Analog_computer

[[Image:Bifnordennomenclature.jpg|thumb|A page from the ''Bombardier's Information File'' (BIF) that describes the components and controls of the [[Norden bombsight]]. The '''Norden bombsight''' was a highly sophisticated optical/mechanical analog computer used by the United States Army Air Force during [[World War II]], the [[Korean War]], and the [[Vietnam War]] to aid the pilot of a [[bomber]] aircraft in dropping [[bomb]]s accurately.]]

An '''analog computer''' (spelled '''analogue''' in British English) is a form of [[computer]] that uses continuous physical quantities such as electrical<ref>Universiteit van Amsterdam Computer Museum, (2007)</ref>, mechanical or hydraulic phenomena to model the problem being solved.

==Timeline of analog computers==

*The [[Antikythera mechanism]] is believed to be the earliest known mechanical analog computer.<ref>[http://www.antikythera-mechanism.gr/project/general/the-project.html ''The Antikythera Mechanism Research Project''], The Antikythera Mechanism Research Project. Retrieved 2007-07-01</ref> It was designed to calculate astronomical positions. It was discovered in 1901 in the [[Antikythera]] wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to ''circa'' 100 BC. Devices of the level of complexity as the Antikythera mechanism would not reappear until a thousand years later.

*The [[astrolabe]] was invented in the [[Hellenistic]] world in either the first or second centuries BCE and is often attributed to [[Hipparchus]]. A combination of the [[planisphere]] and [[dioptra]], the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical [[astronomy]].

*[[Islamic astronomy|Muslim astronomers]] later produced many different types of [[astrolabe]]s and used them for over a thousand different problems related to astronomy, [[Islamic astrology|astrology, horoscopes]], [[Mariner's astrolabe|navigation]], [[surveying]], [[time]]keeping, [[Qibla]] (direction of [[Mecca]]), [[Salah]] (prayer), etc.<ref name=Winterburn>Dr. Emily Winterburn ([[National Maritime Museum]]), [http://www.muslimheritage.com/topics/default.cfm?ArticleID=529 Using an Astrolabe], Foundation for Science Technology and Civilisation, 2005.</ref>

*[[Abū Rayhān al-Bīrūnī]] invented the first mechanical [[gear]]ed [[lunisolar calendar]] astrolabe,<ref>D. De S. Price (1984). "A History of Calculating Machines", ''IEEE Micro'' '''4''' (1), p. 22-52.</ref> an early fixed-[[wire]]d knowledge processing [[machine]]<ref name=Oren>Tuncer Oren (2001). "Advances in Computer and Information Sciences: From Abacus to Holonic Agents", ''Turk J Elec Engin'' '''9''' (1), p. 63-70 [64].</ref> with a [[gear train]] and [[gear]]-wheels,<ref>[[Donald Routledge Hill]] (1985). "Al-Biruni's mechanical calendar", ''Annals of Science'' '''42''', p. 139-163.</ref> ''circa'' [[1000]] AD.

*The [[Planisphere]] was a [[star chart]] astrolabe also invented by [[Abū Rayhān al-Bīrūnī]] in the early [[11th century]].<ref name=Khwarizm>[http://muslimheritage.com/topics/default.cfm?ArticleID=482 Khwarizm], Foundation for Science Technology and Civilisation.</ref><ref name=Wiet>G. Wiet, V. Elisseeff, P. Wolff, J. Naudu (1975). ''History of Mankind, Vol 3: The Great medieval Civilisations'', p. 649. George Allen & Unwin Ltd, [[UNESCO]].</ref>

*The [[Equatorium]] was an [[Astrometry|astrometic]] calculating instrument invented by [[Abū Ishāq Ibrāhīm al-Zarqālī]] (Arzachel) in [[Al-Andalus|Islamic Spain]] ''circa'' [[1015]].

*An [[astrolabe]] incorporating a mechanical [[calendar]] computer and [[gear]]-wheels was invented by Abi Bakr of [[Isfahan]] in [[1235]].<ref>Silvio A. Bedini, Francis R. Maddison (1966). "Mechanical Universe: The Astrarium of Giovanni de' Dondi", ''Transactions of the American Philosophical Society'' '''56''' (5), p. 1-69.</ref>

* The [[slide rule]] is a hand-operated analog computer for doing multiplication and division, invented around 1620–1630, shortly after the publication of the concept of the logarithm.

