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	<title>Mastering Electronics Design&#187; Analog Design</title>
	<atom:link href="http://masteringelectronicsdesign.com/category/analog-design/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 RMS Value of a Trapezoidal Waveform – Part 2</title>
		<link>http://masteringelectronicsdesign.com/the-rms-value-of-a-trapezoidal-waveform-part-2/</link>
		<comments>http://masteringelectronicsdesign.com/the-rms-value-of-a-trapezoidal-waveform-part-2/#comments</comments>
		<pubDate>Fri, 23 Jul 2010 04:05:58 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Waveforms]]></category>
		<category><![CDATA[pulse]]></category>
		<category><![CDATA[RMS]]></category>
		<category><![CDATA[trapezoidal]]></category>
		<category><![CDATA[waveform]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1565</guid>
		<description><![CDATA[In a previous article, How to Derive the RMS Value of Pulse and Square Waveforms, I showed how to derive the RMS value of a pulse signal.  In some applications, the trapezoidal signal plateau is not flat, but rather a ramp, as shown in Figure 1.  A typical example is a DC-DC converter, where the transformer winding current might look like the signal in Figure 1.  The waveform is still considered a trapezoidal waveform. Let’s calculate its RMS value.


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of a Trapezoidal Waveform'>How to Derive the RMS Value of a Trapezoidal Waveform</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of a Triangle Waveform'>How to Derive the RMS Value of a Triangle Waveform</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of Pulse and Square Waveforms'>How to Derive the RMS Value of Pulse and Square Waveforms</a></li></ol>]]></description>
		<wfw:commentRss>http://masteringelectronicsdesign.com/the-rms-value-of-a-trapezoidal-waveform-part-2/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Using the Summing Amplifier as an Average Amplifier</title>
		<link>http://masteringelectronicsdesign.com/using-the-summing-amplifier-as-an-average-amplifier/</link>
		<comments>http://masteringelectronicsdesign.com/using-the-summing-amplifier-as-an-average-amplifier/#comments</comments>
		<pubDate>Sun, 04 Jul 2010 00:28:07 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Electronic Circuits Examples]]></category>
		<category><![CDATA[Summing amplifier]]></category>
		<category><![CDATA[Waveforms]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[summing amplifier examples]]></category>
		<category><![CDATA[summing amplifier formula]]></category>
		<category><![CDATA[waveform]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1539</guid>
		<description><![CDATA[The summing amplifier can output the average of two, three or more signals. This is different than a signal average. The summing amplifier cannot, for example, output the average of a triangle signal. For that, you need an integrator to perform the average in the analog realm, or you need to sample the signal and calculate the average with a microcontroller. This type of average is the signal average in the time domain. I will write an article about the average of a signal in a near future.


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/design-bipolar-unipolar-converter-with-3-input-summ-amplifier/' rel='bookmark' title='Permanent Link: Design a Bipolar to Unipolar Converter with a 3-input Summing Amplifier'>Design a Bipolar to Unipolar Converter with a 3-input Summing Amplifier</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>
		<wfw:commentRss>http://masteringelectronicsdesign.com/using-the-summing-amplifier-as-an-average-amplifier/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>How to Derive the RMS Value of Pulse and Square Waveforms</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/#comments</comments>
		<pubDate>Sun, 13 Jun 2010 01:19:14 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Waveforms]]></category>
		<category><![CDATA[bipolar]]></category>
		<category><![CDATA[pulse]]></category>
		<category><![CDATA[RMS]]></category>
		<category><![CDATA[square]]></category>
		<category><![CDATA[waveform]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1489</guid>
		<description><![CDATA[The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. The pulse waveform is shown in Figure 1. The ratio t1/T is the pulse signal duty-cycle. As shown in other articles in this website (How to Derive the RMS Value of a Trapezoidal Waveform and How to Derive the RMS Value of a Triangle Waveform), the RMS definition is an integral over the signal period as in equation (1).


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of a Triangle Waveform'>How to Derive the RMS Value of a Triangle Waveform</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of a Trapezoidal Waveform'>How to Derive the RMS Value of a Trapezoidal Waveform</a></li><li><a href='http://masteringelectronicsdesign.com/the-rms-value-of-a-trapezoidal-waveform-part-2/' rel='bookmark' title='Permanent Link: The RMS Value of a Trapezoidal Waveform – Part 2'>The RMS Value of a Trapezoidal Waveform – Part 2</a></li></ol>]]></description>
		<wfw:commentRss>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>How to Derive the RMS Value of a Triangle Waveform</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/#comments</comments>
		<pubDate>Mon, 07 Jun 2010 05:26:49 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Waveforms]]></category>
		<category><![CDATA[bipolar]]></category>
		<category><![CDATA[RMS]]></category>
		<category><![CDATA[triangle]]></category>
		<category><![CDATA[waveform]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1455</guid>
		<description><![CDATA[What is the RMS value of a periodic signal?  When a periodic signal is generated by a source connected to a load, a resistor for example, the RMS value is the continuous signal, the DC value which would deliver the same power to the load as the periodic signal.

