Polylogarithm - Revision history

131.91.7.56 at 00:15, 22 August 2014

2014-08-22T00:15:39Z

← Older revision		Revision as of 02:15, 22 August 2014
Line 1:		Line 1:
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2001:760:2C0C:202:29D3:B6AC:88D7:E773: /* Dilogarithm */

2014-02-09T15:57:20Z

Dilogarithm

← Older revision		Revision as of 17:57, 9 February 2014
Line 1:		Line 1:
	~~{{About\|non-linear mixing operating in the frequency domain\|other types of mixers\|electronic mixer}}~~

	~~[[Image:IdealMixer.svg\|thumb\|350px\|Frequency Mixer Symbol.]]~~

	In [[electronics]] a '''mixer''' or '''frequency mixer''' is a [[nonlinear]] electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies ''f<sub>1</sub>'' and ''f<sub>2</~~sub>'' are applied to a mixer, and it produces new signals at the sum ''f<sub>1<~~/~~sub>'' + ''f<sub>2</sub>'' and difference ''f<sub>1</sub>'' - ''f<sub>2</sub>'' of the original frequencies~~. ~~Other frequency components may also be produced in a practical frequency mixer~~.		Human being who wrote the [http://Www.Google.Co.uk/search?hl=en&gl=us&tbm=nws&q=statement&gs_l=news statement] is called Roberto Ledbetter and his wife shouldn't like it at all. In his professional life he is normally a people manager. He's always loved living to Guam and he owns everything that he needs there. The widely used hobby for him and simply his kids is you will need but he's been on new things as of late. He's been working on website for some time now. Check it completly here: http://circuspartypanama.com<br><br>[http://Imgur.com/hot?q=Feel+free Feel free] to visit my page ... hack clash of clans ([http://circuspartypanama.com Continue Reading])

	~~Mixers are widely used to shift signals from one frequency range to another, a process known as [[heterodyning]], for convenience in transmission or further signal processing~~. For example, a key component of a [[superheterodyne receiver]] is a mixer used to move received signals to a common [[intermediate frequency]]. Frequency mixers are also used to [[modulate]] a carrier frequency in [[Transmitter\|radio transmitter]]s.

	==~~Types~~==
	~~A device that has a non-linear (e.g. [[exponential function\|exponential~~]~~]) characteristic can act as a mixer. Passive mixers use one or more diodes~~ and ~~rely on the non-linear relation between voltage and current to provide the multiplying element~~. In a ~~passive mixer, the desired output signal is~~ always ~~of lower power than the input signals.~~

	~~Active mixers use an amplifying device (such as a transistor or vacuum tube)~~ to ~~increase the strength of the product signal. Active mixers improve isolation between the ports, but may have higher noise and more power consumption. An active mixer can be less tolerant of overload.~~

	~~Mixers may be built of discrete components, may be part of integrated circuits, or can be delivered as hybrid modules.~~

	~~[[File:Diode DBM.png\|thumb\|right\|Schematic diagram of a double-balanced passive diode mixer (also known as a [[ring modulator]]). There is no output unless both f1~~ and ~~f2 inputs are present, though f2 (but not f1) can be DC.]]~~
	~~Mixers may also be classified by their topology. Unbalanced mixers allow some of both input signals to pass through to the output. A single balanced mixer is arranged so~~ that ~~either the local oscillator (LO) or signal input (RF) is suppressed at the output, but not both~~. ~~A double balanced mixer has symmetrical paths~~ for ~~both inputs, so that neither of the input signals~~ and only the product signal appears at the output.<ref>{{cite web\|last=Poole\|first=Ian\|title=Double balanced mixer tutorial\|url=http://www.radio-electronics.com/info/rf-technology-design/mixers/double-balanced-mixer-tutorial.php\|publisher=Adrio Communications\|accessdate=30 July 2012}}</ref> Double balanced mixers are more complex and require higher drive levels than unbalanced and single balanced designs. Selection of a mixer type is ~~a trade off for a particular application.~~

