Bitangents of a quartic - Revision history

en>Rjwilmsi: /* References */Added 1 doi to a journal cite using AWB (10209)

2014-05-23T22:44:51Z

References: Added 1 doi to a journal cite using AWB (10209)

← Older revision		Revision as of 00:44, 24 May 2014
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	~~'''Polar modulation'''~~ is ~~analogous to [[quadrature modulation]] in the same way that [[polar coordinates]] are analogous to [[Cartesian coordinates]]. Quadrature modulation makes use of Cartesian coordinates, ''x''~~ and '~~'y''~~. ~~When considering quadrature modulation, the ''x'' axis is called the ''I'' (in-phase) axis,~~ and ~~the ''y'' axis~~ is ~~called the ''Q'' (quadrature) axis. Polar modulation makes use of polar coordinates, ''r'' (amplitude) and ''Θ'' (phase). <ref>http://www.mwrf.com/Articles/Index.cfm?Ad=1&ArticleID=9176</ref>~~		Ed is what people call me and my spouse doesn't like it at all. The favorite pastime for him and his kids is to perform lacross and he would never give it up. Mississippi is exactly where her home is but her husband wants them to move. He works as a bookkeeper.<br><br>Also visit my web site [https://www-ocl.gist.ac.kr/work/xe/?document_srl=605236 best psychics]

	~~The quadrature modulator approach~~ to [[digital radio]] transmission requires a [[linear amplifier\| linear]] [[RF power amplifier]] which creates a design conflict between improving power efficiency or maintaining amplifier linearity. Compromising linearity causes degraded signal quality, usually by adjacent channel degradation, which can be a fundamental factor in limiting network performance and ~~capacity~~. Additional problems with linear RF power amplifiers, including device parametric restrictions, temperature instability, power control accuracy, wideband noise and production yields are also common. On the other hand compromising power efficiency increases power consumption (which reduces battery life in handheld devices) and generates more heat.

	The issue of linearity in a power amplifier can theoretically be mitigated by requiring that the input signal of the power amplifier be "[[constant envelope]]", i.e. contain no amplitude variations. In a polar modulation system, the power amplifier input signal may vary only in phase. Amplitude modulation is ~~then accomplished by directly controlling the gain of the power amplifier through changing or modulating its supply voltage~~. ~~Thus a polar modulation system allows the use of highly [[switching amplifier\| non-linear power amplifier architectures]] such~~ as ~~[[Electronic_amplifier#Class_E\|Class E]] and [[Electronic_amplifier#Class_F_and_the_even_harmonics\|Class F]].~~

	~~In order to create the Polar signal, the phase transfer of the amplifier must be known over at least~~ a ~~17 dB amplitude range~~. ~~As the phase transitions from one to another, there will be an amplitude perturbation that can be calculated during the transition as,~~

	:<~~math~~>~~P(n) = \sqrt {I^2(n) + Q^2(n)}~~<~~/math~~> ~~<!-- Original formulae pre-Tex was... P(n) = sqrt (I(n)^2 + Q(n)^2) -->~~

	where n is the number of samples of I and Q and should be sufficiently large to allow an accurate tracing of the signal. One hundred samples per symbol would be about the lowest number that is workable.

	Now that the amplitude change of the signal is known, the phase error introduced by the amplifier at each amplitude change can be used to pre-distort the signal. One simply subtracts the phase error at each amplitude from the modulating I and Q signals.

	~~== History ==~~
	~~Polar modulation was originally developed by [[Thomas Edison]] in his 1874~~ [[quadruplex telegraph]] – this allowed 4 signals to be sent along a pair of lines, 2 in each direction. Sending a signal in each direction had already been accomplished earlier, and Edison found that by combining amplitude and phase modulation (i.e., by polar modulation), he could double this to 4 signals – hence, quadruplex.

	~~==See also==~~
	* [[Angle modulation]]
	* [[Phase modulation]]
	* [[Phase shift keying]] (PSK)

	~~== External links ==~~
	*[http://rfdesign.com/mag/radio_fundamentals_digital_quadrature/index.html Fundamentals of Digital Quadrature Modulation]
	*[http://www.tropian.com/polarImpact.php Matsushita (formerly Tropian)]
	*[http://www~~.sequoia~~-~~communications~~.~~com/technology~~.~~html Sequoia Communications]~~
	*[http://www.~~rfmd.com~~/~~productGuide.asp RF Micro Devices]~~
	*[http://~~www.skyworksinc.com/rfsbu_helios_II_edge.asp Skyworks]~~
	*[http://www.anadigics.com Anadigics, Inc]

	~~== Articles ==~~
	*[http://www.wsdmag.com/Articles/ArticleID/11479/11479.html Polar Modulation Emerges - Wireless Systems Design]
	*[http://www.commsdesign.com/story/OEG20030904S0013 Polar Modulation Ups Efficiency in Mobile PA Designs - CommsDesign]

	== ~~Notes ==~~
	~~<references />~~

	~~[[Category:Telecommunication theory]]~~
	~~[[Category:Radio modulation modes]]~~
	~~[[Category:Physical layer protocols]]~~
	~~[[Category:Data transmission]~~]

en>4pq1injbok: /* Connections to other structures */ fix condition on Cayley's symbols

