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	<title>Mastering Electronics Design&#187; Operational Amplifier Formulas</title>
	<atom:link href="http://masteringelectronicsdesign.com/category/operational-amplifier-formulas/feed/" rel="self" type="application/rss+xml" />
	<link>http://masteringelectronicsdesign.com</link>
	<description>Electronics Design and Modeling with Emphasis on Analog Design</description>
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		<title>The Non-Inverting Amplifier Output Resistance</title>
		<link>http://masteringelectronicsdesign.com/the-non-inverting-amplifier-output-resistance/</link>
		<comments>http://masteringelectronicsdesign.com/the-non-inverting-amplifier-output-resistance/#comments</comments>
		<pubDate>Wed, 23 Dec 2009 07:38:58 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[dependent sources]]></category>
		<category><![CDATA[non-inverting]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[output resistance]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1003</guid>
		<description><![CDATA[It is customary to consider the output resistance of the non-inverting amplifier as being zero, but why is that?  An Op Amp’s own output resistance is in the range of tens of ohms.  Still, when we connect the Op Amp in a feedback configuration, the output resistance decreases dramatically.  Why?


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/the-common-collector-amplifier-input-and-output-resistance/' rel='bookmark' title='Permanent Link: The Common-Collector Amplifier Input and Output Resistance &#8211; The Proof'>The Common-Collector Amplifier Input and Output Resistance &#8211; The Proof</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Inverting Amplifier Transfer Function'>How to Derive the Inverting Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/' rel='bookmark' title='Permanent Link: How to Derive the Transfer Function of the  Inverting Summing Amplifier'>How to Derive the Transfer Function of the  Inverting Summing Amplifier</a></li></ol>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>How to Derive the Inverting Amplifier Transfer Function</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/#comments</comments>
		<pubDate>Fri, 27 Nov 2009 03:33:40 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[inverting]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[proof]]></category>
		<category><![CDATA[transfer function]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=979</guid>
		<description><![CDATA[Widely used in Analog Design, the inverting amplifier in Figure 1 has a simple transfer function.  What is the proof of this function? 


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/' rel='bookmark' title='Permanent Link: How to Derive the Transfer Function of the  Inverting Summing Amplifier'>How to Derive the Transfer Function of the  Inverting Summing Amplifier</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-non-inverting-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Non-Inverting Amplifier Transfer Function'>How to Derive the Non-Inverting Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Differential Amplifier Transfer Function'>How to Derive the Differential Amplifier Transfer Function</a></li></ol>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>How to Derive the Non-Inverting Amplifier Transfer Function</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-non-inverting-amplifier-transfer-function/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-non-inverting-amplifier-transfer-function/#comments</comments>
		<pubDate>Sat, 29 Aug 2009 06:57:03 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[non-inverting]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[transfer function]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=438</guid>
		<description><![CDATA[One of the most common amplifiers in Analog Design is the non-inverting amplifier.  How do you derive its transfer function?


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Inverting Amplifier Transfer Function'>How to Derive the Inverting Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/' rel='bookmark' title='Permanent Link: How to Derive the Transfer Function of the  Inverting Summing Amplifier'>How to Derive the Transfer Function of the  Inverting Summing Amplifier</a></li><li><a href='http://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Differential Amplifier Transfer Function'>How to Derive the Differential Amplifier Transfer Function</a></li></ol>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Useful Operational Amplifier Formulas and Configurations</title>
		<link>http://masteringelectronicsdesign.com/useful-operational-amplifier-formulas-and-configurations/</link>
		<comments>http://masteringelectronicsdesign.com/useful-operational-amplifier-formulas-and-configurations/#comments</comments>
		<pubDate>Mon, 24 Aug 2009 01:57:49 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[Differential Amplifier]]></category>
		<category><![CDATA[non-inverting]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[Summing amplifier]]></category>
		<category><![CDATA[transfer function]]></category>
		<category><![CDATA[voltage follower]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=577</guid>
		<description><![CDATA[A compilation of Op Amp configurations and transfer functions. 


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/' rel='bookmark' title='Permanent Link: The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals'>The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals</a></li><li><a href='http://masteringelectronicsdesign.com/converting-a-differential-amplifier-into-a-summing-amplifier/' rel='bookmark' title='Permanent Link: Converting a Differential Amplifier into a Summing Amplifier'>Converting a Differential Amplifier into a Summing Amplifier</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Summing Amplifier Transfer Function'>How to Derive the Summing Amplifier Transfer Function</a></li></ol>]]></description>
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		<slash:comments>2</slash:comments>
		</item>
		<item>
		<title>How to Derive the Transfer Function of the  Inverting Summing Amplifier</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/#comments</comments>
		<pubDate>Mon, 17 Aug 2009 04:53:56 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[Summing amplifier]]></category>
		<category><![CDATA[Superposition Theorem]]></category>
		<category><![CDATA[inverting summing amplifier]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[proof]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=541</guid>
		<description><![CDATA[The inverting summing amplifier does exactly what its name says: adds the input signals and inverts the result.  This amplifier presents a major advantage versus the non-inverting summing amplifier.  The input signals are added with their own gain.  The disadvantage is the inversion of the sum, which might not be desirable in some cases.  How can we derive this function?  What is the transfer function of the inverting summing amplifier with 3, 4, or n inputs?  This article answers all these questions.


