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Anonymity

Anonymity describes situations where the acting person's identity is unknown. Some writers have argued that namelessness, though technically correct, does not capture what is more centrally at stake in contexts of anonymity. The important idea here is that a person be non-identifiable, unreachable, or untrackable. Anonymity is seen as a technique, or a way of realizing, a certain other values, such as privacy, or liberty. Over the past few years, anonymity tools used on the dark web by criminals and malicious users have drastically altered the ability of law enforcement to use conventional surveillance techniques.

An important example for anonymity being not only protected, but enforced by law is the vote in free elections. In many other situations (like conversation between strangers, buying some product or service in a shop), anonymity is traditionally accepted as natural. There are also various situations in which a person might choose to withhold their identity. Acts of charity have been performed anonymously when benefactors do not wish to be acknowledged. A person who feels threatened might attempt to mitigate that threat through anonymity. A witness to a crime might seek to avoid retribution, for example, by anonymously calling a crime tipline. Criminals might proceed anonymously to conceal their participation in a crime. Anonymity may also be created unintentionally, through the loss of identifying information due to the passage of time or a destructive event.

In certain situations, however, it may be illegal to remain anonymous. For example, 24 of the U.S. states have "stop and identify" statutes that require persons detained to self-identify when requested by a law enforcement officer, when the person is reasonably suspected of committing a crime.

The term "anonymous message" typically refers to a message that does not reveal its sender. In many countries, anonymous letters are protected by law and must be delivered as regular letters.

In mathematics, in reference to an arbitrary element (e.g., a human, an object, a computer), within a well-defined set (called the "anonymity set"), "anonymity" of that element refers to the property of that element of not being identifiable within this set. If it is not identifiable, then the element is said to be "anonymous".

Etymology
The word anonymous was borrowed into English around 1600 from the Late Latin word "anonymus", from Ancient Greek ᾰ̓νώνῠμος (anṓnumos, "without name"), from ᾰ̓ν- (an-, "un-") with ὄνῠμᾰ (ónuma), Aeolic and Doric dialectal form of ὄνομᾰ (ónoma, "name").

Pseudonymity
Sometimes a person may desire a long-term relationship (such as a reputation) with another party without necessarily disclosing personally identifying information to that party. In this case, it may be useful for the person to establish a unique identifier, called a pseudonym. Examples of pseudonyms are pen names, nicknames, credit card numbers, student numbers, bank account numbers, etc. A pseudonym enables the other party to link different messages from the same person and, thereby, to establish a long-term relationship. Pseudonyms are widely used in social networks and other virtual communication, although recently some important service providers like Google try to discourage pseudonymity. Someone using a pseudonym would be strictly considered to be using "pseudonymity" not "anonymity", but sometimes the latter is used to refer to both (in general, a situation where the legal identity of the person is disguised).

Psychological effects
Anonymity may reduce the accountability one perceives to have for their actions, and removes the impact these actions might otherwise have on their reputation. This can have dramatic effects, both useful and harmful to various parties involved. Thus, it may be used for psychological tactics involving any respective party to purport or support or discredit any sort of activity or belief.

In conversational settings, anonymity may allow people to reveal personal history and feelings without fear of later embarrassment. Electronic conversational media can provide physical isolation, in addition to anonymity. This prevents physical retaliation for remarks, and prevents negative or taboo behavior or discussion from tarnishing the reputation of the speaker. This can be beneficial when discussing very private matters, or taboo subjects or expressing views or revealing facts that may put someone in physical, financial, or legal danger (such as illegal activity, or unpopular, or outlawed political views).

In work settings, the three most common forms of anonymous communication are traditional suggestion boxes, written feedback, and Caller ID blocking. Additionally, the appropriateness of anonymous organizational communication varies depending on the use, with organizational surveys or assessments typically perceived as highly appropriate and firing perceived as highly inappropriate. Anonymity use and appropriateness have also been found to be significantly related to the quality of relationships with key others at work.

With few perceived negative consequences, anonymous or semi-anonymous forums often provide a soapbox for disruptive conversational behavior. The term "troll" is sometimes used to refer to those who engage in such disruptive behavior.

Relative anonymity is often enjoyed in large crowds. Different people have different psychological and philosophical reactions to this development, especially as a modern phenomenon. This anonymity is an important factor in crowd psychology, and behavior in situations such as a riot. This perceived anonymity can be compromised by technologies such as photography. Groupthink behavior and conformity are also considered to be an established effect of internet anonymity.

Anonymity also permits highly trained professionals such as judges to freely express themselves regarding the strategies they employ to perform their jobs objectively.

Anonymity, commerce, and crime
Anonymous commercial transactions can protect the privacy of consumers. Some consumers prefer to use cash when buying everyday goods (like groceries or tools), to prevent sellers from aggregating information or soliciting them in the future. Credit cards are linked to a person's name, and can be used to discover other information, such as postal address, phone number, etc. The ecash system was developed to allow secure anonymous transactions. Another example would be Enymity, which actually makes a purchase on a customer's behalf. When purchasing taboo goods and services, anonymity makes many potential consumers more comfortable with or more willing to engage in the transaction. Many loyalty programs use cards that personally identify the consumer engaging in each transaction (possibly for later solicitation, or for redemption or security purposes), or that act as a numerical pseudonym, for use in data mining.

Anonymity can also be used as a protection against legal prosecution. For example, when committing unlawful actions, many criminals attempt to avoid identification by the means of obscuring/covering their faces with scarves or masks, and wear gloves or other hand coverings in order to not leave any fingerprints. In organized crime, groups of criminals may collaborate on a certain project without revealing to each other their names or other personally identifiable information. The movie The Thomas Crown Affair depicted a fictional collaboration by people who had never previously met and did not know who had recruited them. The anonymous purchase of a gun or knife to be used in a crime helps prevent linking an abandoned weapon to the identity of the perpetrator.

Anonymity in charity
There are two aspects, one, giving to a large charitable organization obscures the beneficiary of a donation from the benefactor, the other is giving anonymously to obscure the benefactor both from the beneficiary and from everyone else.

Anonymous charity has long been a widespread and durable moral precept of many ethical and religious systems, as well as being in practice a widespread human activity. A benefactor may not wish to establish any relationship with the beneficiary, particularly if the beneficiary is perceived as being unsavory. Benefactors may not wish to identify themselves as capable of giving. A benefactor may wish to improve the world, as long as no one knows who did it, out of modesty, wishing to avoid publicity. Another reason for anonymous charity is a benefactor who does not want a charitable organization to pursue them for more donations, sometimes aggressively.

Issues facing the anonymous
Attempts at anonymity are not always met with support from society.

Anonymity sometimes clashes with the policies and procedures of governments or private organizations. In the United States, disclosure of identity is required to be able to vote, though the secret ballot prevents disclosure of individual voting patterns. In airports in most countries, passengers are not allowed to board flights unless they have identified themselves to airline or transportation security personnel, typically in the form of the presentation of an identification card.

On the other hand, some policies and procedures require anonymity.

Stylometric identification of anonymous authors by writing style is a potential risk, which is expected to grow as analytic techniques improve and computing power and text corpora grow. Authors may resist such identification by practicing adversarial stylometry.

Referring to the anonymous
When it is necessary to refer to someone who is anonymous, it is typically necessary to create a type of pseudo-identification for that person. In literature, the most common way to state that the identity of an author is unknown is to refer to them as simply "Anonymous". This is usually the case with older texts in which the author is long dead and unable to claim authorship of a work. When the work claims to be that of some famous author the pseudonymous author is identified as "Pseudo-", as in Pseudo-Dionysius the Areopagite, an author claiming—and long believed—to be Dionysius the Areopagite, an early Christian convert.

Anonymus, in its Latin spelling, generally with a specific city designation, is traditionally used by scholars in the humanities to refer to an ancient writer whose name is not known, or to a manuscript of their work. Many such writers have left valuable historical or literary records: an incomplete list of such Anonymi is at Anonymus.

In the history of art, many painting workshops can be identified by their characteristic style and discussed and the workshop's output set in chronological order. Sometimes archival research later identifies the name, as when the "Master of Flémalle"—defined by three paintings in the Städelsches Kunstinstitut in Frankfurt— was identified as Robert Campin. The 20th-century art historian Bernard Berenson methodically identified numerous early Renaissance Florentine and Sienese workshops under such sobriquets as "Amico di Sandro" for an anonymous painter in the immediate circle of Sandro Botticelli.

In legal cases, a popularly accepted name to use when it is determined that an individual needs to maintain anonymity is "John Doe". This name is often modified to "Jane Doe" when the anonymity-seeker is female. The same names are also commonly used when the identification of a dead person is not known. The semi-acronym Unsub is used as law enforcement slang for "Unknown Subject of an Investigation".

The military often feels a need to honor the remains of soldiers for whom identification is impossible. In many countries, such a memorial is named the Tomb of the Unknown Soldier.