	~~Mixer circuits are characterized by their properties such as conversion [[gain]] (or loss), and [[noise figure]].<ref> D.S. Evans, G. R. Jessop,~~ '~~'VHF-UHF Manual Third Edition'', [[Radio Society of Great Britain]], 1976, page 4-12 </ref>~~

	~~Nonlinear electronic components that are used as mixers include [[diode]]s, [[transistor]]s biased near cutoff, and at lower frequencies, [[analog multiplier]]~~s~~. [[Inductor\|Ferromagnetic-core inductors]] driven into [[saturation (magnetic)\|saturation]] have also~~ been ~~used.~~ ~~In [[nonlinear optics]], crystals with nonlinear characteristics are used to mix two frequencies~~ of ~~laser light to create [[Optical heterodyne detection\|optical heterodynes]]~~.

	~~===Diode===~~
	A [[diode]] can be used to create a simple unbalanced mixer. This type of mixer produces the original frequencies as well as their sum and their difference. The importance of the diode is that it is non-linear (or non-[[Ohm's ~~law\|Ohmic]]), which means its response (current) is not proportional to its input (voltage).~~ ~~The diode therefore does not reproduce the frequencies of its driving voltage in the current through it, which allows the desired frequency manipulation~~.
	~~The current ''I'' through an ideal diode as a function of the voltage ''V'' across~~ it ~~is given by~~
	:~~<math>I=I_\mathrm{S} \left( e^{qV_\mathrm{D} \over nkT}-1 \right)<~~/~~math>~~
	~~where what is important is that ''V'' appears in ''e'''s exponent~~. ~~The exponential can be [[Taylor series\|expanded]] as~~
	:<~~math~~>~~e^x = \sum_{n=0}^\infty \frac{x^n}{n!}~~<~~/math~~>
	~~and can be approximated for small ''x'' (that is, small voltages) by the first few terms of that series:~~
	:~~<math>e^x-1\approx x + \frac{x^2}{2}<~~/~~math>~~

	~~Suppose that the sum of the two input signals <math>v_1+v_2<~~/math> is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode (perhaps by providing the voltage that is present across a [[resistor]] in series with the diode). ~~Then, disregarding the constants in the diode equation, the output voltage will have the form~~
	~~:<math>v_\mathrm{o} = (v_1+v_2)+\frac12 (v_1+v_2)^2 + \dots<~~/~~math>~~
	~~The first term on the right is the original two signals, as expected, followed by the square of the sum, which can be rewritten as <math>(v_1+v_2)^2~~ = ~~v_1^2 + 2 v_1 v_2~~ + ~~v_2^2</math>, where the multiplied signal is obvious. The ellipsis represents all the higher powers of the sum which we assume to be [[negligible~~]~~] for small signals.~~

	~~===Switching===~~
	~~Another form of mixer operates by switching, with the smaller input signal being passed inverted or uninverted according~~ to ~~the phase of the local oscillator (LO)~~. ~~This would be typical of the normal operating mode of a packaged double balanced mixer, with the local oscillator drive considerably higher than the signal amplitude~~.

	~~The aim of a switching mixer is to achieve linear operation over the signal level, and hard switching driven by the local oscillator~~. ~~Mathematically the switching mixer is not much different from a multiplying mixer, just because instead~~ of the LO sine wave term we would use the signum function. In the frequency domain the switching mixer operation leads to the usual sum and difference frequencies, but also to further terms e.g. +-3fLO, +-5fLO, etc.
	The advantage of a switching mixer is that it can achieve - with the same effort - a lower noise figure (NF) and larger conversion gain. This come because the switching diodes or transistors act either like a low resistor (switch closed) or large resistor (switch open) and in both cases only minimum noise is added. From the circuit perspective many multiplying mixers can be used as switching mixers, just by increasing the LO amplitude. So RF engineers simply talk about mixers, and mean switching mixers.


