Positive-definite matrix - Revision history

en>Rangdor: /* Further properties */

2015-01-05T23:57:24Z

Further properties

← Older revision		Revision as of 01:57, 6 January 2015
Line 1:		Line 1:
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216.15.124.67: /* Examples */ For clarity, make implied vector/matrix multiplication explicit.

2014-02-16T14:06:25Z

Examples: For clarity, make implied vector/matrix multiplication explicit.

← Older revision		Revision as of 16:06, 16 February 2014
Line 1:		Line 1:
	~~The~~ '''junction gate field-effect transistor''' ('''JFET''' or '''JUGFET''') is the simplest type of [[field-effect transistor]]. They are three-lead [[semiconductor\|semiconductive]] devices that can be used as [[electronics\|electronically]]-controlled [[switch\|switches]], amplifier controls, or as a voltage-controlled [[Electrical resistance\|resistance]]. Unlike bipolar transistors, JFETs are exclusively voltage-controlled in that they do not need a biasing current. [[Electric charge]] flows through a semiconducting channel between "source" and "drain" terminals. By applying a reverse bias [[voltage]] to a "gate" terminal, the channel is "pinched", so that the [[electric current]] is impeded or switched off completely. A JFET is usually on when there is no potential difference across its gate and source leads. On the contrary, if a potential difference occurs across its gate and source leads, the JFET will be more resistive to current flow, which means less current would flow along the drain-source leads. Thus, JFETs are sometimes referred to as ''depletion devices''. JFETs can have an n-channel or p-channel configuration. In the n-channel configuration, if the voltage applied to its gate is less than that applied to its source lead, a JFET will have a lower current flow from its drain to source lead. In the p-channel configuration, if the voltage applied to its gate is greater than that applied to its source lead, a JFET will have a lower current flow from its drain to source lead. ~~A JFET has a very large input impedance of roughly 10~~<~~sup~~>10</sup> ohms (Ω), which means that it has a negligible effect on external components or circuits connected to its gate since large impedance implies that it has a low input current. JFETs are suitable for simple two-terminal current sources, electronic gain-control logic switches, oscillator circuits, audio mixing circuits, amplifier circuits, bidirectional analog switching circuits, etc.		I'm Zenaida and I live in Memmelsdorf. <br>I'm interested in Biochemistry, Board sports and Portuguese art. I like travelling and reading fantasy.<br><br>Take a look at my web page; [http://seppcms.Freehostia.com/index.php?option=com_easygb& how to get Free fifa 15 coins]

	~~== Structure ==~~
	~~[[Image:Jfet.png\|thumb\|[[Electric current]] from ''source'' to ''drain'~~' in ~~a '''p-channel JFET''' is restricted when a [[voltage]] is applied to the ''gate''.]]~~
	The JFET is a long channel of [[semiconductor]] material, [[doping (semiconductor)\|doped]] to contain an abundance of positive [[electric charge\|charge]] carriers or [[Electron hole\|holes]] (''p-type''), ~~or of negative carriers or [[electron]]s (''n-type''). [[Ohmic contact]]s at each end form the source (S)~~ and ~~drain (D)~~. ~~A [[P-N junction\|pn-junction]] is formed on one or both sides of the channel, or surrounding it, using a region with doping opposite to that of the channel, and biased using an ohmic gate contact (G).~~

	~~== Function ==~~
	~~[[Image:JFET n-channel en.svg\|thumb\|280px\|I–V characteristics and output plot of a JFET n-channel transistor.]]~~
	~~JFET operation is~~ like that of a [[garden hose]]. The flow of water through a hose can be controlled by squeezing it to reduce the [[cross section (geometry)\|cross section]]; the flow of [[electric charge]] through a JFET is controlled by constricting the current-carrying channel. The current also depends on the electric field between source and ~~drain (analogous to the difference in [[Fluid pressure\|pressure]] on either end of the hose).~~