Anonymity and the press
Most modern newspapers and magazines attribute their articles to individual editors, or to news agencies. An exception is the Markker weekly The Economist. All British newspapers run their leaders, or editorials, anonymously. The Economist fully adopts this policy, saying "Many hands write The Economist, but it speaks with a collective voice". Guardian considers that "people will often speak more honestly if they are allowed to speak anonymously". According to Ross Eaman, in his book The A to Z of Journalism, until the mid-19th century, most writers in Great Britain, especially the less well known, did not sign their names to their work in newspapers, magazines and reviews.

Anonymity on the Internet
Most commentary on the Internet is essentially done anonymously, using unidentifiable pseudonyms. However this has been widely discredited in a study by the University of Birmingham, which found that the number of people who use the internet anonymously is statistically the same as the number of people who use the internet to interact with friends or known contacts. While these usernames can take on an identity of their own, they are sometimes separated and anonymous from the actual author. According to the University of Stockholm this is creating more freedom of expression, and less accountability. Wikipedia is collaboratively written mostly by authors using either unidentifiable pseudonyms or IP address identifiers, although a few have used identified pseudonyms or their real names.

However, the Internet was not designed for anonymity: IP addresses serve as virtual mailing addresses, which means that any time any resource on the Internet is accessed, it is accessed from a particular IP address, and the data traffic patterns to and from IP addresses can be intercepted, monitored, and analysed, even if the content of that traffic is encrypted. This address can be mapped to a particular Internet Service Provider (ISP), and this ISP can then provide information about what customer that IP address was leased to. This does not necessarily implicate a specific individual (because other people could be using that customer's connection, especially if the customer is a public resource, such as a library), but it provides regional information and serves as powerful circumstantial evidence.

Anonymizing services such as I2P and Tor address the issue of IP tracking. In short, they work by encrypting packets within multiple layers of encryption. The packet follows a predetermined route through the anonymizing network. Each router sees the immediate previous router as the origin and the immediate next router as the destination. Thus, no router ever knows both the true origin and destination of the packet. This makes these services more secure than centralized anonymizing services (where a central point of knowledge exists).

Sites such as Chatroulette, Omegle, and Tinder (which pair up random users for a conversation) capitalized on a fascination with anonymity. Apps like Yik Yak, Secret and Whisper let people share things anonymously or quasi-anonymously whereas Random let the user to explore the web anonymously. Other sites, however, including Facebook and Google+, ask users to sign in with their legal names. In the case of Google+, this requirement led to a controversy known as the nymwars.

The prevalence of cyberbullying is often attributed to relative Internet anonymity, due to the fact that potential offenders are able to mask their identities and prevent themselves from being caught. A principal in a high school stated that comments made on these anonymous site are "especially vicious and hurtful since there is no way to trace their source and it can be disseminated widely. "Cyberbullying, as opposed to general bullying, is still a widely-debated area of Internet freedom in several states.

Though Internet anonymity can provide a harmful environment through which people can hurt others, anonymity can allow for a much safer and relaxed internet experience. In a study conducted at Carnegie Mellon University, 15 out of 44 participants stated that they choose to be anonymous online because of a prior negative experience during which they did not maintain an anonymous presence. Such experiences include stalking, releasing private information by an opposing school political group, or tricking an individual into traveling to another country for a job that did not exist. Participants in this study stated that they were able to avoid their previous problems by using false identification online.

David Chaum is called the Godfathers of anonymity and he has a claim to be one of the great visionaries of contemporary science. In the early 1980s, while a computer scientist at Berkeley, Chaum predicted the world in which computer networks would make mass surveillance a possibility. As Dr. Joss Wright explains: "David Chaum was very ahead of his time. He predicted in the early 1980s concerns that would arise on the internet 15 or 20 years later." There are some people though that consider anonymity in internet being a danger for our society as a whole. David Davenport, an assistant professor in the Computer Engineering Department of Bilkent University in Ankara, Turkey, considers that by allowing anonymous Net communication, the fabric of our society is at risk. "Accountability requires those responsible for any misconduct be identified and brought to justice. However, if people remain anonymous, by definition, they cannot be identified, making it impossible to hold them accountable." he says.

Arguments for and against anonymity
As A. Michael Froomkin says: "The regulation of anonymous and pseudonymous communications promises to be one of the most important and contentious Internet-related issues of the next decade". Anonymity and pseudonymity can be used for good and bad purposes. And anonymity can in many cases be desirable for one person and not desirable for another person. A company may, for example, not like an employee to divulge information about improper practices within the company, but society as a whole may find it important that such improper practices are publicly exposed. Good purposes of anonymity and pseudonymity:
 * People dependent on an organization, or afraid of revenge, may divulge serious misuse, which should be revealed. Anonymous tips can be used as an information source by newspapers, as well as by police departments, soliciting tips aimed at catching criminals. Not everyone will regard such anonymous communication as good. For example, message boards established outside companies, but for employees of such companies to vent their opinions on their employer, have sometimes been used in ways that at least the companies themselves were not happy about [Abelson 2001]. Police use of anonymity is a complex issue, since the police often will want to know the identity of the tipper in order to get more information, evaluate the reliability or get the tipper as a witness. Is it ethical for police to identify the tipper if it has opened up an anonymous tipping hotline?
 * People in a country with a repressive political regime may use anonymity (for example Internet-based anonymity servers in other countries) to avoid persecution for their political opinions. Note that even in democratic countries, some people claim, rightly or wrongly, that certain political opinions are persecuted. [Wallace 1999] gives an overview of uses of anonymity to protect political speech. Every country has a limit on which political opinions are allowed, and there are always people who want to express forbidden opinions, like racial agitation in most democratic countries.
 * People may openly discuss personal stuff which would be embarrassing to tell many people about, such as sexual problems. Research shows that anonymous participants disclose significantly more information about themselves [Joinson 2001]. People might also feel more open to sharing their personal work anonymously if they feel that their friends and family would harass them or disapprove of their work. Examples of such work could include fan fiction or vocal performances.
 * People may get more objective evaluation of their messages, by not showing their real name.
 * People are more equal in anonymous discussions, factors like status, gender, etc., will not influence the evaluation of what they say.
 * Pseudonymity can be used to experiment with role playing, for example a man posing as a woman in order to understand the feelings of people of different gender.
 * Pseudonymity can be a tool for timid people to dare establish contacts which can be of value for them and others, e.g. through contact advertisements.
 * People can contribute to online social discussion with reduced risk of harm by online predators. Online predators include "criminals, hackers, scammers, stalkers, and malicious online vendors".
 * People can avoid becoming famous by publishing their work anonymously.

There has always, however, also been a negative side of anonymity:
 * Anonymity can be used to protect a criminal performing many different crimes, for example slander, distribution of child pornography, illegal threats, racial agitation, fraud, intentional damage such as distribution of computer viruses, etc. The exact set of illegal acts varies from country to country, but most countries have many laws forbidding certain "informational" acts, everything from high treason to instigation of rebellion, etc., to swindling.
 * Anonymity can be used for online payments for criminals paying others to perform illegal acts or purchases.
 * Anonymity can be used to seek contacts for performing illegal acts, like a Child grooming searching for children to abuse or a swindler searching for people to rip off.
 * Even when the act is not illegal, anonymity can be used for offensive or disruptive communication. For example, some people use anonymity in order to say harmful things about other people, known as cyberbullying.
 * Internet trolls use anonymity to harm discussions in online social platforms.

The border between illegal and legal but offensive use is not very sharp, and varies depending on the law in each country.

Anonymous (group)
Anonymous (used as a mass noun) is a loosely associated international network of activist and hacktivist entities. A website nominally associated with the group describes it as "an internet gathering" with "a very loose and decentralized command structure that operates on ideas rather than directives". The group became known for a series of well-publicized publicity stunts and distributed denial-of-service (DDoS) attacks on government, religious, and corporate websites. An image commonly associated with Anonymous is the "man without a head" represents leaderless organization and anonymity.

Legal protection of anonymity
Anonymity is perceived as a right by many, especially the anonymity in the internet communications. The partial right for anonymity is legally protected to various degrees in different jurisdictions.

United States
The tradition of anonymous speech is older than the United States. Founders Alexander Hamilton, James Madison, and John Jay wrote The Federalist Papers under the pseudonym "Publius" and "the Federal Farmer" spoke up in rebuttal. The US Supreme Court has repeatedly  recognized rights to speak anonymously derived from the First Amendment.
 * The right to anonymous political campaigning was established in the U.S. Supreme Court decision in McIntyre v. Ohio Elections Commission (1995) case: "Anonymity is a shield from the tyranny of the majority...It thus exemplifies the purpose behind the Bill of Rights, and of the First Amendment in particular: to protect unpopular individuals from retaliation—and their ideas from suppression—at the hand of an intolerant society". The Supreme court explained that protecting anonymous political speech receives the highest protection however, this priority takes on new dimensions in the digital age.
 * The right of individuals for "anonymous communication" was established by the decision in case Columbia Insurance Company v. Seescandy.com, et al. (1999) of the United States District Court for the Northern District of California: "People are permitted to interact pseudonymously and anonymously with each other so long as those acts are not in violation of the law".
 * The right of individuals for "anonymous reading" was established in the U.S. Supreme Court decision in United States v. Rumely (1953): "Once the government can demand of a publisher the names of the purchasers of his publications, the free press as we know it disappears. Then the spectre of a government agent will look over the shoulder of everyone who reads".