	~~The mixer circuit can be used not only to shift the frequency of an input signal as in a receiver, but also as a~~ [[product detector]], [[modulator]], [[phase detector]] or frequency multiplier.<ref name=Horowitz89> Paul Horowitz, Winfred Hill ''[[The Art of Electronics]] Second Edition'', Cambridge University Press 1989, pp. 885-887 </ref> For example a [[communications receiver]] might contain two mixer stages for conversion of the input signal to an intermediate frequency, and another mixer employed as a detector for demodulation of the signal.

	~~{{Portal\|Electronics}}~~

	~~== See also ==~~
	* [[Frequency multiplier]]
	* [[Subharmonic mixer]]
	* [[Product detector]]
	* [[Pentagrid converter]]
	* [[Beam deflection tube]]
	* [[Ring modulation]]
	* [[Gilbert cell]]
	* [[Optical heterodyne detection]]
	* [[Intermodulation]]
	* [[Third-order intercept point]]
	* [[Rusty bolt effect]]

	~~==References==~~
	~~{{Reflist}}~~

	~~==External links==~~
	~~{{Commons category\|Radio electronic diagrams}}~~

	~~{{FS1037C}}~~
	~~{{Analogue TV transmitter topics}}~~

	~~{{DEFAULTSORT:Frequency Mixer}}~~
	~~[[Category:Frequency mixers\| ]]~~
	~~[[Category:Electronic circuits]]~~
	~~[[Category:Communication circuits]]~~
	~~[[Category:Radio electronics]]~~
	~~[[Category:Telecommunication theory]~~]

en>Monkbot: /* References */Fix CS1 deprecated date parameter errors

2014-01-28T18:07:13Z

References: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 20:07, 28 January 2014
Line 1:		Line 1:
	~~Luke~~ is ~~really~~ a ~~celebrity while in~~ the ~~creating along with~~ the ~~profession development initially 2nd~~ to ~~his third club recording~~, ~~And~~ , ~~will be~~ the ~~confirmation~~. ~~He broken~~ to the ~~picture in 2007 with his crazy mixture~~ of ~~downward-residence accessibility~~, ~~film celebrity good appears~~ and ~~lines~~, ~~is placed t in the major way~~. [~~http~~:~~//lukebryantickets~~.~~neodga~~.~~com vip luke bryan tickets~~] ~~The brand new record~~ ~~Top around~~ the ~~nation graph~~ or ~~chart and #2 around~~ the ~~pop maps~~, ~~creating it the next highest debut during~~ that ~~time~~ of ~~2011 to get a region designer~~. <br><br>~~The boy~~ of a , ~~is aware perseverance~~ and ~~willpower are important elements in terms~~ of ~~an excellent occupation~~- ~~. His to start with album~~, ~~Continue to be Me~~, ~~generated the most notable hits “All~~ [~~http://lukebryantickets~~.~~flicense~~.~~com meet and greet tickets luke bryan~~] ~~My Buddies Say”~~ and ~~“Country Guy,” although his~~ ~~work~~, ~~Doin’~~ ~~Factor~~, ~~located~~ the ~~artist~~-~~about three~~ right No. ~~9 singles~~: ~~Different Contacting Can~~ be ~~a Wonderful Thing.”~~<br><br>~~While in~~ the ~~drop~~ of ~~2005~~, ~~Concert tour: Luke And~~ that ~~had~~ an ~~outstanding set~~ of , ~~including Metropolitan~~. ~~“It’s much like you are obtaining a authorization~~ to ~~visit~~ to a higher level, ~~says these designers that had been an element~~ of ~~[http://www~~.~~senatorwonderling~~.~~com luke bryan concert 2014]~~ the ~~Concert toursaround~~ in ~~a greater degree of designers~~.~~” It twisted~~ as the ~~most successful tours~~ in ~~its ten-year record~~.<br><br>~~Have~~ a ~~look at my site~~ [~~http~~:~~//www.museodecarruajes.org luke bryan concerts 2014~~]		{{About\|non-linear mixing operating in the frequency domain\|other types of mixers\|electronic mixer}}

			[[Image:IdealMixer.svg\|thumb\|350px\|Frequency Mixer Symbol.]]