	Construction of the conducting channel is accomplished using the [[Field effect (semiconductor)\|field effect]]: a voltage between the gate and source is applied to reverse bias the gate-source pn-junction, thereby widening the [[depletion layer]] of this junction (see top figure), encroaching upon the conducting channel and restricting its cross-sectional area. The depletion layer is so-called because it is depleted of mobile carriers and so is electrically non-conducting for practical purposes.<~~ref name=JFET~~> For a discussion of JFET structure and operation, see for example {{cite book \|title=Electronics (fundamentals and applications) \|url=http://books.google.com/books?id=n0rf9_2ckeYC&pg=PA269 \|chapter=§13.2 Junction field-effect transistor (JFET) \|author=D. Chattopadhyay \|isbn=8122417809 \|publisher=New Age International \|pages=269 ''ff'' \|year=2006}}
	<~~/ref~~>

	~~When the depletion layer spans the width of the conduction channel, "pinch-off" is achieved and drain to source conduction stops. Pinch-off occurs~~ at a particular reverse bias (V<sub>GS</sub>) of the gate-source junction. The pinch-off voltage (V<sub>p</sub>) varies considerably, even among devices of the same type. For example, V<sub>GS(off)</sub> for the Temic J202 device varies from -0.8V to -4V.<ref>[http://~~docs-europe~~.~~origin.electrocomponents~~.com/~~webdocs/0027/0900766b80027bd1~~.~~pdf J201 data sheet]</ref> Typical values vary from -0.3V to -10V.~~

	~~To switch off an '''n'''-channel device requires a '''n'''egative gate-source voltage (V<sub>GS</sub>). Conversely, to switch off a '''p'''-channel device requires '''p'''ositive V<sub>GS</sub>.~~

	~~In normal operation, the electric field developed by the gate blocks source-drain conduction to some extent.~~

	~~Some JFET devices are symmetrical with respect to the source and drain.~~

	=~~= Schematic symbols ==~~
	~~[[Image:JFET N-dep symbol.svg\|thumb\|100px\|[[electronic symbol\|Circuit symbol]] for an n-Channel JFET]]~~
	~~[[Image:JFET P-dep symbol.svg\|thumb\|100px\|Circuit symbol for a p-Channel JFET]]~~
	The JFET gate is sometimes drawn in the middle of the channel (instead of at the drain or source electrode as in these examples). This symmetry suggests that "drain" and "source" are interchangeable, so the symbol should be used only for those JFETs where they are indeed interchangeable.

	Officially, the style of the symbol should show the component inside a circle (representing the envelope of a discrete device). This is true in both the US and Europe. The symbol is usually drawn without the circle when drawing schematics of integrated circuits. More recently, the symbol is often drawn without its circle even for discrete devices.

	In every case the arrow head shows the polarity of the P-N junction formed between the channel and gate. As with an ordinary [[diode]], the arrow points from P to N, the direction of [[Electric current#Conventional current\|conventional current]] when forward-biased. An English [[mnemonic]] is that the arrow of an N-channel device "points i'''n'''".

	~~== Comparison with other transistors ==~~
	At room temperature, JFET gate current (the reverse leakage of the gate-to-channel [[P-n junction\|junction]]) is comparable to that of a [[MOSFET]] (which has insulating oxide between gate and channel), but much less than the base current of a [[bipolar junction transistor]]. The JFET has higher [[transconductance]] than the MOSFET, as well as lower [[flicker noise]], and is therefore used in some low-[[Noise (physics)\|noise]], high input-impedance [[Operational amplifier\|op-amps]].

	~~== History of the JFET ==~~
	~~The JFET was predicted by [[Julius Edgar Lilienfeld\|Julius Lilienfeld]] in 1925 and by the mid-1930s its theory of operation was sufficiently well known~~ to justify a patent. However, it was not possible for many years to make doped crystals with enough precision to show the effect. In 1947, researchers [[John Bardeen]], [[Walter Houser Brattain]], and [[William Shockley]] were trying to make a JFET when they discovered the [[point-contact transistor]]. The first practical JFETs were made many years later, in spite of their conception long before the junction transistor. To some extent it can be treated as a hybrid of a [[MOSFET]] (metal–oxide–semiconductor field-effect transistor) and a [[Bipolar junction transistor\|BJT]] though an [[Insulated-gate bipolar transistor\|IGBT]] resembles more of the hybrid features.