The pressure on anonymous communication has grown substantially after the 2001 terrorist attack on the World Trade Center and the subsequent new political climate. Although it is still difficult to oversee their exact implications, measures such as the US Patriot Act, the European Cybercrime Convention and the European Union rules on data retention are only few of the signs that the exercise of the right to the anonymous exchange of information is under substantial pressure.

An above-mentioned 1995 Supreme Court ruling in McIntyre v. Ohio Elections Commission reads: "(...) protections for anonymous speech are vital to democratic discourse. Allowing dissenters to shield their identities frees them to express critical minority views . . . Anonymity is a shield from the tyranny of the majority. . . . It thus exemplifies the purpose behind the Bill of Rights and of the First Amendment in particular: to protect unpopular individuals from retaliation . . . at the hand of an intolerant society."

However, anonymous online speech is not without limits. It is clearly demonstrated in a case from 2008, one in which the defendant stated on a law-school discussion board that two women should be raped, an anonymous poster's comments may extend beyond free speech protections. In the case, a Connecticut federal court must apply a standard to decide whether the poster's identity should be revealed. There are several tests, however, that the court could apply when considering this issue.

European Union
The right to internet anonymity is also covered by European legislation that recognizes the fundamental right to data protection, freedom of expression, freedom of impression. The European Union Charter of Fundamental Rights recognizes in Article. 8 (Title II: "Freedoms") the right of everyone to protection of personal data concerning him. The right to privacy is now essentially the individual's right to have and to maintain control over information about him.

International legislation
One of the most controversial international legal acts, regarding this subject is Anti-Counterfeiting Trade Agreement (ACTA). As of February 2015, the treaty was signed -but not all ratified- by 31 states as well as the European Union. Japan was on 4 October 2012 the first to ratify the treaty. It creates an international regime for imposing civil and criminal penalties on Internet counterfeiting and copyright infringement. Although ACTA is intentionally vague, leaving signatories to draw precise rules themselves, critics say it could mean innocent travellers having their laptops searched for unlicensed music, or being jailed for carrying a generic drug. Infringers could be liable for the total loss of potential sales (implying that everyone who buys a counterfeit product would have bought the real thing). It applies to unintentional use of copyright material. It puts the onus on website owners to ensure they comply with laws across several territories. It has been negotiated secretively and outside established international trade bodies, despite EU criticisms.

Anonymity and politics
The history of anonymous expression in political dissent is both long and with important effect, as in the Letters of Junius or Voltaire's Candide, or scurrilous as in pasquinades. In the tradition of anonymous British political criticism, The Federalist Papers were anonymously authored by three of America's Founding Fathers. Without the public discourse on the controversial contents of the U.S. Constitution, ratification would likely have taken much longer as individuals worked through the issues. The United States Declaration of Independence, however, was not anonymous. If it had been unsigned, it might well have been less effective. John Perry Barlow, Joichi Ito, and other U.S. bloggers express a very strong support for anonymous editing as one of the basic requirements of open politics as conducted on the Internet.

Anonymity and pseudonymity in art
Anonymity is directly related to the concept of obscurantism or pseudonymity, where an artist or a group attempts to remain anonymous, for various reasons such as adding an element of mystique to themselves or their work, attempting to avoid what is known as the "cult of personality" or hero worship (in which the charisma, good looks, wealth or other unrelated or mildly related aspects of the people is the main reason for interest in their work, rather than the work itself) or to break into a field or area of interest normally dominated by males (as by the famous science fiction author James Tiptree, Jr who was actually a woman named Alice Bradley Sheldon, and likely JT LeRoy). Some seem to want to avoid the "limelight" of popularity and to live private lives, such as Thomas Pynchon, J. D. Salinger, De Onbekende Beeldhouwer (an anonymous sculptor whose exhibited work in Amsterdam attracted strong attention in the 1980s and 1990s ), and by DJ duo Daft Punk (1993-2021). For street artist Banksy, "anonymity is vital to him because graffiti is illegal".

Anonymity has been used in music by avant-garde ensemble The Residents, Jandek (until 2004), costumed comedy rock band The Radioactive Chicken Heads, and DJs Deadmau5 (1998–present) and Marshmello (2015–present).

This is frequently applied in fiction, from The Lone Ranger, Superman, and Batman, where a hidden identity is assumed.

Mathematics of anonymity
Suppose that only Alice, Bob, and Carol have keys to a bank safe and that, one day, contents of the safe go missing (lock not violated). Without additional information, we cannot know for sure whether it was Alice, Bob or Carol who emptied the safe. Notably, each element in {Alice, Bob, Carol} could be the perpetrator with a probability of 1. However, as long as none of them was convicted with 100% certainty, we must hold that the perpetrator remains anonymous and that the attribution of the probability of 1 to one of the players has to remain undecided.

If Carol has a definite alibi at the time of perpetration, then we may deduce that it must have been either Alice or Bob who emptied the safe. In this particular case, the perpetrator is not completely anonymous anymore, as both Alice and Bob now know "who did it" with a probability of 1.

title: Anonymity


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Negative-feedback amplifier

A negative-feedback amplifier (or feedback amplifier) is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal. The applied negative feedback can improve its performance (gain stability, linearity, frequency response, step response) and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback.

An idealized negative-feedback amplifier as shown in the diagram is a system of three elements (see Figure 1):
 * an amplifier with gain AOL,
 * a feedback network β, which senses the output signal and possibly transforms it in some way (for example by attenuating or filtering it),
 * a summing circuit that acts as a subtractor (the circle in the figure), which combines the input and the transformed output.

Overview
Fundamentally, all electronic devices that provide power gain (e.g., vacuum tubes, bipolar transistors, MOS transistors) are nonlinear. Negative feedback trades gain for higher linearity (reducing distortion) and can provide other benefits. If not designed correctly, amplifiers with negative feedback can under some circumstances become unstable due to the feedback becoming positive, resulting in unwanted behavior such as oscillation. The Nyquist stability criterion developed by Harry Nyquist of Bell Laboratories is used to study the stability of feedback amplifiers.

Feedback amplifiers share these properties:

Pros:
 * Can increase or decrease input impedance (depending on type of feedback).
 * Can increase or decrease output impedance (depending on type of feedback).
 * Reduces total distortion if sufficiently applied (increases linearity).
 * Increases the bandwidth.
 * Desensitizes gain to component variations.
 * Can control step response of amplifier.

Cons:
 * May lead to instability if not designed carefully.
 * Amplifier gain decreases.
 * Input and output impedances of a negative-feedback amplifier (closed-loop amplifier) become sensitive to the gain of an amplifier without feedback (open-loop amplifier)—that exposes these impedances to variations in the open-loop gain, for example, due to parameter variations or nonlinearity of the open-loop gain.
 * Changes the composition of the distortion (increasing audibility) if insufficiently applied.

History
Paul Voigt patented a negative feedback amplifier in January 1924, though his theory lacked detail. Harold Stephen Black independently invented the negative-feedback amplifier while he was a passenger on the Lackawanna Ferry (from Hoboken Terminal to Manhattan) on his way to work at Bell Laboratories (located in Manhattan instead of New Jersey in 1927) on August 2, 1927 (US Patent 2,102,671, issued in 1937). Black was working on reducing distortion in repeater amplifiers used for telephone transmission. On a blank space in his copy of The New York Times, he recorded the diagram found in Figure 1 and the equations derived below. On August 8, 1928, Black submitted his invention to the U. S. Patent Office, which took more than 9 years to issue the patent. Black later wrote: "One reason for the delay was that the concept was so contrary to established beliefs that the Patent Office initially did not believe it would work."

Classical feedback
Using the model of two unilateral blocks, several consequences of feedback are simply derived.

Gain reduction
Below, the voltage gain of the amplifier with feedback, the closed-loop gain AFB, is derived in terms of the gain of the amplifier without feedback, the open-loop gain AOL and the feedback factor β, which governs how much of the output signal is applied to the input (see Figure 1). The open-loop gain AOL in general may be a function of both frequency and voltage; the feedback parameter β is determined by the feedback network that is connected around the amplifier. For an operational amplifier, two resistors forming a voltage divider may be used for the feedback network to set β between 0 and 1. This network may be modified using reactive elements like capacitors or inductors to (a) give frequency-dependent closed-loop gain as in equalization/tone-control circuits or (b) construct oscillators. The gain of the amplifier with feedback is derived below in the case of a voltage amplifier with voltage feedback.