This article shows how to derive the RMS value of triangle waveforms with different shapes and duty cycles.


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of a Trapezoidal Waveform'>How to Derive the RMS Value of a Trapezoidal Waveform</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of Pulse and Square Waveforms'>How to Derive the RMS Value of Pulse and Square Waveforms</a></li><li><a href='http://masteringelectronicsdesign.com/using-the-summing-amplifier-as-an-average-amplifier/' rel='bookmark' title='Permanent Link: Using the Summing Amplifier as an Average Amplifier'>Using the Summing Amplifier as an Average Amplifier</a></li></ol>]]></description>
		<wfw:commentRss>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>How to Derive the RMS Value of a Trapezoidal Waveform</title>
		<link>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/#comments</comments>
		<pubDate>Sat, 15 May 2010 04:35:10 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Waveforms]]></category>
		<category><![CDATA[RMS]]></category>
		<category><![CDATA[trapezoidal]]></category>
		<category><![CDATA[waveform]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1402</guid>
		<description><![CDATA[In this article I will show you how to calculate the RMS value of a trapezoidal waveform. This periodic waveform is shown in Figure 1. It has a rise time from 0 to t1 and a fall time from t2 to t3. The plateau is between t1 and t2, and the signal is periodic with the period T. If you know this, then you can derive the RMS value of a triangle, square and pulse waveform as well. 


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of a Triangle Waveform'>How to Derive the RMS Value of a Triangle Waveform</a></li><li><a href='http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/' rel='bookmark' title='Permanent Link: How to Derive the RMS Value of Pulse and Square Waveforms'>How to Derive the RMS Value of Pulse and Square Waveforms</a></li><li><a href='http://masteringelectronicsdesign.com/using-the-summing-amplifier-as-an-average-amplifier/' rel='bookmark' title='Permanent Link: Using the Summing Amplifier as an Average Amplifier'>Using the Summing Amplifier as an Average Amplifier</a></li></ol>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>A Summing and Differential Amplifier with One Op Amp</title>
		<link>http://masteringelectronicsdesign.com/a-summing-and-differential-amplifier-with-one-op-amp/</link>
		<comments>http://masteringelectronicsdesign.com/a-summing-and-differential-amplifier-with-one-op-amp/#comments</comments>
		<pubDate>Sun, 18 Apr 2010 01:27:36 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Differential Amplifier]]></category>
		<category><![CDATA[Summing amplifier]]></category>
		<category><![CDATA[Superposition Theorem]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[inverting]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1366</guid>
		<description><![CDATA[In a comment, one of my readers asked me what is the transfer function of the non-inverting summing amplifier in Figure 1, when R3 is connected to a reference voltage instead of ground.  Well, this is a summing amplifier with a differential configuration. 


Related posts:<ol><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/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><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>
		<wfw:commentRss>http://masteringelectronicsdesign.com/a-summing-and-differential-amplifier-with-one-op-amp/feed/</wfw:commentRss>
		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>An ADC and DAC Least Significant Bit (LSB)</title>
		<link>http://masteringelectronicsdesign.com/an-adc-and-dac-least-significant-bit-lsb/</link>
		<comments>http://masteringelectronicsdesign.com/an-adc-and-dac-least-significant-bit-lsb/#comments</comments>
		<pubDate>Tue, 23 Mar 2010 07:03:05 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Mixed-Signal Design]]></category>
		<category><![CDATA[ADC]]></category>
		<category><![CDATA[analog to digital converters]]></category>
		<category><![CDATA[DAC]]></category>
		<category><![CDATA[digital to analog converters]]></category>
		<category><![CDATA[LSB]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1331</guid>
		<description><![CDATA[Articles on Internet and different books show how to calculate the Least Significant Bit (LSB), but they take into consideration either the voltage reference (Vref) or the full scale (FS) of the ADC or DAC.  Many times this leads to confusion, as a few messages I received from my readers show.  Therefore, this article shows both ways of defining the LSB, so that people will have a clear understanding how to treat an ADC’s (Analog-to-Digital-Converter) or DAC’s (Digital-to-Analog-Converter) LSB.


