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An **analog computer** (spelled **analogue** in British English) is a form of computer that uses electrical^{[1]}, mechanical or hydraulic phenomena to model the problem being solved. More generally an analog computer uses one kind of physical quantity to represent the behavior of another physical system, or mathematical function. Modeling a real physical system in a computer is called simulation.

### Timeline of analog computersEdit

- The Antikythera mechanism is 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. - Al-Biruni invented the first mechanical geared calendar computer,
*circa*1000 AD.^{[2]} - 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 directors and bomb sights used mechanical analog computers.
- General Precision Systems electronic analog computer c. 1950 was a very adaptable machine, that could be configured to solve a range of problems.
- The MONIAC Computer was a hydraulic model of a national economy built in the early 1950s
- Heathkit EC-1 An educational analog computer made by the Heath Company, USA c. 1960.

## Electronic analog computersEdit

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.

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 computersEdit

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 applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation).

## Mechanisms Edit

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. 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 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).

## Components Edit

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.

## Limitations Edit

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. 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 tunnels 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 processes to computations. Thus, from these points of view, the wind tunnel data gathering is either an experiment or a computation.

## Current research Edit

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 Edit

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 predictors
- 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.

## Real computers Edit

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.

## See alsoEdit

- signal (information theory)
- signal (computing)
- set theory
- computability theory
- differential equation
- dynamical system
- chaos theory
- slide rule
- analogue models
- Antikythera mechanism

Other types of computers:

People associated with analog computer development:

## NotesEdit

## ReferencesEdit

- 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*.

## External links Edit

- Introduction to Analog-/Hybrid-Computing
*(PDF file)* - Example programs for Analog Computers
*(PDF file)* - 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
- 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
- Large collection of analog and digital computers

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