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  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Logarithmic Amplifier</name>

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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Don</md:firstname>
      
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      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Carol</md:firstname>
      
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  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Logarithmic amplifiers</md:abstract>
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    <figure 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="diode3">
      <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Diode Circuit</name>
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    </figure>
    <para 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="one"> Here is a circuit involving a diode that is
      actually simpler to analyze than the previous one. We know that
      the current through the resistor must equal that through the
      diode. Thus, the diode's current is proportional to the input
      voltage. As the voltage across the diode is related to the
      logarithm of its current, we see that the input-output relation
      is
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	<m:math>
	  <m:apply>
	    <m:eq/>
	    <m:ci>
	      <m:msub>
		<m:mi>v</m:mi>
		<m:mi>out</m:mi>
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	      <m:minus/>
	      <m:apply>
		<m:times/>
		<m:apply>
		  <m:divide/>
                  <m:apply>
                    <m:times/>
		    <m:ci>k</m:ci>
		    <m:ci>T</m:ci>
                  </m:apply>
                  <m:ci>q</m:ci>
		</m:apply>
		<m:apply>
		  <m:ln/>
                  <m:apply>
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		    <m:apply>
		      <m:divide/>
		      <m:ci>
			<m:msub>
			  <m:mi>v</m:mi>
			  <m:mi>in</m:mi>
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			<m:times/>
			<m:ci>R</m:ci>
			<m:ci>
			  <m:msub>
			    <m:mi>I</m:mi>
			    <m:mn>0</m:mn>
			  </m:msub>
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                  </m:apply>
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	      </m:apply>
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      </equation>  Clearly, the name <term xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">logarithmic amplifier
      </term>is justified for this circuit.  </para>

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