Substitution model - Revision history

129.240.215.211: /* The mathematics of substitution models */

2014-06-13T13:38:51Z

The mathematics of substitution models

← Older revision		Revision as of 15:38, 13 June 2014
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	~~'''Friis formula''' or '''Friis's formula''' (sometimes '''Friis' formula'''), named after Danish~~-~~American electrical engineer [[Harald T. Friis]], refers~~ to ~~either of two formulas used in [[telecommunications engineering]]~~ to ~~calculate the [[signal-~~to~~-noise ratio]] of a multistage [[amplifier]]. One relates to [[noise factor]] while~~ the ~~other relates to [[noise temperature]]~~.

	==The ~~Friis formula~~ for ~~noise factor==~~

	~~Friis's formula~~ is ~~used to calculate~~ the ~~total [[noise factor]]~~ of ~~a cascade of stages, each with its own [[noise factor]] and [[gain]]~~ (~~assuming that the impedances are matched at each stage~~). ~~The total [[noise factor]] can then be used to calculate~~ the ~~total [[noise figure]]. The total [[noise factor]]~~ is ~~given as~~

	~~:<math>F_{total} = F_1 + \frac{F_2~~-~~1}{G_1} + \frac{F_3-1}{G_1 G_2} + \frac{F_4-1}{G_1 G_2 G_3} +~~ .~~.. + \frac{F_n~~ - ~~1}{G_1 G_2 .~~.. ~~G_{n-1}}</math>~~

	~~where <math>F_n~~<~~/math~~> ~~and~~ <~~math~~>~~G_n</math> are~~ the ~~noise factor and available [[power gain]], respectively,~~ of ~~the n-th stage~~. ~~Note that both magnitudes are expressed as ratios~~, ~~not in decibels.~~

	~~An important consequence of this formula~~ is ~~that~~ the ~~overall noise figure of a [[radio receiver]] is primarily established by~~ the ~~noise figure of its first amplifying stage~~. ~~Subsequent stages have~~ a ~~diminishing effect on [[signal-~~to~~-noise ratio]]~~. ~~For~~ this ~~reason, the first stage amplifier~~ in ~~a receiver is often called~~ the ~~[[low-noise amplifier]] (LNA)~~. ~~The overall receiver noise "factor"~~ is ~~then~~

	~~:<math>F_{receiver} = F_{LNA} + \frac{(F_{rest}~~-~~1)}{G_{LNA}}</math>~~

	~~where <math>F_{rest}</math>~~ is ~~the overall noise factor~~ of the ~~subsequent stages. According~~ to the ~~equation,~~ the ~~overall noise factor,~~ <~~math~~>~~F_{receiver}~~<~~/math~~>, is ~~dominated~~ by the ~~noise factor~~ of the ~~LNA~~, <~~math~~>~~F_{LNA}~~<~~/math~~>, ~~if the gain is sufficiently high~~. ~~(The resultant Noise Figure expressed in dB~~ is ~~10 log(Noise Factor)~~.)

	~~==The Friis formula for noise temperature==~~

	~~Friis's formula can be equivalently expressed in terms~~ of ~~[[noise temperature]]:~~

	~~:<math>T_{total} = T_1 + \frac{T_2}{G_1} + \frac{T_3}{G_1 G_2} +~~ ..~~.</math>~~

	~~==Printed references==~~

	*J.D. Kraus, '~~'Radio Astronomy''~~, ~~McGraw-Hill~~, ~~1966.~~

	~~==Online references==~~

	*RF Cafe [http://~~www.rfcafe~~.~~com~~/~~references~~/~~electrical/noise~~-~~figure~~.~~htm] Cascaded noise figure~~.
	*Microwave Encyclopedia [http://www.~~microwaves101~~.~~com/encyclopedia/cascadeanalysis~~.~~cfm] Cascade analysis~~.
	*Friis biography at IEEE [http://www.~~ieeeghn.org/wiki/index.php/Harald_T._Friis]~~