2013-07-18T14:56:55Z

Connections to other structures: fix condition on Cayley's symbols

← Older revision		Revision as of 16:56, 18 July 2013
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	~~The name~~ of the ~~writer~~ is ~~Figures but it~~'~~s not [~~http://~~citymama~~.com~~.ua~~/~~profile_info~~.~~php~~?ID=~~38588 over~~ the ~~counter std test~~] ~~most masucline title out there~~. ~~To do aerobics~~ is a ~~factor~~ that I~~'m completely addicted~~ to. ~~Her husband~~ and ~~her live~~ in ~~Puerto Rico but she will have~~ to ~~move 1 day or another~~. ~~Managing people has~~ been ~~his day occupation for a whilst~~.		'''Polar modulation''' is analogous to [[quadrature modulation]] in the same way that [[polar coordinates]] are analogous to [[Cartesian coordinates]]. Quadrature modulation makes use of Cartesian coordinates, ''x'' and ''y''. When considering quadrature modulation, the ''x'' axis is called the ''I'' (in-phase) axis, and the ''y'' axis is called the ''Q'' (quadrature) axis. Polar modulation makes use of polar coordinates, ''r'' (amplitude) and ''Θ'' (phase). <ref>http://www.mwrf.com/Articles/Index.cfm?Ad=1&ArticleID=9176</ref>

			The quadrature modulator approach to [[digital radio]] transmission requires a [[linear amplifier\| linear]] [[RF power amplifier]] which creates a design conflict between improving power efficiency or maintaining amplifier linearity. Compromising linearity causes degraded signal quality, usually by adjacent channel degradation, which can be a fundamental factor in limiting network performance and capacity. Additional problems with linear RF power amplifiers, including device parametric restrictions, temperature instability, power control accuracy, wideband noise and production yields are also common. On the other hand compromising power efficiency increases power consumption (which reduces battery life in handheld devices) and generates more heat.

			The issue of linearity in a power amplifier can theoretically be mitigated by requiring that the input signal of the power amplifier be "[[constant envelope]]", i.e. contain no amplitude variations. In a polar modulation system, the power amplifier input signal may vary only in phase. Amplitude modulation is then accomplished by directly controlling the gain of the power amplifier through changing or modulating its supply voltage. Thus a polar modulation system allows the use of highly [[switching amplifier\| non-linear power amplifier architectures]] such as [[Electronic_amplifier#Class_E\|Class E]] and [[Electronic_amplifier#Class_F_and_the_even_harmonics\|Class F]].

			In order to create the Polar signal, the phase transfer of the amplifier must be known over at least a 17 dB amplitude range. As the phase transitions from one to another, there will be an amplitude perturbation that can be calculated during the transition as,

			:<math>P(n) = \sqrt {I^2(n) + Q^2(n)}</math> <!-- Original formulae pre-Tex was... P(n) = sqrt (I(n)^2 + Q(n)^2) -->

			where n is the number of samples of I and Q and should be sufficiently large to allow an accurate tracing of the signal. One hundred samples per symbol would be about the lowest number that is workable.

			Now that the amplitude change of the signal is known, the phase error introduced by the amplifier at each amplitude change can be used to pre-distort the signal. One simply subtracts the phase error at each amplitude from the modulating I and Q signals.

			== History ==
			Polar modulation was originally developed by [[Thomas Edison]] in his 1874 [[quadruplex telegraph]] – this allowed 4 signals to be sent along a pair of lines, 2 in each direction. Sending a signal in each direction had already been accomplished earlier, and Edison found that by combining amplitude and phase modulation (i.e., by polar modulation), he could double this to 4 signals – hence, quadruplex.

			==See also==
			* [[Angle modulation]]
			* [[Phase modulation]]
			* [[Phase shift keying]] (PSK)

			== External links ==
			*[http://rfdesign.com/mag/radio_fundamentals_digital_quadrature/index.html Fundamentals of Digital Quadrature Modulation]
			*[http://www.tropian.com/polarImpact.php Matsushita (formerly Tropian)]
			*[http://www.sequoia-communications.com/technology.html Sequoia Communications]
			*[http://www.rfmd.com/productGuide.asp RF Micro Devices]
			*[http://www.skyworksinc.com/rfsbu_helios_II_edge.asp Skyworks]
			*[http://www.anadigics.com Anadigics, Inc]

			== Articles ==
			*[http://www.wsdmag.com/Articles/ArticleID/11479/11479.html Polar Modulation Emerges - Wireless Systems Design]
			*[http://www.commsdesign.com/story/OEG20030904S0013 Polar Modulation Ups Efficiency in Mobile PA Designs - CommsDesign]

			== Notes ==
			<references />

			[[Category:Telecommunication theory]]
			[[Category:Radio modulation modes]]
			[[Category:Physical layer protocols]]
			[[Category:Data transmission]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-06T22:29:38Z

ISBNs (Build KC)

New page

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