	~~==Mathematical model==~~
	~~The current in N-JFET due to a small voltage V<sub>DS</sub> is given by:~~
	~~::<math>I_{DSS} = (2a) \frac{W}{L} q N_d \mu_n V_{DS}</math>~~
	~~where~~
	* ''I<sub>DSS</sub>'' = drain-source saturation current
	* ''2a'' = channel thickness
	* ''W'' = width
	* ''L'' = length
	* ''q'' = electronic charge = 1.6 x 10<sup>-19</sup> C
	* ''μ<sub>n</sub>'' = [[electron mobility]]
	* ''N<sub>d</sub>'' = n type doping concentration
	~~In the saturation region:~~
	~~::<math>I_{DS} = I_{DSS}\left[1 - \frac{V_{GS}}{V_P}\right]^2</math>~~
	~~In the linear region~~
	~~::<math>I_D = (2a) \frac{W}{L} q N_d {{\mu}_n} \left[1 - \sqrt{\frac{V_{GS}}{V_P}}\right]V_{DS}</math>~~
	~~or (in terms of <math>I_{DSS}</math>):~~
	~~::<math>I_D = \frac{2I_{DSS}}{V_P^2} (V_{GS} - V_P - \frac{V_{DS}}{2})V_{DS}</math>~~
	~~where~~
	<math>{V_P}</math> is the pinch off voltage, the minimum voltage across G-S to completely turn off conduction. When <math>V_{DS}</math> is small compared with <math>V_{GS}</math> - <math>V_P</math>, the device acts like a voltage controlled resistor.

	~~==See also==~~
	~~{{Portal\|Electronics}}~~
	* [[Constant-current diode]]

	~~==References==~~
	~~{{Reflist}}<!--added above External links/Sources by script-assisted edit-->~~

	~~== External links ==~~
	* [http://ist-socrates.berkeley.edu/~phylabs/bsc/PDFFiles/bsc5.pdf Physics 111 Laboratory -- JFET Circuits I pdf]
	* [http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/jfet.html Interactive Explanation of n-channel JFET]

	~~{{Transistor amplifiers}}~~
	~~{{Electronic component}}~~

	~~[[Category:Transistor types]~~]

en>Manoguru: /* Examples */

2014-02-02T16:08:01Z

Examples

← Older revision		Revision as of 18:08, 2 February 2014
Line 1:		Line 1:
	~~Reina~~ is ~~what people call me though I don~~'~~t love being named~~ that ~~way~~. ~~One~~ of the ~~issues he loves many~~ is ~~hot~~-~~air balooning~~ and he is ~~been doing~~ it for ~~quite~~ a ~~while~~ ~~Nebraska~~ has ~~always been my house~~ and it is ~~loved~~ by ~~my family~~ ~~Auditing has been his occupation for quite~~ a ~~while~~ ~~Observe what~~ is ~~fresh on my website below http~~://is.gd/~~F9c7zN~~<br><br>~~Here is my blog post~~ [http://is.gd/~~F9c7zN Sex Toys~~]		The '''junction gate field-effect transistor''' ('''JFET''' or '''JUGFET''') is the simplest type of [[field-effect transistor]]. They are three-lead [[semiconductor\|semiconductive]] devices that can be used as [[electronics\|electronically]]-controlled [[switch\|switches]], amplifier controls, or as a voltage-controlled [[Electrical resistance\|resistance]]. Unlike bipolar transistors, JFETs are exclusively voltage-controlled in that they do not need a biasing current. [[Electric charge]] flows through a semiconducting channel between "source" and "drain" terminals. By applying a reverse bias [[voltage]] to a "gate" terminal, the channel is "pinched", so that the [[electric current]] is impeded or switched off completely. A JFET is usually on when there is no potential difference across its gate and source leads. On the contrary, if a potential difference occurs across its gate and source leads, the JFET will be more resistive to current flow, which means less current would flow along the drain-source leads. Thus, JFETs are sometimes referred to as ''depletion devices''. JFETs can have an n-channel or p-channel configuration. In the n-channel configuration, if the voltage applied to its gate is less than that applied to its source lead, a JFET will have a lower current flow from its drain to source lead. In the p-channel configuration, if the voltage applied to its gate is greater than that applied to its source lead, a JFET will have a lower current flow from its drain to source lead. A JFET has a very large input impedance of roughly 10<sup>10</sup> ohms (Ω), which means that it has a negligible effect on external components or circuits connected to its gate since large impedance implies that it has a low input current. JFETs are suitable for simple two-terminal current sources, electronic gain-control logic switches, oscillator circuits, audio mixing circuits, amplifier circuits, bidirectional analog switching circuits, etc.

