Editing Negative feedback (section)

===Negative feedback amplifier===
{{main|Negative feedback amplifier}}
The negative feedback amplifier was invented by [[Harold Stephen Black]] at [[Bell Laboratories]] in 1927, and granted a patent in 1937 (US Patent 2,102,671)<ref>{{Cite web |last=Black |first=Harold |date=1937-12-21 |title=U.S. Patent 2,102,671: Wave Translation System |url=http://www.sos.siena.edu/~aweatherwax/electronics/black_patent.pdf |url-status=dead |archive-url=https://web.archive.org/web/20141006074403/http://www.sos.siena.edu/~aweatherwax/electronics/black_patent.pdf |archive-date=2014-10-06 |access-date= |website=www.eepatents.com}}</ref> "a continuation of application Serial No. 298,155, filed August 8, 1928 ...").<ref name=Brittain>{{cite journal |author=James E Brittain |title=Electrical engineering hall of fame: Harold S Black |journal=Proceedings of the IEEE |date=February 2011 |issue=2 |volume=99 |pages=351–353 |url=http://www.ieee.org/documents/proc_scanpast0211.pdf |archive-url=https://web.archive.org/web/20141129085736/http://www.ieee.org/documents/proc_scanpast0211.pdf |url-status=dead |archive-date=November 29, 2014 |doi=10.1109/jproc.2010.2090997}}</ref><ref name=Desoer>{{cite journal |author=CA Desoer |title=In Memoriam: Harold Stephen Black |journal=IEEE Transactions on Automatic Control |volume=AC-29 |pages=673–674 |number=8 |date=August 1984 |doi=10.1109/tac.1984.1103645 }}</ref>
:"The patent is 52 pages long plus 35 pages of figures. The first 43 pages amount to a small treatise on feedback amplifiers!"<ref name=Desoer/>

There are many advantages to feedback in amplifiers.<ref name=Kal1>{{cite book |author=Santiram Kal |title=Basic electronics: Devices, circuits and its fundamentals |chapter=§6.3 Advantages of negative feedback amplifiers |pages=193 ''ff'' |chapter-url=https://books.google.com/books?id=_Bw_-ZyGL6YC&pg=PA193 |isbn=9788120319523 |year=2009 |publisher=PHI Learning Pvt. Ltd}}</ref>  In design, the type of feedback and amount of feedback are carefully selected to weigh and optimize these various benefits.

====Advantages of amplifier negative voltage feedback====
{{refimprove section|date=March 2025}}
Negative voltage feedback in amplifiers has the following advantages; it
# reduces non-linear distortion, i.e., produces higher fidelity;{{cn|date=March 2025}}
# increases circuit stability: i.e., gains remain stable over variations in ambient temperature, frequency, and signal amplitude;{{cn|date=March 2025}}
# slightly increases bandwidth;{{cn|date=March 2025}}
# modifies input and output impedances;{{cn|date=March 2025}}
# considerably reduces harmonic, phase, amplitude, and frequency distortions;{{cn|date=March 2025}} and
# considerably reduces noise.{{cn|date=March 2025}}

<!--NOTE: WIKILINKS DO NOT REPLACE REQUIREMENT FOR CITATIONS IN THIS ARTICLE, SEE [[WP:VERIFY]].-->
Though negative feedback has many advantages, amplifiers with feedback can [[oscillate]] (see  [[Step response#Step response of feedback amplifiers|Step response of feedback amplifiers]]),{{cn|date=March 2025}} and they may exhibit [[instability]].{{cn|date=March 2025}} [[Harry Nyquist]] of [[Bell Laboratories]] proposed the [[Nyquist stability criterion|a stability criterion]] and a [[Nyquist plot|plot]] to identify stable feedback systems, including amplifiers and control systems.{{cn|date=March 2025}}

<!--TEXT CHECKS/VERIFICATIONS MADE THROUGH THIS POINT OF THIS SECTION. REST OF SECTION NOT YET CHECKED.-->
[[File:Negative feedback amplifier with disturbance.png|200px|thumb|Negative feedback amplifier with external disturbance.<ref name=Thompson>
{{cite book |author=Marc Thomson |title=Intuitive Analog Circuit Design |chapter=Figure 11-4: Classical single input, single output control loop |chapter-url=https://books.google.com/books?id=d8EJP8qQQcwC&q=%22Classical+single+input,+single+output+control+loop%22&pg=PA308 |isbn=9780080478753 |year=2006 |publisher=Newnes}}
</ref> The feedback is negative if &beta;''A''&thinsp;>0.]]
The figure shows a simplified block diagram of a [[negative feedback amplifier]].