	~~[[Category:Noise]]~~
	~~[[Category:Equations]]~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-30T11:55:00Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 13:55, 30 January 2014
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	~~28 years old Medical Laboratory Technician Catanzaro from Saint John~~, ~~enjoys~~ to ~~spend some time physical exercise~~ (~~aerobics weights~~), ~~new launch property singapore and educational courses~~. In the ~~previous year has completed~~ a ~~journey~~ to ~~Archaeological Ruins at Moenjodaro~~.<br><br>~~Feel free~~ to ~~surf to my web site~~ - [http://~~zoom2x~~.~~net~~/x2/~~?document_srl=138281 the Skywoods developer~~]		{{Distinguish\|Friis transmission equation}}

			'''Friis formula''' or '''Friis's formula''' (sometimes '''Friis' formula'''), named after Danish-American electrical engineer [[Harald T. Friis]], refers to either of two formulas used in [[telecommunications engineering]] to calculate the [[signal-to-noise ratio]] of a multistage [[amplifier]]. One relates to [[noise factor]] while the other relates to [[noise temperature]].

			==The Friis formula for noise factor==

			Friis's formula is used to calculate the total [[noise factor]] of a cascade of stages, each with its own [[noise factor]] and [[gain]] (assuming that the impedances are matched at each stage). The total [[noise factor]] can then be used to calculate the total [[noise figure]]. The total [[noise factor]] is given as

			:<math>F_{total} = F_1 + \frac{F_2-1}{G_1} + \frac{F_3-1}{G_1 G_2} + \frac{F_4-1}{G_1 G_2 G_3} + ... + \frac{F_n - 1}{G_1 G_2 ... G_{n-1}}</math>

			where <math>F_n</math> and <math>G_n</math> are the noise factor and available [[power gain]], respectively, of the n-th stage. Note that both magnitudes are expressed as ratios, not in decibels.

			An important consequence of this formula is that the overall noise figure of a [[radio receiver]] is primarily established by the noise figure of its first amplifying stage. Subsequent stages have a diminishing effect on [[signal-to-noise ratio]]. For this reason, the first stage amplifier in a receiver is often called the [[low-noise amplifier]] (LNA). The overall receiver noise "factor" is then

			:<math>F_{receiver} = F_{LNA} + \frac{(F_{rest}-1)}{G_{LNA}}</math>

			where <math>F_{rest}</math> is the overall noise factor of the subsequent stages. According to the equation, the overall noise factor, <math>F_{receiver}</math>, is dominated by the noise factor of the LNA, <math>F_{LNA}</math>, if the gain is sufficiently high. (The resultant Noise Figure expressed in dB is 10 log(Noise Factor).)

			==The Friis formula for noise temperature==

			Friis's formula can be equivalently expressed in terms of [[noise temperature]]:

			:<math>T_{total} = T_1 + \frac{T_2}{G_1} + \frac{T_3}{G_1 G_2} + ...</math>

			==Printed references==

			*J.D. Kraus, ''Radio Astronomy'', McGraw-Hill, 1966.

			==Online references==

			*RF Cafe [http://www.rfcafe.com/references/electrical/noise-figure.htm] Cascaded noise figure.
			*Microwave Encyclopedia [http://www.microwaves101.com/encyclopedia/cascadeanalysis.cfm] Cascade analysis.
			*Friis biography at IEEE [http://www.ieeeghn.org/wiki/index.php/Harald_T._Friis]

			[[Category:Noise]]
			[[Category:Equations]]

141.14.31.21: /* Mechanistic vs. empirical models */

2012-03-16T12:58:48Z

Mechanistic vs. empirical models

New page

28 years old Medical Laboratory Technician Catanzaro from Saint John, enjoys to spend some time physical exercise (aerobics weights), new launch property singapore and educational courses. In the previous year has completed a journey to Archaeological Ruins at Moenjodaro.<br><br>Feel free to surf to my web site - [http://zoom2x.net/x2/?document_srl=138281 the Skywoods developer]