Without feedback, the input voltage V′in is applied directly to the amplifier input. The according output voltage is

 * $$V_\text{out} = A_\text{OL}\cdot V'_\text{in}.$$

Suppose now that an attenuating feedback loop applies a fraction $$\beta \cdot V_\text{out}$$ of the output to one of the subtractor inputs so that it subtracts from the circuit input voltage Vin applied to the other subtractor input. The result of subtraction applied to the amplifier input is

 * $$V'_\text{in} = V_\text{in} - \beta \cdot V_\text{out}.$$

Substituting for V′in in the first expression,

 * $$V_\text{out} = A_\text{OL} (V_\text{in} - \beta \cdot V_\text{out}).$$

Rearranging:

 * $$V_\text{out} (1 + \beta \cdot A_\text{OL}) = V_\text{in} \cdot A_\text{OL}.$$

Then the gain of the amplifier with feedback, called the closed-loop gain, AFB is given by

 * $$A_\text{FB} = \frac{V_\text{out}}{V_\text{in}} = \frac{A_\text{OL}}{1 + \beta \cdot A_\text{OL}}.$$

If AOL ≫ 1, then AFB ≈ 1 / β, and the effective amplification (or closed-loop gain) AFB is set by the feedback constant β, and hence set by the feedback network, usually a simple reproducible network, thus making linearizing and stabilizing the amplification characteristics straightforward. If there are conditions where β AOL = −1, the amplifier has infinite amplification – it has become an oscillator, and the system is unstable. The stability characteristics of the gain feedback product β AOL are often displayed and investigated on a Nyquist plot (a polar plot of the gain/phase shift as a parametric function of frequency). A simpler, but less general technique, uses Bode plots.

The combination L = −β AOL appears commonly in feedback analysis and is called the loop gain. The combination (1 + β AOL) also appears commonly and is variously named as the desensitivity factor, return difference, or improvement factor.

Summary of terms

 * Open-loop gain = $$A_\text{OL}$$
 * Closed-loop gain = $$\frac{A_\text{OL}}{1 + \beta \cdot A_\text{OL}}$$
 * Feedback factor = $$\beta$$
 * Noise gain = $$1 / \beta$$
 * Loop gain = $$-\beta \cdot A_\text{OL}$$
 * Desensitivity factor = $$1 + \beta \cdot A_\text{OL}$$

Bandwidth extension
Feedback can be used to extend the bandwidth of an amplifier at the cost of lowering the amplifier gain. Figure 2 shows such a comparison. The figure is understood as follows. Without feedback the so-called open-loop gain in this example has a single-time-constant frequency response given by

 * $$ A_\text{OL}(f) = \frac{A_0}{1 + j f / f_\text{C}},$$

where fC is the cutoff or corner frequency of the amplifier: in this example fC = 104 Hz, and the gain at zero frequency A0 = 105 V/V. The figure shows that the gain is flat out to the corner frequency and then drops. When feedback is present, the so-called closed-loop gain, as shown in the formula of the previous section, becomes

 * $$\begin{align}

A_\text{FB}(f) &= \frac{A_\text{OL}}{1 + \beta A_\text{OL}} \\ &= \frac{A_0 / (1 + jf/f_\text{C})}{1 + \beta A_0 / (1 + jf/f_\text{C})} \\ &= \frac{A_0}{1 + jf/f_\text{C} + \beta A_0} \\ &= \frac{A_0}{(1 + \beta A_0) \left(1 + j \frac{f}{(1 + \beta A_0) f_\text{C}}\right)}. \end{align}$$

The last expression shows that the feedback amplifier still has a single-time-constant behavior, but the corner frequency is now increased by the improvement factor (1 + β A0), and the gain at zero frequency has dropped by exactly the same factor. This behavior is called the gain–bandwidth tradeoff. In Figure 2, (1 + β A0) = 103, so AFB(0) = 105 / 103 = 100 V/V, and fC increases to 104 × 103 = 107 Hz.

Multiple poles
When the close-loop gain has several poles, rather than the single pole of the above example, feedback can result in complex poles (real and imaginary parts). In a two-pole case, the result is peaking in the frequency response of the feedback amplifier near its corner frequency and ringing and overshoot in its step response. In the case of more than two poles, the feedback amplifier can become unstable and oscillate. See the discussion of gain margin and phase margin. For a complete discussion, see Sansen.

Signal-flow analysis
A principal idealization behind the formulation of the Introduction is the network's division into two autonomous blocks (that is, with their own individually determined transfer functions), a simple example of what often is called "circuit partitioning", which refers in this instance to the division into a forward amplification block and a feedback block. In practical amplifiers, the information flow is not unidirectional as shown here. Frequently these blocks are taken to be two-port networks to allow inclusion of bilateral information transfer. Casting an amplifier into this form is a non-trivial task, however, especially when the feedback involved is not global (that is directly from the output to the input) but local (that is, feedback within the network, involving nodes that do not coincide with input and/or output terminals). In these more general cases, the amplifier is analyzed more directly without the partitioning into blocks like those in the diagram, using instead some analysis based upon signal-flow analysis, such as the return-ratio method or the asymptotic gain model. Commenting upon the signal-flow approach, Choma says:
 * "In contrast to block diagram and two-port approaches to the feedback network analysis problem, signal flow methods mandate no a priori assumptions as to the unilateral or bilateral properties of the open loop and feedback subcircuits. Moreover, they are not predicated on mutually independent open loop and feedback subcircuit transfer functions, and they do not require that feedback be implemented only globally. Indeed signal flow techniques do not even require explicit identification of the open loop and feedback subcircuits. Signal flow thus removes the detriments pervasive of conventional feedback network analyses but additionally, it proves to be computationally efficient as well."

Following up on this suggestion, a signal-flow graph for a negative-feedback amplifier is shown in the figure, which is patterned after one by D'Amico et al.. Following these authors, the notation is as follows:
 * "Variables xS, xO represent the input and output signals, moreover, two other generic variables, xi, xj linked together through the control (or critical) parameter P are explicitly shown. Parameters aij are the weight branches. Variables xi, xj and the control parameter, P, model a controlled generator, or the relation between voltage and current across two nodes of the circuit.

 * The term a11 is the transfer function between the input and the output [after] setting the control parameter, P, to zero; term a12 is the transfer function between the output and the controlled variable xj  [after]  setting the input source, xS, to zero; term a21 represents the transfer function between the source variable and the inner variable, xi when the controlled variable  xj is set to zero (i.e., when the control parameter, P is set to zero); term a22 gives the relation between the independent and the controlled inner variables setting control parameter, P and input variable, xS, to zero."

Using this graph, these authors derive the generalized gain expression in terms of the control parameter P that defines the controlled source relationship xj = Pxi:
 * $$x_\text{O} = a_{11} x_\text{S} + a_{12} x_j,$$
 * $$x_i = a_{21} x_\text{S} + a_{22} x_j,$$
 * $$x_j = P x_i.$$

Combining these results, the gain is given by
 * $$\frac{x_\text{O}}{x_\text{S}} = a_{11} + \frac{a_{12} a_{21} P}{1 - P a_{22}}.$$

To employ this formula, one has to identify a critical controlled source for the particular amplifier circuit in hand. For example, P could be the control parameter of one of the controlled sources in a two-port network, as shown for a particular case in D'Amico et al. As a different example, if we take a12 = a21 = 1, P = A, a22 = –β (negative feedback) and a11 = 0 (no feedforward), we regain the simple result with two unidirectional blocks.

Two-port analysis of feedback
Although, as mentioned in the section Signal-flow analysis, some form of signal-flow analysis is the most general way to treat the negative-feedback amplifier, representation as two two-ports is the approach most often presented in textbooks and is presented here. It retains a two-block circuit partition of the amplifier, but allows the blocks to be bilateral. Some drawbacks of this method are described at the end.

Electronic amplifiers use current or voltage as input and output, so four types of amplifier are possible (any of two possible inputs with any of two possible outputs). See classification of amplifiers. The objective for the feedback amplifier may be any one of the four types of amplifier and is not necessarily the same type as the open-loop amplifier, which itself may be any one of these types. So, for example, an op amp (voltage amplifier) can be arranged to make a current amplifier instead.

Negative-feedback amplifiers of any type can be implemented using combinations of two-port networks. There are four types of two-port network, and the type of amplifier desired dictates the choice of two-ports and the selection of one of the four different connection topologies shown in the diagram. These connections are usually referred to as series or shunt (parallel) connections. In the diagram, the left column shows shunt inputs; the right column shows series inputs. The top row shows series outputs; the bottom row shows shunt outputs. The various combinations of connections and two-ports are listed in the table below.