* The [[differential analyser]], a mechanical analog computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. Invented in 1876, they were first built in the 1920s and 1930s.

* [[World War II]] era [[gun director]]s and [[bomb sight]]s used mechanical analog computers.

* Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi.<ref>[http://www.me.caltech.edu/centennial/history/nastran.htm Caltech NASTRAN history]</ref><ref>[http://books.google.com/books?id=X0UYAAAAIAAJ&q=caltech+analog-computer+intitle:analog&dq=caltech+analog-computer+intitle:analog&as_brr=0&ei=sgbuRpeoJIfmpwL0rZi6Dw&pgis=1 ''Analog Simulation: Solution of Field Problems'']</ref>

* The [[MONIAC Computer]] was a hydraulic model of a national economy built in the early 1950s

* [[Heathkit|Heathkit EC-1]] An educational analog computer made by the Heath Company, USA c. 1960.

==Electronic analog computers==
[[Image:AKAT-1.JPG|thumb|250px|Polish analog computer AKAT-1]]

The similarity between linear mechanical components, such as [[spring (device)|spring]]s and [[dashpot]]s, and electrical components, such as [[capacitor]]s, [[inductor]]s, and [[resistor]]s is striking in terms of mathematics: They can be modeled using equations that are of essentially the same form.

However, the difference between these systems is what makes analog computing useful. If one considers a simple mass-spring system, constructing the physical system would require buying the springs and masses. This would be proceeded by attaching them to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking (somewhat difficult) measurements.

The electrical equivalent can be constructed with a few operational amplifiers ([[Op amp]]s) and some passive linear components; all measurements can be taken directly with an [[oscilloscope]]. In the circuit, the (simulated) 'mass of the spring' can be changed by adjusting a [[potentiometer]]. The electrical system is an analogy to the physical system, hence the name, but it is less expensive to construct, safer, and easier to modify. Also, an electronic circuit can typically operate at higher frequencies than the system being simulated. This allows the simulation to run faster than real time, for quicker results.

The drawback of the mechanical-electrical analogy is that electronics are limited by the range over which the variables may vary. This is called [[dynamic range]]. They are also limited by [[noise (physics)|noise levels]].

These electric circuits can also easily perform other simulations. For example, [[voltage]] can simulate [[water pressure]] and [[ampere]]s can simulate water flow in terms of [[cubic metre]]s per second.

There is a lack of understanding about electrical systems that sometimes leads to the terms ''analog'' and ''digital'' having seemingly confusing and somewhat dubious meanings. Analog systems are sometimes understood only as continuous, time variant electrical systems. From the above discussion ''this is not correct,'' since discontinuous functions may also be modeled. In fact, ''digital'' also has a precise technical definition. In the context of circuits, it refers to the use of discrete electrical voltage levels as codes for symbols and ''the manipulation of these symbols'' in the operation of the digital computer. The electronic analog computer manipulates the physical quantities of (waveforms) of volts or amperes. Consequently, the precision of the analog computer readout (of rational numbers) is limited only by the [[quantization]] of the readout equipment used (generally three or four places). The digital computer precision must necessarily be finite, but the precision of its result is limited only by time.

==Analog digital hybrid computers==

There is an intermediate device, a [[hybrid computer]], in which a [[digital computer]] is combined with an analog computer. Hybrid computers are used to obtain a very [[accurate]] but imprecise 'seed' value, using an analog computer front-end, which is then fed into a digital computer [[iterative]] process to achieve the final desired degree of [[precision]]. With a three or four digit, highly accurate numerical seed, the total digital computation time necessary to reach the desired precision is dramatically reduced, since many fewer iterations are required. Or, for example, the analog computer might be used to solve a non-analytic differential equation problem for use at some stage of an overall computation (where precision is not very important). In any case, the hybrid computer is usually substantially faster than a digital computer, but can supply a far more precise computation than an analog computer. It is useful for [[real-time computing|real-time]] applications requiring such a combination (e.g., a high frequency [[phased-array radar]] or a weather system computation).
[[Image:ELWAT.jpg|thumb|300px|Polish Analog computer [[ELWAT]].]]