The feedback sets the overall (closed-loop) amplifier gain at a value:

:<math>\frac{O}{I} =\frac {A}  { 1+\beta A }  \approx \frac {1}{\beta} \ ,</math>

where the approximate value assumes &beta;''A '' >> 1. This expression shows that a gain greater than one requires &beta; < 1. Because the approximate gain 1/&beta; is independent of the open-loop gain ''A'', the feedback is said to 'desensitize' the closed-loop gain to variations in ''A '' (for example, due to manufacturing variations between units, or temperature effects upon components), provided only that the gain ''A'' is sufficiently large.<ref name=Kal3>
{{cite book |chapter-url=https://books.google.com/books?id=_Bw_-ZyGL6YC&q=%22the+percentage+change+in%22,+%22is+smaller+than+the+percentage+change+in%22,+%22by+an+amount+of+feedback+factor%22&pg=PA194 |chapter=§6.3.1 Gain stability |author=Santiram Kal |title=Basic Electronics: Devices, Circuits, and IT Fundamentals |isbn=9788120319523 |year=2009 |publisher= PHI Learning Pvt. Ltd |pages=193–194}}
</ref> In this context, the factor (1+&beta;''A'') is often called the 'desensitivity factor',<ref name=Thompson2>
[https://books.google.com/books?id=d8EJP8qQQcwC&dq=%22is+called+the+desensitivity+of+the+system%22&pg=PA309 Marc T Thompson, p. 309]</ref><ref name=Lee>
{{cite book |title=The Design of CMOS Radio Frequency Circuits |author1=Thomas H Lee |page=447 |edition=2nd |publisher=Cambridge University Press |year=2004 |url=https://books.google.com/books?id=io1hL48OqBsC&q=%22of+a+feedback+system%22+%22is+often+called%22&pg=PA447 |isbn=9780521835398}}
</ref> and in the broader context of feedback effects that include other matters like [[Negative feedback amplifier#Input and output resistances|electrical impedance]] and [[Negative feedback amplifier#Bandwidth extension|bandwidth]], the 'improvement factor'.<ref name=Malik>
{{cite book |title=Electronic Circuits: Analysis simulation and design |author=Norbert A Malik |page=671 |chapter=Improvement Factor |chapter-url=https://books.google.com/books?id=7AJTAAAAMAAJ&q=improvement+factor |isbn=9780023749100 |year=1995 |publisher=Prentice Hall}}
</ref>

If the disturbance ''D'' is included, the amplifier output becomes:
:<math>O =\frac {AI}  { 1+\beta A }  +\frac {D}{1+ \beta A} \ , </math>

which shows that the feedback reduces the effect of the disturbance by the 'improvement factor' (1+&beta; ''A''). The disturbance ''D'' might arise from fluctuations in the amplifier output due to noise and nonlinearity (distortion) within this amplifier, or from other noise sources such as power supplies.<ref name=Kal4>
{{cite book |title=Basic Electronics: Devices, Circuits and ''IT'' fundamentals |author=Santiram Kal |chapter-url=https://books.google.com/books?id=_Bw_-ZyGL6YC&q=%22The+sources+of+noise+in+an+amplifier%22&pg=PA194 |page=194 |chapter=§6.3.2 Noise Reduction|date=14 January 2009 |publisher=PHI Learning Pvt. |isbn=9788120319523 }}
</ref><ref name=Bhattacharya3>
{{cite book |title=Linear Control Systems: For Punjab Technical University |author=SK Bhattacharya |chapter=§5.3.3 Effect of feedback on disturbance signal |publisher=Pearson Education India |chapter-url=https://books.google.com/books?id=e5Z1A_6jxAUC&q=%22Effect+of+feedback+on+disturbance+signal%22&pg=PA137 |isbn=9788131759523}}
</ref>

The difference signal ''I''–&beta;''O'' at the amplifier input is sometimes called the "error signal".<ref name=Rashid>
{{cite book |url=https://www.google.com/search?q=%22the+difference+between+the+input+and+the+feedback+signals,+called+the+error+signal%22 |page=642 |author=Muhammad Rashid |title=Microelectronic Circuits: Analysis & Design |isbn=9780495667728 |publisher=Cengage Learning |edition=2nd  |year=2010}}
</ref> According to the diagram, the error signal is:
:<math> \text{Error signal} = I - \beta O = I \left ( 1-\beta \frac{O}{I} \right ) =\frac {I} {1 + \beta A} - \frac { \beta D} {1+\beta A} \ . </math>

From this expression, it can be seen that a large 'improvement factor' (or a large [[loop gain]] &beta;''A'') tends to keep this error signal small.

Although the diagram illustrates the principles of the negative feedback amplifier, modeling a real amplifier as a [[Amplifier#Unilateral or bilateral|unilateral forward amplification block]] and a unilateral feedback block has significant limitations.<ref name=Chen>
{{cite book |title=Circuit Analysis and Feedback Amplifier Theory |author=Wai-Kai Chen |chapter=Chapter 13: General feedback theory |chapter-url=https://books.google.com/books?id=ZlJM1OLDQx0C&q=%22THe+ideal+feedback+model+is+not+an+adequate+representation+of+a+practical+amplifier%22&pg=SA13-PA1 |quote=[In a practical amplifier] the forward path may not be strictly unilateral, the feedback path is usually bilateral, and the input and output coupling networks are often complicated. |pages=13–1 |isbn=9781420037272 |year=2005 |publisher=CRC Press}}
</ref> For methods of analysis that do not make these idealizations, see the article [[Negative feedback amplifier#Signal flow analysis|Negative feedback amplifier]].