For example, for a current-feedback amplifier, current from the output is sampled for feedback and combined with current at the input. Therefore, the feedback ideally is performed using an (output) current-controlled current source (CCCS), and its imperfect realization using a two-port network also must incorporate a CCCS, that is, the appropriate choice for feedback network is a g-parameter two-port. Here the two-port method used in most textbooks is presented,  using the circuit treated in the article on asymptotic gain model. Figure 3 shows a two-transistor amplifier with a feedback resistor Rf. The aim is to analyze this circuit to find three items: the gain, the output impedance looking into the amplifier from the load, and the input impedance looking into the amplifier from the source.

Replacement of the feedback network with a two-port
The first step is replacement of the feedback network by a two-port. Just what components go into the two-port?

On the input side of the two-port we have Rf. If the voltage at the right side of Rf changes, it changes the current in Rf that is subtracted from the current entering the base of the input transistor. That is, the input side of the two-port is a dependent current source controlled by the voltage at the top of resistor R2.

One might say the second stage of the amplifier is just a voltage follower, transmitting the voltage at the collector of the input transistor to the top of R2. That is, the monitored output signal is really the voltage at the collector of the input transistor. That view is legitimate, but then the voltage follower stage becomes part of the feedback network. That makes analysis of feedback more complicated. An alternative view is that the voltage at the top of R2 is set by the emitter current of the output transistor. That view leads to an entirely passive feedback network made up of R2 and Rf. The variable controlling the feedback is the emitter current, so the feedback is a current-controlled current source (CCCS). We search through the four available two-port networks and find the only one with a CCCS is the g-parameter two-port, shown in Figure 4. The next task is to select the g-parameters so that the two-port of Figure 4 is electrically equivalent to the L-section made up of R2 and Rf. That selection is an algebraic procedure made most simply by looking at two individual cases: the case with V1 = 0, which makes the VCVS on the right side of the two-port a short-circuit; and the case with I2 = 0. which makes the CCCS on the left side an open circuit. The algebra in these two cases is simple, much easier than solving for all variables at once. The choice of g-parameters that make the two-port and the L-section behave the same way are shown in the table below.

Small-signal circuit
The next step is to draw the small-signal schematic for the amplifier with the two-port in place using the hybrid-pi model for the transistors. Figure 5 shows the schematic with notation R3 = RC2 || RL and R11 = 1 / g11, R22 = g22.

Loaded open-loop gain
Figure 3 indicates the output node, but not the choice of output variable. A useful choice is the short-circuit current output of the amplifier (leading to the short-circuit current gain). Because this variable leads simply to any of the other choices (for example, load voltage or load current), the short-circuit current gain is found below.

First the loaded open-loop gain is found. The feedback is turned off by setting g12 = g21 = 0. The idea is to find how much the amplifier gain is changed because of the resistors in the feedback network by themselves, with the feedback turned off. This calculation is pretty easy because R11, RB, and rπ1 all are in parallel and v1 = vπ. Let R1 = R11 || RB || rπ1. In addition, i2 = −(β+1) iB. The result for the open-loop current gain AOL is:

 * $$ A_\mathrm{OL} = \frac { \beta i_\mathrm{B} } {i_\mathrm{S}} = g_m R_\mathrm{C} \left( \frac { \beta }{ \beta +1} \right)

\left( \frac {R_1} {R_{22} + \frac {r_{ \pi 2} + R_\mathrm{C} } {\beta + 1 } } \right)  \. $$

Gain with feedback
In the classical approach to feedback, the feedforward represented by the VCVS (that is, g21 v1) is neglected. That makes the circuit of Figure 5 resemble the block diagram of Figure 1, and the gain with feedback is then:

 * $$ A_\mathrm{FB} = \frac { A_\mathrm{OL} } {1 + { \beta }_\mathrm{FB} A_\mathrm{OL} } $$
 * $$ A_\mathrm{FB} = \frac {A_\mathrm{OL} } {1 + \frac {R_2} {R_2+R_\mathrm{f}} A_\mathrm{OL} } \, $$

where the feedback factor βFB = −g12. Notation βFB is introduced for the feedback factor to distinguish it from the transistor β.

Input and output resistances
Feedback is used to better match signal sources to their loads. For example, a direct connection of a voltage source to a resistive load may result in signal loss due to voltage division, but interjecting a negative feedback amplifier can increase the apparent load seen by the source, and reduce the apparent driver impedance seen by the load, avoiding signal attenuation by voltage division. This advantage is not restricted to voltage amplifiers, but analogous improvements in matching can be arranged for current amplifiers, transconductance amplifiers and transresistance amplifiers.

To explain these effects of feedback upon impedances, first a digression on how two-port theory approaches resistance determination, and then its application to the amplifier at hand.

Background on resistance determination
Figure 6 shows an equivalent circuit for finding the input resistance of a feedback voltage amplifier (left) and for a feedback current amplifier (right). These arrangements are typical Miller theorem applications.

In the case of the voltage amplifier, the output voltage βVout of the feedback network is applied in series and with an opposite polarity to the input voltage Vx travelling over the loop (but in respect to ground, the polarities are the same). As a result, the effective voltage across and the current through the amplifier input resistance Rin decrease so that the circuit input resistance increases (one might say that Rin apparently increases). Its new value can be calculated by applying Miller theorem (for voltages) or the basic circuit laws. Thus Kirchhoff's voltage law provides:

 * $$ V_x = I_x R_\mathrm{in} + \beta v_\mathrm{out} \, $$

where vout = Av vin = Av Ix Rin. Substituting this result in the above equation and solving for the input resistance of the feedback amplifier, the result is:

 * $$ R_\mathrm{in}(fb) = \frac {V_x} {I_x} = \left( 1 + \beta A_v \right ) R_\mathrm{in} \ . $$

The general conclusion from this example and a similar example for the output resistance case is: A series feedback connection at the input (output) increases the input (output) resistance by a factor ( 1 + β AOL ), where AOL = open loop gain.

On the other hand, for the current amplifier, the output current βIout of the feedback network is applied in parallel and with an opposite direction to the input current Ix. As a result, the total current flowing through the circuit input (not only through the input resistance Rin) increases and the voltage across it decreases so that the circuit input resistance decreases (Rin apparently decreases). Its new value can be calculated by applying the dual Miller theorem (for currents) or the basic Kirchhoff's laws:

 * $$ I_x = \frac {V_\mathrm{in}} {R_\mathrm{in}} + \beta i_\mathrm{out} \ . $$

where iout = Ai iin = Ai Vx / Rin. Substituting this result in the above equation and solving for the input resistance of the feedback amplifier, the result is:

 * $$ R_\mathrm{in}(fb) = \frac {V_x} {I_x} = \frac { R_\mathrm{in} } { \left( 1 + \beta A_i \right ) } \ . $$

The general conclusion from this example and a similar example for the output resistance case is: A parallel feedback connection at the input (output) decreases the input (output) resistance by a factor ( 1 + β AOL ), where AOL = open loop gain.

These conclusions can be generalized to treat cases with arbitrary Norton or Thévenin drives, arbitrary loads, and general two-port feedback networks. However, the results do depend upon the main amplifier having a representation as a two-port – that is, the results depend on the same current entering and leaving the input terminals, and likewise, the same current that leaves one output terminal must enter the other output terminal.

A broader conclusion, independent of the quantitative details, is that feedback can be used to increase or to decrease the input and output impedance.

Application to the example amplifier
These resistance results now are applied to the amplifier of Figure 3 and Figure 5. The improvement factor that reduces the gain, namely ( 1 + βFB AOL), directly decides the effect of feedback upon the input and output resistances of the amplifier. In the case of a shunt connection, the input impedance is reduced by this factor; and in the case of series connection, the impedance is multiplied by this factor. However, the impedance that is modified by feedback is the impedance of the amplifier in Figure 5 with the feedback turned off, and does include the modifications to impedance caused by the resistors of the feedback network.

Therefore, the input impedance seen by the source with feedback turned off is Rin = R1 = R11 || RB || rπ1, and with the feedback turned on (but no feedforward)

 * $$ R_\mathrm{in} = \frac {R_1} {1 + { \beta }_\mathrm{FB} A_\mathrm{OL} } \, $$

where division is used because the input connection is shunt: the feedback two-port is in parallel with the signal source at the input side of the amplifier. A reminder: AOL is the loaded open loop gain found above, as modified by the resistors of the feedback network.

The impedance seen by the load needs further discussion. The load in Figure 5 is connected to the collector of the output transistor, and therefore is separated from the body of the amplifier by the infinite impedance of the output current source. Therefore, feedback has no effect on the output impedance, which remains simply RC2 as seen by the load resistor RL in Figure 3.

If instead we wanted to find the impedance presented at the emitter of the output transistor (instead of its collector), which is series connected to the feedback network, feedback would increase this resistance by the improvement factor ( 1 + βFB AOL).