== Mechanisms ==

In analog computers, computations are often performed by using properties of electrical resistance, voltages and so on. For example, a simple two variable adder can be created by two [[current source]]s in parallel. The first value is set by adjusting the first current source (to say ''x'' [[milli]][[ampere]]s), and the second value is set by adjusting the second current source (say ''y'' milliamperes). Measuring the current across the two at their junction to signal ground will give the sum as a current through a resistance to signal ground, i.e., ''x''+''y'' milliamperes. (See [[Kirchhoff's circuit laws|Kirchhoff's current law]]) Other calculations are performed similarly, using [[operational amplifier]]s and specially designed circuits for other tasks.

The use of electrical properties in analog computers means that calculations are normally performed in [[real time]] (or faster), at a significant fraction of the speed of light, without the relatively large calculation delays of digital computers. This property allows certain useful calculations that are comparatively "difficult" for digital computers to perform— for example numerical integration. These computers can integrate— essentially calculating the integral of a (nondiscrete) voltage waveform, usually by means of a [[capacitor]], which accumulates charge over time.

[[Nonlinear]] functions and calculations can be constructed to a limited precision (three or four digits) by designing [[function generator]]s— special circuits of various combinations of [[capacitance]], [[inductance]], [[electrical resistance|resistance]], in combination with diodes (e.g., [[Zener diode|Zener]] diodes) to provide the nonlinearity. Generally, a nonlinear function is simulated by a nonlinear waveform whose shape varies with voltage (or current). For example, as voltage increases, the total [[Electrical impedance|impedance]] may change as the diodes successively permit current to flow.

Any physical process which models some computation can be interpreted as an analog computer. Some examples, invented for the purpose of illustrating the concept of analog computation, include using a bundle of [[spaghetti]] as a model of ''sorting numbers''; a board, a set of nails, and a rubber band as a model of finding the ''[[convex hull]] of a set of points;'' and strings tied together as a model of ''finding the shortest path in a network.'' These are all described ''in'' A.K. Dewdney (see [[#Reference|citation]] below).

== Components ==

[[Image:NewmarkAnalogueComputer.jpg|thumb|A 1960 Newmark analogue computer, made up of five units. This computer was used to solve [[differential equation]]s and is currently housed at the Cambridge Museum of Technology.]]

Analog computers often have a complicated framework, but they have, at their core, a set of key components which perform the calculations, which the operator manipulates through the computer's framework.

Key hydraulic components might include pipes, valves or towers; mechanical components might include gears and levers; key electrical components might include:

* [[potentiometer]]s
* [[operational amplifier]]s
* [[integrator]]s
* fixed-[[function generator]]s

The core mathematical operations used in an electric analog computer are:

* [[summation]]
* [[additive inverse|inversion]]
* [[exponentiation]]
* [[logarithm]]
* [[Integral|integration]] with respect to time
* [[Derivative|differentiation]] with respect to time
* [[multiplication]] and [[Division (mathematics)|division]]

Differentiation with respect to time is not frequently used. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified.

== Limitations ==

In general, analog computers are limited by real, non-ideal effects. An analog signal is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the [[noise floor]], [[non-linearity|non-linearities]], [[temperature coefficient]], and [[Microelectronics|parasitic effects]] within semiconductor devices, and the finite charge of an [[electron]]. Incidentally, for commercially available electronic components, ranges of these aspects of input and output signals are always [[figures of merit]].

Analog computers, however, have been replaced by digital computers for almost all uses. It may be stretching a point to regard some physical simulations such as [[wind tunnel]]s as analog computers, because the data so obtained must then also be scaled, for example, for [[Reynolds number]] and [[Mach number]]. There is a point of view in physics based on [[information processing]] which attempts to map the physical [[Process (general)|processes]] to [[computation]]s. Thus, from these points of view, the wind tunnel data gathering is either an [[experiment]] or a [[computation]].

== Current research ==

While digital computation is extremely popular, research in analog computation is being done by a handful of people worldwide. In the United States, [[Jonathan Mills]] from Indiana University, Bloomington, Indiana has been working on research using Extended Analog Computers. At the [[Harvard Robotics Laboratory]], analog computation is a research topic.