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Inverting Amplifier Transfer Function'>How to Derive the Inverting Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/' rel='bookmark' title='Permanent Link: The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals'>The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Summing Amplifier Transfer Function'>How to Derive the Summing Amplifier Transfer Function</a></li></ol>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals</title>
		<link>http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/</link>
		<comments>http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/#comments</comments>
		<pubDate>Sun, 09 Aug 2009 21:52:02 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[Summing amplifier]]></category>
		<category><![CDATA[Superposition Theorem]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[analog]]></category>
		<category><![CDATA[non-inverting]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[proof]]></category>
		<category><![CDATA[summing amplifier formula]]></category>
		<category><![CDATA[transfer function]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=486</guid>
		<description><![CDATA[In a previous article, How to Derive the Summing Amplifier Transfer Function, I deduced the formula for the non-inverting summing amplifier with two signals in its input.  But what if we have 3, 4 or an n number of signals?  Can we add them all with one amplifier?


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/' rel='bookmark' title='Permanent Link: How to Derive the Transfer Function of the  Inverting Summing Amplifier'>How to Derive the Transfer Function of the  Inverting Summing Amplifier</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Summing Amplifier Transfer Function'>How to Derive the Summing Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Inverting Amplifier Transfer Function'>How to Derive the Inverting Amplifier Transfer Function</a></li></ol>]]></description>
		<wfw:commentRss>http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/feed/</wfw:commentRss>
		<slash:comments>4</slash:comments>
		</item>
		<item>
		<title>How to Derive the Summing Amplifier Transfer Function</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/#comments</comments>
		<pubDate>Thu, 09 Jul 2009 06:21:45 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[Summing amplifier]]></category>
		<category><![CDATA[Superposition Theorem]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[analog]]></category>
		<category><![CDATA[non-inverting]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[proof]]></category>
		<category><![CDATA[summing amplifier formula]]></category>
		<category><![CDATA[transfer function]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=413</guid>
		<description><![CDATA[The summing amplifier, or the non-inverting summing amplifier, is an analog processing circuit with the transfer function (the summing amplifier formula as some say) shown in the following equation.




(1)



The first term of the product is the actual summing, while the second term is a gain due to the R3 and R4 resistors.  I prefer this [...]


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-transfer-function-of-the-inverting-summing-amplifier/' rel='bookmark' title='Permanent Link: How to Derive the Transfer Function of the  Inverting Summing Amplifier'>How to Derive the Transfer Function of the  Inverting Summing Amplifier</a></li><li><a href='http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/' rel='bookmark' title='Permanent Link: The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals'>The Transfer Function of the Non-Inverting Summing Amplifier with “N” Input Signals</a></li><li><a href='http://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Differential Amplifier Transfer Function'>How to Derive the Differential Amplifier Transfer Function</a></li></ol>]]></description>
		<wfw:commentRss>http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/feed/</wfw:commentRss>
		<slash:comments>19</slash:comments>
		</item>
		<item>
		<title>How to Derive the Differential Amplifier Transfer Function</title>
		<link>http://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/</link>
		<comments>http://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/#comments</comments>
		<pubDate>Thu, 07 May 2009 12:14:46 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Differential Amplifier]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[Superposition Theorem]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[differential amplifier formula]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[proof]]></category>
		<category><![CDATA[transfer function]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=156</guid>
		<description><![CDATA[The transfer function of the differential amplifier, also known as difference amplifier, can be found in articles, websites, formula tables, but where is it coming from? Why is the differential amplifier transfer function as in the following mathematical relation? ...


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Summing Amplifier Transfer Function'>How to Derive the Summing Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-instrumentation-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Instrumentation Amplifier Transfer Function'>How to Derive the Instrumentation Amplifier Transfer Function</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/' rel='bookmark' title='Permanent Link: How to Derive the Inverting Amplifier Transfer Function'>How to Derive the Inverting Amplifier Transfer Function</a></li></ol>]]></description>
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		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>Solving the Differential Amplifier &#8211; Part 1</title>
		<link>http://masteringelectronicsdesign.com/solving-the-differential-amplifier-part-1/</link>
		<comments>http://masteringelectronicsdesign.com/solving-the-differential-amplifier-part-1/#comments</comments>
		<pubDate>Fri, 24 Apr 2009 06:25:49 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Differential Amplifier]]></category>
		<category><![CDATA[Electronic Circuits Examples]]></category>
		<category><![CDATA[Operational Amplifier Formulas]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[design]]></category>
		<category><![CDATA[operational amplifier]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=26</guid>
		<description><![CDATA[Design a Differential Amplifier based on the Input and Output Range Requirements. 
What is the common usage of the differential amplifier? The circuit is used to amplify the difference between the input signals.  However, there are times when the electronics designer is faced with the following problem:  Given an input range of, say, -0.5V to 5.5V, the output has to swing between, say -1.25V and +2.365V. It is clear that this requires an amplifier with a certain gain and an offset different than zero.  How can we design the differential amplifier to achieve such a function? 


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		<slash:comments>2</slash:comments>
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