			== Structure ==
			[[Image:Jfet.png\|thumb\|[[Electric current]] from ''source'' to ''drain'' in a '''p-channel JFET''' is restricted when a [[voltage]] is applied to the ''gate''.]]
			The JFET is a long channel of [[semiconductor]] material, [[doping (semiconductor)\|doped]] to contain an abundance of positive [[electric charge\|charge]] carriers or [[Electron hole\|holes]] (''p-type''), or of negative carriers or [[electron]]s (''n-type''). [[Ohmic contact]]s at each end form the source (S) and drain (D). A [[P-N junction\|pn-junction]] is formed on one or both sides of the channel, or surrounding it, using a region with doping opposite to that of the channel, and biased using an ohmic gate contact (G).

			== Function ==
			[[Image:JFET n-channel en.svg\|thumb\|280px\|I–V characteristics and output plot of a JFET n-channel transistor.]]
			JFET operation is like that of a [[garden hose]]. The flow of water through a hose can be controlled by squeezing it to reduce the [[cross section (geometry)\|cross section]]; the flow of [[electric charge]] through a JFET is controlled by constricting the current-carrying channel. The current also depends on the electric field between source and drain (analogous to the difference in [[Fluid pressure\|pressure]] on either end of the hose).

			Construction of the conducting channel is accomplished using the [[Field effect (semiconductor)\|field effect]]: a voltage between the gate and source is applied to reverse bias the gate-source pn-junction, thereby widening the [[depletion layer]] of this junction (see top figure), encroaching upon the conducting channel and restricting its cross-sectional area. The depletion layer is so-called because it is depleted of mobile carriers and so is electrically non-conducting for practical purposes.<ref name=JFET> For a discussion of JFET structure and operation, see for example {{cite book \|title=Electronics (fundamentals and applications) \|url=http://books.google.com/books?id=n0rf9_2ckeYC&pg=PA269 \|chapter=§13.2 Junction field-effect transistor (JFET) \|author=D. Chattopadhyay \|isbn=8122417809 \|publisher=New Age International \|pages=269 ''ff'' \|year=2006}}
			</ref>

			When the depletion layer spans the width of the conduction channel, "pinch-off" is achieved and drain to source conduction stops. Pinch-off occurs at a particular reverse bias (V<sub>GS</sub>) of the gate-source junction. The pinch-off voltage (V<sub>p</sub>) varies considerably, even among devices of the same type. For example, V<sub>GS(off)</sub> for the Temic J202 device varies from -0.8V to -4V.<ref>[http://docs-europe.origin.electrocomponents.com/webdocs/0027/0900766b80027bd1.pdf J201 data sheet]</ref> Typical values vary from -0.3V to -10V.

			To switch off an '''n'''-channel device requires a '''n'''egative gate-source voltage (V<sub>GS</sub>). Conversely, to switch off a '''p'''-channel device requires '''p'''ositive V<sub>GS</sub>.

			In normal operation, the electric field developed by the gate blocks source-drain conduction to some extent.

			Some JFET devices are symmetrical with respect to the source and drain.

			== Schematic symbols ==
			[[Image:JFET N-dep symbol.svg\|thumb\|100px\|[[electronic symbol\|Circuit symbol]] for an n-Channel JFET]]
			[[Image:JFET P-dep symbol.svg\|thumb\|100px\|Circuit symbol for a p-Channel JFET]]
			The JFET gate is sometimes drawn in the middle of the channel (instead of at the drain or source electrode as in these examples). This symmetry suggests that "drain" and "source" are interchangeable, so the symbol should be used only for those JFETs where they are indeed interchangeable.

