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	<title>Weak trace-class operator - Revision history</title>
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	<updated>2026-05-19T21:36:10Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://en.formulasearchengine.com/index.php?title=Weak_trace-class_operator&amp;diff=29978&amp;oldid=prev</id>
		<title>en&gt;Yobot: Category first letter small using AWB (9513)</title>
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		<updated>2013-10-08T06:10:57Z</updated>

		<summary type="html">&lt;p&gt;Category first letter small using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt; (9513)&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Legg&amp;#039;s equation&amp;#039;&amp;#039;&amp;#039; models magnetic material core loss at low flux densities.  The equation has three loss components: hysteresis, residual, and eddy current.&amp;lt;ref&amp;gt;{{harvnb|Arnold Engineering Company|unknown|p=70}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{harvnb|Legg|1936}}&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;{{harvnb|Snelling|1988|p=38}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Equation==&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{R_{\text{ac}}}{\mu L} = a B_{\text{max}} f + c f + e f^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where&lt;br /&gt;
:: &amp;#039;&amp;#039;R&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;ac&amp;lt;/sub&amp;gt; is the effective core loss resistance (ohms)&lt;br /&gt;
:: &amp;#039;&amp;#039;&amp;amp;mu;&amp;#039;&amp;#039; is the material permeability&lt;br /&gt;
:: &amp;#039;&amp;#039;L&amp;#039;&amp;#039; is the inductance (henrys)&lt;br /&gt;
:: &amp;#039;&amp;#039;a&amp;#039;&amp;#039; hysteresis loss coefficient&lt;br /&gt;
:: &amp;#039;&amp;#039;B&amp;#039;&amp;#039;&amp;lt;sub&amp;gt;max&amp;lt;/sub&amp;gt; is the maximum flux density (gauss)&lt;br /&gt;
:: &amp;#039;&amp;#039;c&amp;#039;&amp;#039; is the residual loss coefficient&lt;br /&gt;
:: &amp;#039;&amp;#039;f&amp;#039;&amp;#039; is the frequency (hertz)&lt;br /&gt;
:: &amp;#039;&amp;#039;e&amp;#039;&amp;#039; is the eddy loss coefficient&lt;br /&gt;
&lt;br /&gt;
IEC Technical Committee is the modern definition.&amp;lt;ref&amp;gt;{{harvnb|Snelling|1988|p=38}} refers to Publication 401&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
*{{Citation |last=Arnold Engineering Company |title=MPP Cores |publisher=Arnold Engineering Company |location=Marengo, IL }}&lt;br /&gt;
*{{Citation |last=Legg |first=Victor E. |title=Magnetic Measurements at Low Flux Densities Using the Alternating Current Bridge |publisher=Bell Telephone Laboratories |journal=[[Bell System Technical Journal]] |volume=15 |issue=1 |pages=39&amp;amp;ndash;63 |date=January 1936 |url=http://www3.alcatel-lucent.com/bstj/vol15-1936/articles/bstj15-1-39.pdf }}&lt;br /&gt;
*{{Citation |last=Snelling |first=E. C. |title=Soft Ferrites: Properties and Applications |edition=second |publisher=Butterworths |location=London |year=1988 |isbn=0-408-02760-6 }}&lt;br /&gt;
&lt;br /&gt;
[[Category:Electromagnetic components]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{sci-stub}}&lt;/div&gt;</summary>
		<author><name>en&gt;Yobot</name></author>
	</entry>
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