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	<title>Cutler&#039;s bar notation - Revision history</title>
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	<updated>2026-06-05T09:52:09Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<title>72.208.80.113: /* Advantages and drawbacks */</title>
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		<updated>2014-08-14T21:53:08Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Advantages and drawbacks&lt;/span&gt;&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Cutler%27s_bar_notation&amp;amp;diff=252415&amp;amp;oldid=16024&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>72.208.80.113</name></author>
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		<id>https://en.formulasearchengine.com/index.php?title=Cutler%27s_bar_notation&amp;diff=16024&amp;oldid=prev</id>
		<title>en&gt;GoingBatty: Disambiguated: notation system → Mathematical notation</title>
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		<updated>2012-08-19T19:39:56Z</updated>

		<summary type="html">&lt;p&gt;Disambiguated: &lt;a href=&quot;/index.php?title=Notation_system&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Notation system (page does not exist)&quot;&gt;notation system&lt;/a&gt; → &lt;a href=&quot;/index.php?title=Mathematical_notation&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Mathematical notation (page does not exist)&quot;&gt;Mathematical notation&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;In [[electronics]], a &amp;#039;&amp;#039;&amp;#039;step recovery diode&amp;#039;&amp;#039;&amp;#039; (&amp;#039;&amp;#039;&amp;#039;SRD&amp;#039;&amp;#039;&amp;#039;) is a [[Diode#Semiconductor_diodes|semiconductor junction diode]] having the ability to generate extremely short pulses. It is also called &amp;#039;&amp;#039;&amp;#039;snap-off diode&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;charge-storage diode&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;memory [[varactor]]&amp;#039;&amp;#039;&amp;#039;, and has a variety of uses in [[microwave]] electronics as [[pulse generator]] or [[parametric amplifier]].&lt;br /&gt;
&lt;br /&gt;
When diodes switch from forward conduction to reverse cut-off, a reverse current flows briefly as stored charge is removed.  It is the abruptness with which this reverse current ceases which characterises the step recovery diode.&lt;br /&gt;
&lt;br /&gt;
== Historical note ==&lt;br /&gt;
The first published paper on the SRD is {{Harv|Boff|Moll|Shen|1960}}: the authors start the brief survey stating that &amp;quot;the recovery characteristics of certain types of [[Diode#pn-junction diode|pn-junction diodes]] exhibit a discontinuity which may be used to advantage for the generation of harmonics or for the production of [[nanosecond|millimicrosecond]] pulses&amp;quot;. They also refer that they first observed this phenomenon in February, 1959.&lt;br /&gt;
&lt;br /&gt;
== Operating the SRD ==&lt;br /&gt;
&lt;br /&gt;
=== Physical principles ===&lt;br /&gt;
The main phenomenon used in SRDs is the storage of [[electric charge]] during forward [[Electrical conduction|conduction]], which is present in all [[Diode#Semiconductor_diodes|semiconductor junction diodes]] and is due to finite lifetime of [[minority carrier]]s in [[semiconductor]]s. Assume that the SRD is forward [[Voltage bias|biased]] and in &amp;#039;&amp;#039;[[steady state]]&amp;#039;&amp;#039; i.e. the [[anode]] [[current bias|bias current]] does not change with time: since charge transport in a junction diode is mainly due to diffusion, i.e. to   a non constant spatial charge carrier density caused by bias voltage, a charge &amp;#039;&amp;#039;Q&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039; is stored in the device. This &amp;#039;&amp;#039;stored charge&amp;#039;&amp;#039; depends on&lt;br /&gt;
&lt;br /&gt;
#&amp;#039;&amp;#039;Intensity of the forward anode current&amp;#039;&amp;#039; &amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;I&amp;lt;sub&amp;gt;A&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039; flowing in the device during its steady state.&lt;br /&gt;