			In [[electronics]] a '''mixer''' or '''frequency mixer''' is a [[nonlinear]] electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies ''f<sub>1</sub>'' and ''f<sub>2</sub>'' are applied to a mixer, and it produces new signals at the sum ''f<sub>1</sub>'' + ''f<sub>2</sub>'' and difference ''f<sub>1</sub>'' - ''f<sub>2</sub>'' of the original frequencies. Other frequency components may also be produced in a practical frequency mixer.

			Mixers are widely used to shift signals from one frequency range to another, a process known as [[heterodyning]], for convenience in transmission or further signal processing. For example, a key component of a [[superheterodyne receiver]] is a mixer used to move received signals to a common [[intermediate frequency]]. Frequency mixers are also used to [[modulate]] a carrier frequency in [[Transmitter\|radio transmitter]]s.

			==Types==
			A device that has a non-linear (e.g. [[exponential function\|exponential]]) characteristic can act as a mixer. Passive mixers use one or more diodes and rely on the non-linear relation between voltage and current to provide the multiplying element. In a passive mixer, the desired output signal is always of lower power than the input signals.

			Active mixers use an amplifying device (such as a transistor or vacuum tube) to increase the strength of the product signal. Active mixers improve isolation between the ports, but may have higher noise and more power consumption. An active mixer can be less tolerant of overload.

			Mixers may be built of discrete components, may be part of integrated circuits, or can be delivered as hybrid modules.

			[[File:Diode DBM.png\|thumb\|right\|Schematic diagram of a double-balanced passive diode mixer (also known as a [[ring modulator]]). There is no output unless both f1 and f2 inputs are present, though f2 (but not f1) can be DC.]]
			Mixers may also be classified by their topology. Unbalanced mixers allow some of both input signals to pass through to the output. A single balanced mixer is arranged so that either the local oscillator (LO) or signal input (RF) is suppressed at the output, but not both. A double balanced mixer has symmetrical paths for both inputs, so that neither of the input signals and only the product signal appears at the output.<ref>{{cite web\|last=Poole\|first=Ian\|title=Double balanced mixer tutorial\|url=http://www.radio-electronics.com/info/rf-technology-design/mixers/double-balanced-mixer-tutorial.php\|publisher=Adrio Communications\|accessdate=30 July 2012}}</ref> Double balanced mixers are more complex and require higher drive levels than unbalanced and single balanced designs. Selection of a mixer type is a trade off for a particular application.

			Mixer circuits are characterized by their properties such as conversion [[gain]] (or loss), and [[noise figure]].<ref> D.S. Evans, G. R. Jessop, ''VHF-UHF Manual Third Edition'', [[Radio Society of Great Britain]], 1976, page 4-12 </ref>

			Nonlinear electronic components that are used as mixers include [[diode]]s, [[transistor]]s biased near cutoff, and at lower frequencies, [[analog multiplier]]s. [[Inductor\|Ferromagnetic-core inductors]] driven into [[saturation (magnetic)\|saturation]] have also been used. In [[nonlinear optics]], crystals with nonlinear characteristics are used to mix two frequencies of laser light to create [[Optical heterodyne detection\|optical heterodynes]].

