for the collector-base terminals of the bipolar transistor
      </caption>
    </figure>

    <para id="para2">What happens if we now <emphasis>also</emphasis> have some bias
      applied to the emitter-base junction?  As we saw, so long as the
      base-collector junction is reverse biased, almost all of the
      collector current consists of electrons which have been injected
      into the base by the emitter, diffuse across the base region,
      and then fall down the base-collector junction.  The rate at
      which electrons fall down the junction does not depend on how
      large a drop there is (e.g. how big
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>V</m:mi>
				<m:mi>CB</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      is).  The only thing that matters, in so far as the collector
      current is concerned, is how fast electrons are being injected
      into the base region, which is, of course, determined by the
      emitter current
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:mi>E</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      Thus for several different values of emitter current,
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:msub>
					<m:mi>E</m:mi>
					<m:mn>1</m:mn>
				</m:msub>
			</m:msub>
		</m:ci>
	</m:math>,

      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:msub>
					<m:mi>E</m:mi>
					<m:mn>2</m:mn>
				</m:msub>
			</m:msub>
		</m:ci>
	</m:math>, and

      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:msub>
					<m:mi>E</m:mi>
					<m:mn>1</m:mn>
				</m:msub>
			</m:msub>
		</m:ci>
	</m:math>, we might see something like <cnxn target="fig05"/>.
      In the first quadrant, which is in the "forward active bias
      mode," the output from the collector terminal looks more or
      less like a current source; that is

      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:mi>C</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      is a constant, regardless of what
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>V</m:mi>
				<m:mi>CB</m:mi>
			</m:msub>
		</m:ci>
	</m:math>
      is.  Note however, that we must use a <term>controlled
      source</term>, in this case, a current-controlled current
      source, since

      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:mi>C</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      depends on what
      <m:math>
		<m:ci>
			<m:msub>
				<m:mi>I</m:mi>
				<m:mi>E</m:mi>
			</m:msub>
		</m:ci>
	</m:math>

      happens to be.  Obviously, looking in the (forward biased)
      emitter-base terminal, we see the usual p-n junction.  Thus, if
      we were interested in building a "model" of this device, we
      might come up with something like <cnxn target="fig06"/>.  Note
      that the base terminal is common to both inputs.  Since we would
      actually like to think of the transistor as a two-port device
      (with an input and an output) the model for the transistor is
      often drawn as shown in <cnxn target="fig07"/>.
    </para>

    <figure id="fig05">
      <media type="image/png" src="3_5.png"/>
      <caption>
	Common base characteristics of the bipolar transistor
      </caption>
    </figure>

    <figure id="fig06">
      <media type="image/png" src="3_6.png"/>
      <caption>Model for the common base transistor</caption>
    </figure>

    <figure id="fig07">
      <media type="image/png" src="3_7.png"/>
      <caption>Re-drawn common base transistor</caption>
    </figure>

    <para id="para3">
      The only drawback with what we have so far is that except in
      some specialized high-frequency circuits, the bipolar transistor
      is very rarely used in the common base configuration.  Most of
      the time, you will see it in either <cnxn target="fig08">the
      common emitter configuration</cnxn>, or the common collector
      configuration.  The common emitter is probably the way the
      transistor is most often used.
    </para>

    <figure id="fig08"><media type="image/png" src="3_8.png"/>
	<caption>Configuration for the common emitter circuit</caption>
</figure>

    <para id="para4">
      Note that we have a current source driving the base, and we have
      applied just one battery all the way from the collector to the
      emitter.  The battery now has to do two thing: a) It has to
      provide reverse bias for the base-collector junction and b) it
      has to provide forward bias for the base emitter junction.  For
      this reason, the

      <m:math>
        <m:ci>
          <m:msub>
            <m:mi>I</m:mi>
            <m:mi>C</m:mi>
          </m:msub>
        </m:ci>
      </m:math>

      as a function of
      <m:math>
        <m:ci>
          <m:msub>
            <m:mi>V</m:mi>
            <m:mi>CE</m:mi>
          </m:msub>
        </m:ci>
      </m:math>

      curves look a little different now.  It is now necessary for
      <m:math>
        <m:ci>
          <m:msub>
            <m:mi>V</m:mi>
            <m:mi>CE</m:mi>
          </m:msub>
        </m:ci>
      </m:math>

      to become slightly positive in order to get the transistor into
      its active mode.  The other difference, of course, is that the
      collector current is now shown as being

      <m:math>
        <m:apply><m:times/>
          <m:ci>β</m:ci>
          <m:ci>
            <m:msub>
              <m:mi>I</m:mi>
              <m:mi>B</m:mi>
            </m:msub>
          </m:ci>
        </m:apply>
      </m:math>

      the base current instead of
      <m:math>
        <m:apply><m:times/>
          <m:ci>α</m:ci>
          <m:ci>
            <m:msub>
              <m:mi>I</m:mi>
              <m:mi>E</m:mi>
            </m:msub>
          </m:ci>
        </m:apply>
      </m:math>
      the emitter current.
    </para>

    <figure id="fig09"><media type="image/png" src="3_9.png"/>
	<caption>
	Common emitter characteristic curves for the transistor
      </caption>
</figure> 
  </content>
  
</document>