#&amp;#039;&amp;#039;Minority carrier lifetime&amp;#039;&amp;#039; &amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;τ&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;, i.e. the mean time a free [[charge carrier]] moves inside a semiconductor region before [[Carrier generation and recombination|recombining]].&lt;br /&gt;
&lt;br /&gt;
Quantitatively, if the steady state of forward conduction lasts for a time much greater than &amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;τ&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;, the stored charge has the following approximate expression&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;Q_S\cong I_A\cdot\tau&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Now suppose that the voltage bias abruptly changes, switching from its stationary positive value to a higher [[Magnitude (mathematics)|magnitude]] constant negative value: then, since a certain amount of charge has been stored during forward conduction, diode resistance is still low (&amp;#039;&amp;#039;i.e. the anode-to-cathode voltage &amp;#039;&amp;#039;&amp;#039;V&amp;lt;sub&amp;gt;AK&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039;&amp;#039; has nearly the same forward conduction value&amp;#039;&amp;#039;). Anode current does not cease but reverses its polarity (i.e. the direction of its flow) and stored charge &amp;#039;&amp;#039;Q&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039; starts to flow out of the device at an almost constant rate &amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;I&amp;lt;sub&amp;gt;R&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;. All the stored charge is thus removed in a certain amount of time: this time is the &amp;#039;&amp;#039;storage time &amp;#039;&amp;#039;&amp;#039;t&amp;lt;sub&amp;gt;S&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039; and its approximate expression is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;t_S\cong\frac{Q_S}{I_R}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
When all stored charge has been removed, diode resistance suddenly changes, rising to its [[Cut-off (electronics)|cut-off]] value at [[P-n_junction#Reverse bias|reverse bias]] within a time &amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;t&amp;lt;sub&amp;gt;Tr&amp;lt;/sub&amp;gt;&amp;#039;&amp;#039;&amp;#039;&amp;#039;&amp;#039;, the &amp;#039;&amp;#039;transition time&amp;#039;&amp;#039;: this behavior can be used to produce pulses with rise time equal to this time.&lt;br /&gt;
&lt;br /&gt;
== Operation of the Drift Step Recovery Diode (DSRD) ==&lt;br /&gt;
Drift Step Recovery Diode (DSRD) was discovered by Russian scientists in 1981 (Grekhov et al., 1981). The Principle of the DSRD operation is similar to the SRD, with one n essential difference - the forward pumping current should be pulsed, not continuous, because drift diodes function with slow carriers.&lt;br /&gt;
&lt;br /&gt;
The principle of DSRD operation can be explained as follows:  Short pulse of current is applied in the forward direction of the DSRD effectively &amp;quot;pumping&amp;quot; the P-N junction, or in other words, “charging” the P-N junction capacitively.  When the current direction reverses, the accumulated charges are removed from the base region. &lt;br /&gt;
&lt;br /&gt;
As soon as the accumulated charge decreases to zero, the diode opens rapidly. A high voltage spike can appear due to the self-induction of the diode circuit.&lt;br /&gt;
The larger the [[commutation current]] and the shorter the transition from forward to reverse conduction, the higher the pulse amplitude and efficiency of the pulse generator (Kardo-Sysoev et al., 1997).&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
* [[Minority carrier]].&lt;br /&gt;
* [[P-n junction]].&lt;br /&gt;
* [[Pulse generator]]&lt;br /&gt;
* [[Diode#Semiconductor_diodes|Semiconductor diode]].&lt;br /&gt;
&lt;br /&gt;
== References ==&lt;br /&gt;
*{{Citation&lt;br /&gt;
| first =  A. F.&lt;br /&gt;
| last =  Boff&lt;br /&gt;
| author-link = &lt;br /&gt;
| first2 = J. &lt;br /&gt;
| last2 = Moll&lt;br /&gt;
| author2-link = &lt;br /&gt;
| first3 = R. &lt;br /&gt;
| last3 = Shen&lt;br /&gt;
| contribution = A new high speed effect in solid state diodes&lt;br /&gt;