			===Diode===
			A [[diode]] can be used to create a simple unbalanced mixer. This type of mixer produces the original frequencies as well as their sum and their difference. The importance of the diode is that it is non-linear (or non-[[Ohm's law\|Ohmic]]), which means its response (current) is not proportional to its input (voltage). The diode therefore does not reproduce the frequencies of its driving voltage in the current through it, which allows the desired frequency manipulation.
			The current ''I'' through an ideal diode as a function of the voltage ''V'' across it is given by
			:<math>I=I_\mathrm{S} \left( e^{qV_\mathrm{D} \over nkT}-1 \right)</math>
			where what is important is that ''V'' appears in ''e'''s exponent. The exponential can be [[Taylor series\|expanded]] as
			:<math>e^x = \sum_{n=0}^\infty \frac{x^n}{n!}</math>
			and can be approximated for small ''x'' (that is, small voltages) by the first few terms of that series:
			:<math>e^x-1\approx x + \frac{x^2}{2}</math>

			Suppose that the sum of the two input signals <math>v_1+v_2</math> is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode (perhaps by providing the voltage that is present across a [[resistor]] in series with the diode). Then, disregarding the constants in the diode equation, the output voltage will have the form
			:<math>v_\mathrm{o} = (v_1+v_2)+\frac12 (v_1+v_2)^2 + \dots</math>
			The first term on the right is the original two signals, as expected, followed by the square of the sum, which can be rewritten as <math>(v_1+v_2)^2 = v_1^2 + 2 v_1 v_2 + v_2^2</math>, where the multiplied signal is obvious. The ellipsis represents all the higher powers of the sum which we assume to be [[negligible]] for small signals.

			===Switching===
			Another form of mixer operates by switching, with the smaller input signal being passed inverted or uninverted according to the phase of the local oscillator (LO). This would be typical of the normal operating mode of a packaged double balanced mixer, with the local oscillator drive considerably higher than the signal amplitude.

			The aim of a switching mixer is to achieve linear operation over the signal level, and hard switching driven by the local oscillator. Mathematically the switching mixer is not much different from a multiplying mixer, just because instead of the LO sine wave term we would use the signum function. In the frequency domain the switching mixer operation leads to the usual sum and difference frequencies, but also to further terms e.g. +-3fLO, +-5fLO, etc.
			The advantage of a switching mixer is that it can achieve - with the same effort - a lower noise figure (NF) and larger conversion gain. This come because the switching diodes or transistors act either like a low resistor (switch closed) or large resistor (switch open) and in both cases only minimum noise is added. From the circuit perspective many multiplying mixers can be used as switching mixers, just by increasing the LO amplitude. So RF engineers simply talk about mixers, and mean switching mixers.


			The mixer circuit can be used not only to shift the frequency of an input signal as in a receiver, but also as a [[product detector]], [[modulator]], [[phase detector]] or frequency multiplier.<ref name=Horowitz89> Paul Horowitz, Winfred Hill ''[[The Art of Electronics]] Second Edition'', Cambridge University Press 1989, pp. 885-887 </ref> For example a [[communications receiver]] might contain two mixer stages for conversion of the input signal to an intermediate frequency, and another mixer employed as a detector for demodulation of the signal.

			{{Portal\|Electronics}}

			== See also ==
			* [[Frequency multiplier]]
			* [[Subharmonic mixer]]
			* [[Product detector]]
			* [[Pentagrid converter]]
			* [[Beam deflection tube]]
			* [[Ring modulation]]
			* [[Gilbert cell]]
			* [[Optical heterodyne detection]]
			* [[Intermodulation]]
			* [[Third-order intercept point]]
			* [[Rusty bolt effect]]

			==References==
			{{Reflist}}

			==External links==
			{{Commons category\|Radio electronic diagrams}}

			{{FS1037C}}
			{{Analogue TV transmitter topics}}

			{{DEFAULTSORT:Frequency Mixer}}
			[[Category:Frequency mixers\| ]]
			[[Category:Electronic circuits]]
			[[Category:Communication circuits]]
			[[Category:Radio electronics]]
			[[Category:Telecommunication theory]]

76.120.181.41: edit

2012-08-08T21:34:34Z

edit

New page

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