- Analog computer
An

**analog computer**(spelt**analogue**in British English) is a form ofcomputer that uses "continuous" physical phenomena such as electrical, [*Universiteit van Amsterdam Computer Museum, (2007)*] mechanical, or hydraulic quantities to model the problem being solved.**Timeline of analog computers***The

Antikythera mechanism is believed to be the earliest known mechanical analog computer. [*[*] It was designed to calculate astronomical positions. It was discovered in 1901 in the*http://www.antikythera-mechanism.gr/project/general/the-project.html "The Antikythera Mechanism Research Project"*] , The Antikythera Mechanism Research Project. Retrieved 2007-07-01Antikythera 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 theHellenistic world in either the first or second centuries BCE and is often attributed toHipparchus . A combination of theplanisphere anddioptra , the astrolabe was effectively an analog computer capable of working out several different kinds of problems in sphericalastronomy .*Muslim astronomers later produced many different types of

astrolabe s and used them for over a thousand different problems related to astronomy, astrology, horoscopes, navigation,surveying ,time keeping,Qibla (direction ofMecca ),Salah (prayer), etc.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.]*

Abū Rayhān al-Bīrūnī invented the first mechanicalgear edlunisolar calendar astrolabe, [*D. De S. Price (1984). "A History of Calculating Machines", "IEEE Micro"*] an early fixed-**4**(1), p. 22-52.wire d knowledge processingmachine Tuncer Oren (2001). "Advances in Computer and Information Sciences: From Abacus to Holonic Agents", "Turk J Elec Engin"**9**(1), p. 63-70 [64] .] with agear train andgear -wheels, [] "circa"Donald Routledge Hill (1985). "Al-Biruni's mechanical calendar", "Annals of Science"**42**, p. 139-163.1000 AD.*The

Planisphere was astar chart astrolabe also invented byAbū Rayhān al-Bīrūnī in the early11th century . [*http://muslimheritage.com/topics/default.cfm?ArticleID=482 Khwarizm*] , Foundation for Science Technology and Civilisation.] 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 .]*The

Equatorium was an astrometic calculating instrument invented byAbū Ishāq Ibrāhīm al-Zarqālī (Arzachel) in Islamic Spain "circa"1015 .*The "castle clock", an

astronomical clock invented byAl-Jazari in 1206, is considered to be the first programmable analog computer.citation|title=Ancient Discoveries , Episode 11: Ancient Robots|publisher=History Channel |url=http://www.youtube.com/watch?v=rxjbaQl0ad8|accessdate=2008-09-06] It displayed thezodiac , the solar andlunar orbit s, a crescent moon-shaped pointer travelling across a gateway causing automatic doors to open everyhour , [*Howard R. Turner (1997), "Science in Medieval Islam: An Illustrated Introduction", p. 184,*]University of Texas Press , ISBN 0292781490Donald Routledge Hill , "Mechanical Engineering in the Medieval Near East", "Scientific American", May 1991, pp. 64-9 (cf. Donald Routledge Hill , [*http://home.swipnet.se/islam/articles/HistoryofSciences.htm Mechanical Engineering*] )] and fiverobot ic musicians who play music when struck bylever s operated by acamshaft attached to awater wheel . The length of day andnight could be re-programmed every day in order to account for the changing lengths of day and night throughout the year.*An

astrolabe incorporating a mechanicalcalendar computer andgear -wheels was invented by Abi Bakr ofIsfahan in1235 . [*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.* 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 thelogarithm .* 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 byJames Thomson (engineer) , they were first built in the 1920s and 1930s.Fact|date=October 2008* By 1912

Arthur Pollen had developed an electrically driven mechanical analog computer forfire-control system , based on thedifferential analyser . It was used by theImperial Russian Navy inWorld War I .Fact|date=October 2008*

World War II eragun director s andbomb sight s used mechanical analog computers.Fact|date=October 2008* The

MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.Fact|date=October 2008* 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. [

*[*] [*http://www.me.caltech.edu/centennial/history/nastran.htm Caltech NASTRAN history*]*[*]*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"*]*

Heathkit EC-1, an educational analog computer made by the Heath Company, USA c. 1960.Fact|date=October 2008* Comdyna GP-6 analog computer introduced in 1968 and produced for 36 years.Fact|date=October 2008

**Electronic analog computers**The similarity between linear mechanical components, such as springs and

dashpot s, and electrical components, such ascapacitor s,inductor s, andresistor 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 amplifier s (Op amps) and some passive linear components; all measurements can be taken directly with anoscilloscope . In the circuit, the (simulated) 'mass of the spring' can be changed by adjusting apotentiometer . 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 levels.These electric circuits can also easily perform other simulations. For example,

voltage can simulatewater pressure andampere s can simulate water flow in terms ofcubic metre s per second.A digital system uses discrete electrical voltage levels as codes for symbols. The manipulation of these symbols is the method of operation of the digital computer. The electronic analog computer manipulates the physical quantities of waveforms, (voltage or current). The precision of the analog computer readout is limited chiefly by the precision of the readout equipment used, generally three or four significant figures. The digital computer precision must necessarily be finite, but the precision of its result is limited only by time. A digital computer can calculate many digits in parallel, or obtain the same number of digits by carrying out computations in time sequence.

**Analog digital hybrid computers**There is an intermediate device, a

hybrid computer , in which adigital computer is combined with an analog computer. Hybrid computers are used to obtain a veryaccurate but not exact 'seed' value, using an analog computer front-end, which is then fed into a digital computeriterative process to achieve the final desired degree ofprecision . 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 applications requiring such a combination (e.g., a high frequencyphased-array radar or a weather system computation).**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 current law) Other calculations are performed similarly, usingoperational 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. Analog computers can integrate a 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 designingfunction generator s— special circuits of various combinations ofcapacitance ,inductance , resistance, in combination with diodes (e.g., 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 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 citation below).**Components**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 sThe core mathematical operations used in an electric analog computer are:

*

summation

* inversion

*exponentiation

*logarithm

* integration with respect to time

* differentiation with respect to time

*multiplication and divisionDifferentiation 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-linearities,temperature coefficient , and parasitic effects within semiconductor devices, and the finite charge of anelectron . For commercially available electronic components, ranges of these aspects of input and output signals are alwaysfigures of merit .**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 theHarvard 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

*thermostat

*Tide predictor s

*Torpedo Data Computer

*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 ofreal number s). Digital computers, by contrast, must firstquantize the signal into a finite number of values, and so can only work with therational number set (or, with an approximation of irrational numbers).These idealized analog computers may "in theory" solve problems that are

intractable on 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**ee also***

Signal (electrical engineering)

*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****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.comdyna.com/ Comdyna - a current manufacturer of analog computing hardware*]

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