Load voltage and load current
The gain derived above is the current gain at the collector of the output transistor. To relate this gain to the gain when voltage is the output of the amplifier, notice that the output voltage at the load RL is related to the collector current by Ohm's law as vL = iC (RC2 || RL). Consequently, the transresistance gain vL / iS is found by multiplying the current gain by RC2 || RL:

 * $$ \frac {v_\mathrm{L}} {i_\mathrm{S}} = A_\mathrm{FB} (R_\mathrm{C2} \parallel R_\mathrm{L} ) \ . $$

Similarly, if the output of the amplifier is taken to be the current in the load resistor RL, current division determines the load current, and the gain is then:

 * $$ \frac {i_\mathrm{L}} {i_\mathrm{S}} = A_\mathrm{FB} \frac {R_\mathrm{C2}} {R_\mathrm{C2} + R_\mathrm{L}} \ . $$

Is the main amplifier block a two-port?
Some drawbacks of the two two-port approach follow, intended for the attentive reader.

Figure 7 shows the small-signal schematic with the main amplifier and the feedback two-port in shaded boxes. The feedback two-port satisfies the port conditions: at the input port, Iin enters and leaves the port, and likewise at the output, Iout enters and leaves.

Is the main amplifier block also a two-port? The main amplifier is shown in the upper shaded box. The ground connections are labeled. Figure 7 shows the interesting fact that the main amplifier does not satisfy the port conditions at its input and output unless the ground connections are chosen to make that happen. For example, on the input side, the current entering the main amplifier is IS. This current is divided three ways: to the feedback network, to the bias resistor RB and to the base resistance of the input transistor rπ. To satisfy the port condition for the main amplifier, all three components must be returned to the input side of the main amplifier, which means all the ground leads labeled G1 must be connected, as well as emitter lead GE1. Likewise, on the output side, all ground connections G2 must be connected and also ground connection GE2. Then, at the bottom of the schematic, underneath the feedback two-port and outside the amplifier blocks, G1 is connected to G2. That forces the ground currents to divide between the input and output sides as planned. Notice that this connection arrangement splits the emitter of the input transistor into a base-side and a collector-side – a physically impossible thing to do, but electrically the circuit sees all the ground connections as one node, so this fiction is permitted.

Of course, the way the ground leads are connected makes no difference to the amplifier (they are all one node), but it makes a difference to the port conditions. This artificiality is a weakness of this approach: the port conditions are needed to justify the method, but the circuit really is unaffected by how currents are traded among ground connections.

However, if no possible arrangement of ground conditions leads to the port conditions, the circuit might not behave the same way. The improvement factors (1 + βFB AOL) for determining input and output impedance might not work. This situation is awkward, because a failure to make a two-port may reflect a real problem (it just is not possible), or reflect a lack of imagination (for example, just did not think of splitting the emitter node in two). As a consequence, when the port conditions are in doubt, at least two approaches are possible to establish whether improvement factors are accurate: either simulate an example using Spice and compare results with use of an improvement factor, or calculate the impedance using a test source and compare results.

A more practical choice is to drop the two-port approach altogether, and use various alternatives based on signal flow graph theory, including the Rosenstark method, the Choma method, and use of Blackman's theorem. That choice may be advisable if small-signal device models are complex, or are not available (for example, the devices are known only numerically, perhaps from measurement or from SPICE simulations).

Feedback amplifier formulas
Summarizing the two-port analysis of feedback, one can get this table of formulas. The variables and their meanings are

$$A$$- gain, $$I$$- current, $$V$$- voltage,$$\beta$$- feedback gain and $$R$$- resistance.

The subscripts and their meanings are

$$f$$- feedback amplifier, $$v$$- voltage,$$g$$- transconductance, $$Z$$- transresistance, $$o$$- output and $$i$$- current for gains and feedback and $$i$$- input for resistances.

For example $$A_{vf}$$means voltage feedback amplifier gain.

Distortion
Simple amplifiers like the common emitter configuration have primarily low-order distortion, such as the 2nd and 3rd harmonics. In audio systems, these can be minimally audible because musical signals are typically already a harmonic series, and the low-order distortion products are hidden by the masking effect of the human hearing system.

After applying moderate amounts of negative feedback (10–15 dB), the low-order harmonics are reduced, but higher-order harmonics are introduced. Since these are not masked as well, the distortion becomes audibly worse, even though the overall THD may go down. This has led to a persistent myth that negative feedback is detrimental in audio amplifiers, leading audiophile manufacturers to market their amplifiers as "zero feedback" (even when they use local feedback to linearize each stage).

However, as the amount of negative feedback is increased further, all harmonics are reduced, returning the distortion to inaudibility, and then improving it beyond the original zero-feedback stage (provided the system is strictly stable). So the problem is not negative feedback, but insufficient amounts of it.

References and notes
Negative Rückkopplung Realimentación negativa Contre réaction Realimentación negativa Tegenkoppeling Negativ tilbakekobling Отрицательная обратная связь Negativna povratna sprega Negativ återkoppling

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Negative-feedback amplifier


text:
Oxford Canal

The Oxford Canal is a 78 mi narrowboat canal in southern central England linking the City of Oxford with the Coventry Canal at Hawkesbury (just north of Coventry and south of Bedworth) via Banbury and Rugby. Completed in 1790, it connects to the River Thames at Oxford, and links with the Grand Union Canal, which it is combined with for 5 mi between to the villages of Braunston and Napton-on-the-Hill.

The canal is usually divided into the North Oxford Canal (north of Napton, via Rugby to Hawkesbury Junction near Coventry) and the South Oxford Canal, south of Napton to Banbury and Oxford.

The canal was for about 15 years the main canal artery of trade between the Midlands and London, via its connection to the Thames, until the Grand Union Canal (then called the Grand Junction Canal) took most of the London-bound traffic following its opening in 1805. The North Oxford Canal (which had been straightened in the 1830s) remained an important artery of trade carrying coal and other commodities until the 1960s; the more rural South Oxford Canal however became something of a backwater, especially following the opening of the Grand Junction Canal, and it faced closure proposals in the 1950s. Since the end of regular commercial goods carriage on the canal in the 1960s, it has gained a new use as a leisure resource, and become used primarily for narrowboat pleasure boating.

The Oxford Canal traverses Oxfordshire, Northamptonshire and east Warwickshire through broad, shallow valleys and lightly rolling hills; the canal's route northeast and then northwest forms part of the Warwickshire ring.

The route

The canal begins in Warwickshire near Hawkesbury Village at Hawkesbury Junction, also known as Sutton Stop, where it connects with the Coventry Canal, a little over 4 miles (or about 7 km) from the centre of Coventry and 5 mi from Nuneaton. Within a mile were the late 18th- and 19th-century coal field/pit and colliery of the small town of Bedworth. From Hawkesbury, it runs southeast through the Warwickshire countryside for 15 mi to Rugby.

The route between Coventry and Rugby is level, with no locks, apart from the stop lock at the junction. Parts of this section were straightened by raising and waterproofing in the 1820s; the remains of a more circuitous route (which kept to the chosen contour) can still be seen in places.

The canal winds through the northern part of Rugby. It passes through the 270 yd Newbold Tunnel. In the churchyard in Newbold-on-Avon remains can be seen of an earlier canal tunnel built in the 1770s. It scales a flight of three locks at Hillmorton about 3 mi east-southeast of the town.

East of Rugby, the canal passes southwest then south. It crosses under the M45 motorway and through broad low fields interspersed by views of wooded knolls and modest hills of Northamptonshire and Warwickshire to reach Braunston.

West of Braunston village centre, by a pub, the canal converges with the Grand Union Canal where both change direction to west-southwest. The latter canal has a major wharf, Braunston Marina, 700 m east and a campsite. The combined canal splits north of Napton-on-the-Hill:
 * The Oxford Canal runs southwest and then turns south towards Oxford via Banbury.
 * The Grand Union Canal runs north passing opposing marinas within a mile then northwest to Birmingham via Warwick.

After winding round Napton Hill, the canal ascends the Napton flight of nine locks to a local summit reach, well below the hilltop. After passing an old wharf and a pub at Fenny Compton, the canal enters a long cutting which until some time in the 19th century was a tunnel. This section is normally referred to as a "tunnel straight" or the Fenny Compton Tunnel.

The route between the farms of Priors Hardwick and Fenny Compton was never straightened, and is the most circuitous in the region: taking 9 km to cover 3.5 km (geodesically, as the crow flies). This coincides with the canal's highest "summit" reach in navigational terms. This reach is the "eleven-mile pound" mentioned in Tom Rolt's Narrow Boat.

The canal then descends the Claydon flight of locks and into the vale of the nascent Cherwell at Cropredy. The canal descends the valley to Oxford.

Banbury has many visitor moorings alongside the historic and modern shopping areas in the middle of town. Banbury Town Council and Cherwell District Council treat the canal as an attraction to be encouraged; examples of its work include an old boatyard which has been incorporated into the town centre: Tooley's Historic Boatyard. About 4 mi south is a lightly settled locality, Twyford Wharf, where narrow boats up to 60 ft can be turned. Two villages nearby, Kings Sutton and Adderbury (Twyford), are within 30 minutes' walking distance along the road. Both offer several pubs.