| contribution-url = http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1157249&lt;br /&gt;
| series = IRE International Solid-State Circuits Conference&lt;br /&gt;
| title = 1960 IEEE International Solid-State Circuits Conference. Digest of Technical Papers.  &lt;br /&gt;
| volume = III&lt;br /&gt;
|date=February 1960&lt;br /&gt;
| pages = 50–51&lt;br /&gt;
| place = New York&lt;br /&gt;
| publisher = [[IEEE]] Press &lt;br /&gt;
| url = http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=8304}}. The first paper dealing with SRDs: interesting but &amp;quot;&amp;#039;&amp;#039;restricted access&amp;#039;&amp;#039;&amp;quot;.&lt;br /&gt;
The following two books contain a comprehensive analysis of the theory of non-equilibrium charge transport in semiconductor [[diode]]s, and give also an overview of applications (at least up to the end of the seventies).&lt;br /&gt;
*{{Citation&lt;br /&gt;
| last = Nosov&lt;br /&gt;
| first = Yurii Romanovich&lt;br /&gt;
| author-link = &lt;br /&gt;
| title = Switching in semiconductor diodes&lt;br /&gt;
| place = [[New York]]&lt;br /&gt;
| publisher = [[Plenum Press]]&lt;br /&gt;
| year = 1969&lt;br /&gt;
| series = Monographs in Semiconductor Physics&lt;br /&gt;
| volume = 4&lt;br /&gt;
| doi = &lt;br /&gt;
| id = &lt;br /&gt;
| isbn = }}.&lt;br /&gt;
*{{Citation&lt;br /&gt;
| last = Tkhorik&lt;br /&gt;
| first = Yurii Aleksandrovich&lt;br /&gt;
| author-link = &lt;br /&gt;
| title = Transients in pulsed semiconductor diodes&lt;br /&gt;
| place = [[Jerusalem]]&lt;br /&gt;
| publisher = [[Keter Publishing House#History|Israel Program for Scientific Translations, Ltd.]]&lt;br /&gt;
| year = 1968&lt;br /&gt;
| doi = &lt;br /&gt;
| id = &lt;br /&gt;
| isbn = }}.&lt;br /&gt;
The following application notes deals extensively with practical circuits and applications using SRDs.&lt;br /&gt;
*{{Citation&lt;br /&gt;
| contribution = Pulse and Waveform Generation with Step Recovery Diodes&lt;br /&gt;
| contribution-url = http://www.hp.woodshot.com/hprfhelp/5_downld/lit/diodelit/an918.pdf&lt;br /&gt;
| series = Application note AN 918&lt;br /&gt;
|date=October 1984&lt;br /&gt;
| place = [[Palo Alto]]&lt;br /&gt;
| publisher = [[Hewlett-Packard]]&lt;br /&gt;
| url = &lt;br /&gt;
| doi = &lt;br /&gt;
| id = }}. Available at Hewlett-Packard [http://www.hp.woodshot.com/hprfhelp/hprfhelp.htm HPRFhelp].&lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
{{Commons cat|Step-recovery diodes}}&lt;br /&gt;
*{{Citation&lt;br /&gt;
| first = Michael R.&lt;br /&gt;
| last = Tan&lt;br /&gt;
| author-link = &lt;br /&gt;
| first2 = S. Y.&lt;br /&gt;
| last2 = Wang&lt;br /&gt;
| author2-link = &lt;br /&gt;
| first3 = D. E.&lt;br /&gt;
| last3 = Mars&lt;br /&gt;
| author3-link = &lt;br /&gt;
| first4 = J. L.&lt;br /&gt;
| last4 = Moll&lt;br /&gt;
| author4-link = &lt;br /&gt;
| title = A 12 psec GaAs Double Heterostructure Step Recovery Diode&lt;br /&gt;
| series = [http://www.hpl.hp.com/techreports/ HP Labs Technical Reports]&lt;br /&gt;
| volume = HPL-91-187&lt;br /&gt;
| date = 31 December 1991&lt;br /&gt;
| place = [[Palo Alto]]&lt;br /&gt;
| publisher = [[Hewlett-Packard]]&lt;br /&gt;
| url = http://www.hpl.hp.com/techreports/91/HPL-91-187.html&lt;br /&gt;
| doi = &lt;br /&gt;
| id = }}. An interesting paper describing the construction and reporting the measured performance of an extremely fast [[heterojunction]] SRD.&lt;br /&gt;
*{{Citation&lt;br /&gt;
| last = Kirkby&lt;br /&gt;
| first = David &lt;br /&gt;
| author-link = &lt;br /&gt;
| title = A Picosecond Optoelectronic Cross Correlator using a Gain Modulated Avalanche Photodiode for Measuring the Impulse Response of Tissue&lt;br /&gt;
| chapter = Chapter 5 - Pulse Generators&lt;br /&gt;
| chapterurl = http://www.medphys.ucl.ac.uk/research/borl/homepages/davek/phd/chapter5.pdf&lt;br /&gt;
|date=April 1999&lt;br /&gt;
| url = http://www.medphys.ucl.ac.uk/research/borl/homepages/davek/phd/phd.html&lt;br /&gt;
| doi = &lt;br /&gt;
| id = }}. It is a PhD thesis in which an SRD is a key element. Chapter 5 is particularly relevant.&lt;br /&gt;
&lt;br /&gt;
[[Category:Diodes]]&lt;/div&gt;</summary>
		<author><name>en&gt;GoingBatty</name></author>
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