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The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Computer in which continuously variable physical quantities, such as electrical potential, fluid pressure, or mechanical motion, are used to represent (analogously) the quantities in the problem to be solved. The analog system is set up according to initial conditions and then allowed to change freely. Answers to the problem are obtained by measuring the variables in the analog model. Analog computers are especially well suited to simulating dynamic systems; such simulations may be conducted in real time or at greatly accelerated rates, allowing experimentation by performing many runs with different variables. They have been widely used in simulating the operation of aircraft, nuclear power plants, and industrial chemical processes. *Seealso* digital computer.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

An analog computer (spelt analogue in British English) is a form of computer that uses continuous physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved.

- 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 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.
- Muslim astronomers later produced many different types of astrolabes and used them for over a thousand different problems related to astronomy, astrology, horoscopes, navigation, surveying, timekeeping, Qibla (direction of Mecca), Salah (prayer), etc.
- Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, circa 1000 AD.
- The Planisphere was a star chart astrolabe also invented by Abū Rayhān al-Bīrūnī in the early 11th century.
- The Equatorium was an astrometic calculating instrument invented by Abū Ishāq Ibrāhīm al-Zarqālī (Arzachel) in Islamic Spain circa 1015.
- The "castle clock", an astronomical clock invented by Al-Jazari in 1206, is considered to be the first programmable analog computer. It displayed the zodiac, the solar and lunar orbits, a crescent moon-shaped pointer travelling across a gateway causing automatic doors to open every hour, and five robotic musicians who play music when struck by levers operated by a camshaft attached to a water wheel. The length of day and night 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 mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan in 1235.

- 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 by James Thomson (engineer), they were first built in the 1920s and 1930s.
- By 1912 Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control system, based on the differential analyser. It was used by the Imperial Russian Navy in World War I.
- World War II era gun directors and bomb sights used mechanical analog computers.
- The MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.
- 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.
- Heathkit EC-1, an educational analog computer made by the Heath Company, USA c. 1960.
- Comdyna GP-6 analog computer introduced in 1968 and produced for 36 years.

The similarity between linear mechanical components, such as springs and dashpots, and electrical components, such as capacitors, inductors, and resistors 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 amps) 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 levels.

These electric circuits can also easily perform other simulations. For example, voltage can simulate water pressure and amperes can simulate water flow in terms of cubic metres 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.

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 not exact '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 applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation).

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 sources in parallel. The first value is set by adjusting the first current source (to say x milliamperes), 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, using operational amplifiers 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 designing function generators— special circuits of various combinations of capacitance, 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).

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:

The 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 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.

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 an electron. For commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit.

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.

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 predictors
- Torpedo Data Computer
- Torquetum
- Water integrator

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

Computer theorists often refer to idealized analog computers as real computers (because they operate on the set of real numbers). 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 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.

- Signal (electrical engineering)
- Signal (computing)
- Differential equation
- Dynamical system
- Chaos theory
- Slide rule
- Analogical models
- Antikythera mechanism

Other types of computers:

People associated with analog computer development:

- 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). Analog Computers

- Introduction to Analog-/Hybrid-Computing (PDF file)
- Example programs for Analog Computers (PDF file)
- Large collection of old analog and digital computers at Old Computer Museum
- A great disappearing act: the electronic analogue computer Chris Bissell, The Open University, Milton Keynes, UK Accessed February 2007
- Lots of documentation about analog computers as well as detailed descriptions of some historic machines
- German computer museum with still runnable analog computers
- Analog computer basics
- Lecture 20: Analog vs Digital (in a series of lectures on "History of computing and information technology")
- Analog computer trumps Turing model

- Jonathan W. Mills's Analog Notebook
- Indiana University Extended Analog Computer
- Harvard Robotics Laboratory Analog Computation
- Comdyna - a current manufacturer of analog computing hardware

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