Within Oxford's conurbation, the end of the canal has two links to the Thames:
 * 3 mi north of the city where Dukes Cut leads to King's Lock;
 * a few hundred yards (metres) from the heart of the city centre by Oxford railway station. below Isis Lock (known to boatmen as 'Louse Lock') through Sheepwash Channel. This leads to an elongated navigable circuit at the Thames called "Four Rivers" above Osney Lock.

After 330 yd below Isis Lock the Oxford Canal ends abruptly at Hythe Bridge Street near to the current Hythe Bridge over the Castle Mill Stream, a backwater of the River Thames that runs parallel to the Oxford Canal for its southernmost part. The canal used to continue through a bridge under Hythe Bridge Street to a turning basin and goods wharf south of Hythe Bridge Street. It then continued via a bridge under Worcester Street to end in a coal wharf beside New Road. In 1951 the basin and wharves were filled in and Nuffield College has taken part of the site.

The locks on the canal are as follows. The canal rises from Hawkesbury Junction to Hilmorton Top Lock, there is then a 6+1/2 mi pound to Braunston Junction, where it joins the Grand Union canal. From Napton Junction the Oxford canal rises again though the Napton Locks. After Napton Top Lock there is a 10+1/2 mi pound to Claydon Top Lock, from where the canal falls towards Oxford.

Construction
The Oxford Canal was constructed in several stages over a period of more than twenty years.

In 1769 the Coventry to Oxford Canal Act 1769 (9 Geo. 3. c. 70) authorising the Oxford Canal was passed, having been promoted in Parliament by Sir Roger Newdigate MP, who chaired the canal company. The intention was to link the industrial English Midlands to London via the River Thames. Construction began shortly after near Coventry. The principal motivation for the canal was the transport of coal from the Midlands to Oxford and London.

Surveying of the route and initial construction were originally supervised by the celebrated engineer James Brindley, assisted by Samuel Simcock who was also Brindley's brother-in-law. Brindley died in 1772, when the canal had only reached Brinklow, and Simcock took over. By 1774 the canal had reached Napton, but the company was already running out of money.

In 1775, a second act (15 Geo. 3. c. 9) was passed allowing the company to raise more funds. Construction soon started again and by 1778 the canal had reached Banbury. Financial problems meant that work on the final stretch from Banbury to Oxford did not begin until 1786, and when it did, James Barnes was appointed as the engineer. As funds were limited, the Banbury-Oxford stretch was built more cheaply, and to lower standards than the rest of the canal, and many cost saving measures were used whenever possible: Wooden lift or swing bridges were built, instead of more expensive fixed brick bridges. Deep locks were used wherever possible, with single gates at both end instead of double gates. A stretch of the River Cherwell at Shipton-on-Cherwell was incorporated into the canal. This reduced construction costs, but the behaviour of the river makes the canal more difficult to use.

The Oxford Canal reached the outskirts of Oxford in 1789, when a coal wharf was opened at Heyfield Hutt, now the site of Hayfield Road. The final section into central Oxford was ceremonially opened on 1 January 1790.

The Duke's Cut, a short link from the Oxford Canal to the River Thames, just north of Oxford, was built in 1789 by the Duke of Marlborough.

The River Swift (a tributary of the River Avon) connected to the original route of the Oxford Canal near Cosford and was used as a water feeder to the canal. In 1785 there was a proposal to make the river navigable from the Oxford Canal at Cosford to the town of Lutterworth in Leicestershire. This proposal however never came to fruition. The River Swift, however is still an important feeder to the northern Oxford Canal, via the now unnavigable Brownsover Arm; a part of the canal which was bypassed when the canal was straightened.

Heyday
For the next 15 years the Oxford Canal became one of the most important and profitable transport links in Britain, with most commercial traffic between London and the Midlands using the route. Its principal traffic was coal from Warwickshire. It also carried stone, agricultural products and other goods.

A much more direct route between London and the Midlands, the Grand Junction Canal, was completed in 1805, connecting Braunston to London in much less distance. Much of the London-bound traffic switched to this faster route, as it avoided the passage of the River Thames which still had many flash locks. This greatly reduced Oxford Canal traffic south of Napton. However, the short section between Braunston and Napton became the link between the Warwick and Napton Canal and the Grand Junction Canal, making it part of the busy direct route between Birmingham and London. Despite these developments, the Oxford Canal remained highly profitable during this period; from 1824 to 1826, the company paid dividends of up to 55% to its shareholders.

The Grand Junction and Oxford canal companies were bitter rivals. When Parliament considered the Act of Parliament for the building of the Grand Junction, the Oxford Canal successfully petitioned to make the Grand Junction pay "bar tolls" to the Oxford Canal to compensate for the loss of traffic south of Napton.

Traffic from Birmingham had to use 5 mi of the Oxford Canal to get from Braunston to join the Grand Junction at Napton. The Oxford Canal exploited this by charging high tolls for Grand Junction traffic on this short section.

Straightening
The Oxford Canal was originally built as a contour canal, meaning that it twisted around hills to minimise vertical deviations from a level contour. This meant however that the canal followed a very winding and circuitous route: Although the distance between Coventry and Napton was only 16 mi as the crow flies, the distance by the original route of the canal was 43 mi. This mattered little when the Oxford Canal had no competition, however, with increased canal competition, and one eye on the developing railway network, the company decided to straighten the route.

In 1827 Marc Isambard Brunel (father of Isambard Kingdom Brunel) re-surveyed the northern section of the canal between Braunston and Hawkesbury Junction to straighten it out and reduce navigation time. The following year another survey was carried out by Charles Vignoles. The work to straighten the canal was carried out between 1831 and 1834, the majority of the work being in the Rugby area, and this reduced the distance by 14+3/4 mi. The original tunnel at Newbold-on-Avon was abandoned when the canal was straightened, and replaced by a new one on a different alignment. The south portal of the old tunnel can still be seen next to the churchyard. The old line of the canal was either abandoned, or remained in use as arms serving various village wharves. The section south of Napton was never straightened.

Slow decline
The straightening of the canal coincided with the beginning of the railway age, and the opening of the London and Birmingham Railway in 1838, signalled the end of the dominance of the canals. However, despite the railway competition, the total tonnages of cargo carried on the canal did not decline immediately, and in fact continued to rise for some time, however, the company was forced to slash its tolls in order to remain competitive, and this put an end to the large profits which had previously been made, although ironically the railways provided a new source of income to the canal, who paid them to provide water for their locomotives at Rugby. Traffic on the canal remained such that the three locks at Hillmorton, the first on the canal after the stop lock at Hawkesbury Junction, became severely congested. The solution to the congestion was to duplicate or twin the existing locks at Hillmorton, creating three pairs of two parallel narrow locks, which allowed twice the traffic to pass the lock at any time. The work to double the locks was completed in August 1840. In 1842, nearly 21,000 boats passed through the locks.

In 1833 a section of the new line of canal in Barby Fields near Dunchurch was used as a test site for a new wrought iron boat, Swallow, built by Graham and Houston. Drawn by two horses, the boat completed a distance of 1.5 mile in 7 minutes 35 seconds, a speed of almost 12 miles per hour.

Traffic on the Oxford Canal held up reasonably well in the face of railway competition compared to many other navigations, but did see a gradual decline; in 1838, 520,000 tons were carried, which declined to 482,000 tons in 1868. However, income declined much more sharply due to the company slashing its tolls; takings which had gone from £18,478 in 1791/3, and then risen to a maximum of £90,446 in 1827/29, then fell to £26,312 in 1855. Nevertheless, the company was still profitable, and was able to pay dividends.

The northern section of the Oxford Canal between Coventry, Braunston and Napton remained an important trunk route, and remained extremely busy with freight traffic until the 1960s. The staple traffic was coal from the Warwickshire and Leicestershire coalfields to London via the Grand Union Canal. However, the southern section from Napton to Oxford became something of a backwater, and carried mostly local traffic.

20th century
In 1934, the Braunston-Napton stretch of the canal was taken over by the recently formed Grand Union Canal company, and widened as part of that company's London to Birmingham main-line.

In a bid to raise funds to overcome an arrears of maintenance, in 1936, the Oxford Canal Company decided to sell off their terminal basin at Oxford. In 1937 Baron Nuffield (Later Viscount Nuffield) bought the canal basin at Oxford for £133,373. In 1951 he filled it in and built Nuffield College on part of the former coal wharf. Coal traffic was relocated to a canal wharf in Juxon Street, in Jericho, Oxford. The goods wharf and the remainder of the coal wharf are now under a public car park that Nuffield College lets to Oxford City Council. For this reason, the canal today ends abruptly in central Oxford.