== Practical examples ==

These are examples of analog computers that have been constructed or practically used:
* [[Antikythera mechanism]]
* [[astrolabe]]
* [[differential analyzer]]
* [[Kerrison Predictor]]
* [[mechanical integrator]]
* [[MONIAC Computer]] (hydraulic model of UK economy)
* [[nomogram]]
* [[Norden bombsight]]
* [[operational amplifier]]
* [[planimeter]]
* [[Rangekeeper]]
* [[slide rule]]
* [[Torpedo Data Computer]]
* [[Tide predictor]]s
* [[Torquetum]]
* [[Water integrator]]

[[Analog synthesizer]]s can also be viewed as a form of analog computer, and their technology was originally based on electronic analog computer technology.

== Real computers ==

Computer theorists often refer to idealized analog computers as [[real computer]]s (because they operate on the set of [[real number]]s). Digital computers, by contrast, must first [[quantize]] the signal into a finite number of values, and so can only work with the [[rational number]] set (or, with an approximation of irrational numbers).

These idealized analog computers may ''in theory'' solve problems that are [[intractable]] on [[computer|digital computers]]; however as mentioned, in reality, analog computers are far from attaining this ideal, largely because of noise minimization problems. Moreover, given ''unlimited'' time and memory, the (ideal) digital computer may also solve real number problems. {{Fact|date=December 2007}}

==See also==

{{commonscat|Analog computer}}
*[[Signal (information theory)]]
*[[Signal (computing)]]
*[[Differential equation]]
*[[Dynamical system]]
*[[Chaos theory]]
*[[Slide rule]]
*[[Analogical models]]
*[[Antikythera mechanism]]

Other types of computers:
* [[DNA computer]]
* [[Molecular computer]]
* [[Quantum computer]]
* [[Wetware computer]]
* [[Digital computer]]

People associated with analog computer development:
* [[George A. Philbrick]]

==Notes==

{{reflist}}

==References==

* A.K. Dewdney. "On the Spaghetti Computer and Other Analog Gadgets for Problem Solving", ''Scientific American'', 250(6):19-26, June 1984. Reprinted in ''The Armchair Universe'', by A.K. Dewdney, published by W.H. Freeman & Company (1988), ISBN 0-7167-1939-8.

* Universiteit van Amsterdam Computer Museum. (2007). [http://www.science.uva.nl/museum/AnalogComputers.html ''Analog Computers''].

== External links ==

* [http://fafner.dyndns.org/~vaxman/publications/anhyb.pdf Introduction to Analog-/Hybrid-Computing] ''(PDF file)''
* [http://fafner.dyndns.org/~vaxman/publications/handson.pdf Example programs for Analog Computers] ''(PDF file)''
*[http://www.oldcomputermuseum.com/index.html Large collection of old analog and digital computers at Old Computer Museum]
* [http://technology.open.ac.uk/tel/people/bissell/bletchley_paper.pdf A great disappearing act: the electronic analogue computer] Chris Bissell, The Open University, Milton Keynes, UK Accessed February 2007
* [http://www.vaxman.de/analog_computing/analog_computing.html Lots of documentation about analog computers as well as detailed descriptions of some historic machines]
* [http://technikum29.de/en/computer/analog German computer museum with still runnable analog computers]
* [http://www.play-hookey.com/analog/ Analog computer basics]
* [http://www.yorku.ca/sasit/sts/sts3700b/lecture20a.html Lecture 20: Analog vs Digital] ''(in a series of lectures on "History of computing and information technology")''
* [http://www.eetimes.com/story/OEG19981103S0017 Analog computer trumps Turing model]

* [http://www.cs.indiana.edu/~jwmills/ANALOG.NOTEBOOK/klm/klm.html Jonathan W. Mills's Analog Notebook]
* [http://www.cs.indiana.edu/Facilities/hardware/extended_analog_computer/ Indiana University Extended Analog Computer]
* [http://hrl.harvard.edu/analog/ Harvard Robotics Laboratory Analog Computation]
* [http://www.oldcomputermuseum.com Large collection of analog and digital computers]

[[Category:Classes of computers]]
[[Category:History of computing hardware]]

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