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/an-adc-and-dac-integral-non-linearity-inl/' rel='bookmark' title='Permanent Link: An ADC and DAC Integral Non-Linearity (INL)'>An ADC and DAC Integral Non-Linearity (INL)</a></li><li><a href='http://masteringelectronicsdesign.com/an-adc-and-dac-differential-non-linearity-dnl/' rel='bookmark' title='Permanent Link: An ADC and DAC Differential Non-Linearity (DNL)'>An ADC and DAC Differential Non-Linearity (DNL)</a></li><li><a href='http://masteringelectronicsdesign.com/design-a-unipolar-to-bipolar-converter-for-a-unipolar-voltage-output-dac/' rel='bookmark' title='Permanent Link: Design a Unipolar to Bipolar Converter for a Unipolar Voltage Output DAC'>Design a Unipolar to Bipolar Converter for a Unipolar Voltage Output DAC</a></li></ol>]]></description>
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		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>Differential Amplifier Output Common-Mode Voltage Calculator</title>
		<link>http://masteringelectronicsdesign.com/differential-amplifier-output-common-mode-voltage-calculator/</link>
		<comments>http://masteringelectronicsdesign.com/differential-amplifier-output-common-mode-voltage-calculator/#comments</comments>
		<pubDate>Sun, 28 Feb 2010 23:47:20 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Calculators]]></category>
		<category><![CDATA[Differential Amplifier]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[calculator]]></category>
		<category><![CDATA[common-mode]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[operational amplifier]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1314</guid>
		<description><![CDATA[A differential amplifier frequent use is the amplification of the voltage difference between its input signals, while rejecting the common-mode level.  However, the output common-mode level cannot be zero.  The operational amplifier technological limitations, as well as the outside resistor tolerances let the common-mode voltage to make it to the amplifier output as an output error.  As a consequence, the amplifier output voltage is the input signal difference times gain, plus the output common-mode voltage.

Based on the resistor tolerances, this calculator will show the output common-mode voltage, Vocm, and the total voltage, Vout, at the differential amplifier output.  Vocm will alter the ideal output voltage, which can be calculated when the resistors are perfectly matched.


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/the-differential-amplifier-common-mode-error-part-1/' rel='bookmark' title='Permanent Link: The Differential Amplifier Common-Mode Error – Part 1'>The Differential Amplifier Common-Mode Error – Part 1</a></li><li><a href='http://masteringelectronicsdesign.com/the-differential-amplifier-common-mode-error-part-2/' rel='bookmark' title='Permanent Link: The Differential Amplifier Common-Mode Error – Part 2'>The Differential Amplifier Common-Mode Error – Part 2</a></li><li><a href='http://masteringelectronicsdesign.com/differential-amplifier-calculator-2/' rel='bookmark' title='Permanent Link: Differential Amplifier Calculator'>Differential Amplifier Calculator</a></li></ol>]]></description>
		<wfw:commentRss>http://masteringelectronicsdesign.com/differential-amplifier-output-common-mode-voltage-calculator/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>How to Design a Circuit from its Transfer Function Graph</title>
		<link>http://masteringelectronicsdesign.com/how-to-design-a-circuit-from-its-transfer-function-graph/</link>
		<comments>http://masteringelectronicsdesign.com/how-to-design-a-circuit-from-its-transfer-function-graph/#comments</comments>
		<pubDate>Sun, 21 Feb 2010 02:53:23 +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[amplifier]]></category>
		<category><![CDATA[differential amplifier formula]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[operational amplifier]]></category>
		<category><![CDATA[transfer function]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1297</guid>
		<description><![CDATA[Sometimes all we know about a circuit is its transfer function graph.  The transfer function might look like the one in Figure 1.  How can we design a circuit so that its input-output behavior will match the graph?


Related posts:<ol><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><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></ol>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Differential Amplifier Calculator</title>
		<link>http://masteringelectronicsdesign.com/differential-amplifier-calculator-2/</link>
		<comments>http://masteringelectronicsdesign.com/differential-amplifier-calculator-2/#comments</comments>
		<pubDate>Sun, 07 Feb 2010 01:58:59 +0000</pubDate>
		<dc:creator>Adrian S. Nastase</dc:creator>
				<category><![CDATA[Analog Design]]></category>
		<category><![CDATA[Calculators]]></category>
		<category><![CDATA[Differential Amplifier]]></category>
		<category><![CDATA[bipolar]]></category>
		<category><![CDATA[converter]]></category>
		<category><![CDATA[differential amplifier formula]]></category>
		<category><![CDATA[op amp]]></category>
		<category><![CDATA[op amp (opamp) formulas]]></category>
		<category><![CDATA[unipolar]]></category>

		<guid isPermaLink="false">http://masteringelectronicsdesign.com/?p=1287</guid>
		<description><![CDATA[If you need to design a differential amplifier, here is a handy calculator.  All you need to define are the input range, the output range and a choice of a voltage reference.  The default values for this calculator are set for a unipolar to bipolar converter.


Related posts:<ol><li><a href='http://masteringelectronicsdesign.com/differential-amplifier-output-common-mode-voltage-calculator/' rel='bookmark' title='Permanent Link: Differential Amplifier Output Common-Mode Voltage Calculator'>Differential Amplifier Output Common-Mode Voltage Calculator</a></li><li><a href='http://masteringelectronicsdesign.com/design-a-differential-amplifier-the-easy-way-with-mathcad/' rel='bookmark' title='Permanent Link: Design a Differential Amplifier the Easy Way with Mathcad'>Design a Differential Amplifier the Easy Way with Mathcad</a></li><li><a href='http://masteringelectronicsdesign.com/summing-amplifier-calculator-java/' rel='bookmark' title='Permanent Link: Summing Amplifier Calculator'>Summing Amplifier Calculator</a></li></ol>]]></description>
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		<slash:comments>0</slash:comments>
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