Many Oxford Canal boatmen and women favoured horse traction long after those on other canals had changed their narrowboats to diesel power. In the 1930s, only around one in thirty of the boats trading on the canal's southern section was mechanically powered. One narrowboat carrying coal on the Oxford Canal was drawn by a mule until 1959 and was the last horse-drawn freight narrowboat in Great Britain. This boat, Friendship, is preserved at the National Waterways Museum, Ellesmere Port.

The Oxford Canal remained independent until it was nationalised in 1948 and became part of the Docks and Inland Waterways Executive, later the British Waterways Board. The Oxford Canal remained profitable until the mid-1950s, paying a dividend right up until nationalisation. As with most of Britain's narrow canal system, the Oxford Canal suffered from a rapid decline in freight traffic after the Second World War. By the mid-1950s very few narrowboats traded south of Napton and the southern section was at one point being threatened with closure, although the northern section (Napton to Coventry) remained well-used by commercial traffic until the 1960s.

Revival
During the 1960s pleasure boating began to grow in popularity and replace the old trading boats, After a fact-finding cruise on the canal, Barbara Castle (Minister for Transport) rejected a proposal for closure. The canal was designated as a cruiseway under the Transport Act 1968, which defined at as being a waterway to be maintained for leisure use.

The canal is now thriving. In the summer it is one of the most crowded canals on the network.

Oxford Canal Walk
The towpath of the canal, with a 5+1/2 mi extension from Hawkesbury Junction to Coventry on the towpath of the Coventry Canal, forms the 82 mi Oxford Canal Walk. The 10 mi stretch from Oxford to Kirtlington, where the Oxfordshire Way meets the canal, is also part of European walking route E2. The Canal Walk is popular with geocachers with many Geocache sites located alongside the canal.

title: Oxford Canal


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Forward-looking infrared

Forward-looking infrared (FLIR) cameras, typically used on military and civilian aircraft, use a thermographic camera that senses infrared radiation.

The sensors installed in forward-looking infrared cameras, as well as those of other thermal imaging cameras, use detection of infrared radiation, typically emitted from a heat source (thermal radiation), to create an image assembled for video output.

They can be used to help pilots and drivers steer their vehicles at night and in fog, or to detect warm objects against a cooler background. The wavelength of infrared that thermal imaging cameras detect is 3 to 12 μm and differs significantly from that of night vision, which operates in the visible light and near-infrared ranges (0.4 to 1.0 μm).

Design

Infrared light falls into two basic ranges: long-wave and medium-wave. Long-wave infrared (LWIR) cameras, sometimes called "far-infrared", operate at 8 to 12 μm and can see heat sources, such as hot engine parts or human body heat, several kilometers away. Longer-distance viewing is made more difficult with LWIR because the infrared light is absorbed, scattered, and refracted by air and by water vapor.

Some long-wave cameras require their detector to be cryogenically cooled, typically for several minutes before use, although some moderately sensitive infrared cameras do not require this. Many thermal imagers, including some forward-looking infrared cameras (such as some LWIR enhanced vision systems (EVS)) are also uncooled.

Medium-wave (MWIR) cameras operate in the 3–5 μm range. These can see almost as well, since those frequencies are less affected by water-vapor absorption, but generally require a more expensive sensor array, along with cryogenic cooling.

Many camera systems use digital image processing to improve the image quality. Infrared imaging sensor arrays often have wildly inconsistent sensitivities from pixel to pixel, due to limitations in the manufacturing process. To remedy this, the response of each pixel is measured at the factory, and a transform, most often linear, maps the measured input signal to an output level.

Some companies offer advanced "fusion" technologies that blend a visible-spectrum image with an infrared-spectrum image to produce better results than a single-spectrum image alone.

Properties
Thermal imaging cameras such as the Raytheon AN/AAQ-26 are used in a variety of applications, including naval vessels, fixed-wing aircraft, helicopters, armored fighting vehicles, and military-grade smartphones.

In warfare, they have three distinct advantages over other imaging technologies:
 * 1) The imager itself is nearly impossible to detect for the enemy, as it detects energy emitted from the target rather than sending out energy that is reflected from the target, as with radar or sonar.
 * 2) It sees radiation in the infrared spectrum, which is difficult to camouflage.
 * 3) These camera systems can see through smoke, fog, haze, and other atmospheric obscurants better than a visible light camera can.

Etymology
The term "forward-looking" is used to distinguish fixed forward-looking thermal imaging systems from sideways-tracking infrared systems, also known as "push broom" imagers, and other thermal imaging systems such as gimbal-mounted imaging systems, handheld imaging systems, and the like. Pushbroom systems typically have been used on aircraft and satellites.

Sideways-tracking imagers normally involve a one-dimensional (1D) array of pixels, which uses the motion of the aircraft or satellite to move the view of the 1D array across the ground to build up a 2D image over time. Such systems cannot be used for real-time imaging and must look perpendicular to the direction of travel.

History
In 1956, Texas Instruments began research on infrared technology that led to several line scanner contracts and, with the addition of a second scan mirror, the invention of the first forward-looking infrared camera occurred in 1963, with production beginning in 1966. In 1972, TI introduced the Common Module concept, which greatly reduced costs and allowed for the reuse of common components.

Uses

 * Traffic video detection and monitoring
 * Surveillance and/or capture of mammals
 * e.g. Detection of illegal immigrants hidden in lorries/trucks
 * Warning drivers about sudden road obstructions caused by deer
 * Location through smoke and/or haze
 * Search and rescue operations for missing persons especially in wooded areas or water
 * Target acquisition and tracking by military or civil aircraft
 * Drainage basin temperature monitoring and monitoring wild game habitats
 * Detection of energy loss or consumption, or insulation defects
 * e.g. insulation level mapping (pipes, walls, joints etc.) in order to reduce HVAC energy consumption
 * Quality control for especially electrical installations (a picture can reveal if loads are higher than expected, or show bad and potentially failing joints)
 * Search for drug labs and/or indoor cannabis producers (especially at night)
 * Piloting of aircraft in low visibility (IMC) conditions
 * Pinpoint sources of ignition during firefighting operations
 * Monitoring active volcanoes
 * Detecting faulty or overheating electrical joints, connections, and components
 * Night driving
 * Identification or visual acquirement of hostile ground vehicles or personnel

Cost
The cost of thermal imaging equipment in general has fallen dramatically after inexpensive portable and fixed infrared detectors and systems based on microelectromechanical technology were designed and manufactured for commercial, industrial, and military application. Also, older camera designs used rotating mirrors to scan the image to a small sensor. More modern cameras no longer use this method; the simplification helps reduce cost. Uncooled technology available in many Enhanced Flight Vision System (EFVS or EVS) products have reduced the costs to fractions of the price of older cooled technology, with similar performance. EVS is rapidly becoming mainstream on many fixed wing and rotary wing operators from Cirrus and Cessna aircraft to large business jets.

Police actions
In 2001, the United States Supreme Court decided in Kyllo v. United States that performing surveillance of private property (ostensibly to detect high emission grow lights used in clandestine cannabis farming) using thermal imaging cameras without a search warrant by law enforcement violates the Fourth Amendment's protection from unreasonable searches and seizures.

In the 2004 R. v. Tessling judgment, the Supreme Court of Canada determined that the use of airborne FLIR in surveillance by police was permitted without requiring a search warrant. The Court determined that the general nature of the data gathered by FLIR did not reveal personal information of the occupants and therefore was not in violation of Tessling's Section 8 rights afforded under the Charter of Rights and Freedoms (1982). Ian Binnie distinguished the Canadian law with respect to the Kyllo judgment, by agreeing with the Kyllo minority that public officials should not have to avert their senses or their equipment from detecting emissions in the public domain such as excessive heat, traces of smoke, suspicious odors, odorless gases, airborne particulates, or radioactive emissions, any of which could identify hazards to the community.

In June 2014, the Canadian National Aerial Surveillance Program DHC-8M-100 aircraft mounted with infrared sensors was instrumental in the search for Justin Bourque, a fugitive who had killed three Royal Canadian Mounted Police members in Moncton. The plane's crew used its advanced heat-sensing camera to discover Bourque's heat signature in the deep brushwoods at midnight.

During 2015 Baltimore protests, the FBI conducted 10 aerial surveillance missions between April 29 and May 3, which included "infrared and day color, full-motion FLIR video evidence" collection, according to FBI spokesman Christopher Allen. A FLIR Talon multi-sensor camera system equipped with an infrared laser pointer (which is invisible to casual observers) for illumination purposes was used to gather data at night. The American Civil Liberties Union raised concerns over the fact that new surveillance technology is implemented without judicial guidance and public discussion. According to Nathan Wessler, an ACLU attorney, "this is a dynamic we see again and again when it comes to advances in surveillance. By the time details leak out, programs are firmly entrenched, and it's all but impossible to roll them back – and very hard to put in place restrictions and oversight."

title: Forward-looking infrared