			Officially, the style of the symbol should show the component inside a circle (representing the envelope of a discrete device). This is true in both the US and Europe. The symbol is usually drawn without the circle when drawing schematics of integrated circuits. More recently, the symbol is often drawn without its circle even for discrete devices.

			In every case the arrow head shows the polarity of the P-N junction formed between the channel and gate. As with an ordinary [[diode]], the arrow points from P to N, the direction of [[Electric current#Conventional current\|conventional current]] when forward-biased. An English [[mnemonic]] is that the arrow of an N-channel device "points i'''n'''".

			== Comparison with other transistors ==
			At room temperature, JFET gate current (the reverse leakage of the gate-to-channel [[P-n junction\|junction]]) is comparable to that of a [[MOSFET]] (which has insulating oxide between gate and channel), but much less than the base current of a [[bipolar junction transistor]]. The JFET has higher [[transconductance]] than the MOSFET, as well as lower [[flicker noise]], and is therefore used in some low-[[Noise (physics)\|noise]], high input-impedance [[Operational amplifier\|op-amps]].

			== History of the JFET ==
			The JFET was predicted by [[Julius Edgar Lilienfeld\|Julius Lilienfeld]] in 1925 and by the mid-1930s its theory of operation was sufficiently well known to justify a patent. However, it was not possible for many years to make doped crystals with enough precision to show the effect. In 1947, researchers [[John Bardeen]], [[Walter Houser Brattain]], and [[William Shockley]] were trying to make a JFET when they discovered the [[point-contact transistor]]. The first practical JFETs were made many years later, in spite of their conception long before the junction transistor. To some extent it can be treated as a hybrid of a [[MOSFET]] (metal–oxide–semiconductor field-effect transistor) and a [[Bipolar junction transistor\|BJT]] though an [[Insulated-gate bipolar transistor\|IGBT]] resembles more of the hybrid features.

			==Mathematical model==
			The current in N-JFET due to a small voltage V<sub>DS</sub> is given by:
			::<math>I_{DSS} = (2a) \frac{W}{L} q N_d \mu_n V_{DS}</math>
			where
			* ''I<sub>DSS</sub>'' = drain-source saturation current
			* ''2a'' = channel thickness
			* ''W'' = width
			* ''L'' = length
			* ''q'' = electronic charge = 1.6 x 10<sup>-19</sup> C
			* ''μ<sub>n</sub>'' = [[electron mobility]]
			* ''N<sub>d</sub>'' = n type doping concentration
			In the saturation region:
			::<math>I_{DS} = I_{DSS}\left[1 - \frac{V_{GS}}{V_P}\right]^2</math>
			In the linear region
			::<math>I_D = (2a) \frac{W}{L} q N_d {{\mu}_n} \left[1 - \sqrt{\frac{V_{GS}}{V_P}}\right]V_{DS}</math>
			or (in terms of <math>I_{DSS}</math>):
			::<math>I_D = \frac{2I_{DSS}}{V_P^2} (V_{GS} - V_P - \frac{V_{DS}}{2})V_{DS}</math>
			where
			<math>{V_P}</math> is the pinch off voltage, the minimum voltage across G-S to completely turn off conduction. When <math>V_{DS}</math> is small compared with <math>V_{GS}</math> - <math>V_P</math>, the device acts like a voltage controlled resistor.

			==See also==
			{{Portal\|Electronics}}
			* [[Constant-current diode]]

			==References==
			{{Reflist}}<!--added above External links/Sources by script-assisted edit-->

			== External links ==
			* [http://ist-socrates.berkeley.edu/~phylabs/bsc/PDFFiles/bsc5.pdf Physics 111 Laboratory -- JFET Circuits I pdf]
			* [http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/jfet.html Interactive Explanation of n-channel JFET]

			{{Transistor amplifiers}}
			{{Electronic component}}

			[[Category:Transistor types]]

en>Maschen: add link and notice to Totally positive matrix

2012-08-31T14:34:28Z

add link and notice to Totally positive matrix

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