Analog computer
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An analog computer (American English) or analogue computer (British English) is a form of computer using electronic or mechanical phenomena to model the problem being solved by using one kind of physical quantity to represent another. The term analog signal is used to describe varying signals, which analog computers deal with, as opposed to discrete variations in signals, which digital computers deal with. Within the limits of operation, where the noise levels are understood, this hardware circuit might be pressed into operation to perform computations. This sort of circuitry is still in use today, when speed of response is at a premium, and the problem being solved is hard-wired into the circuitry, for some electrical systems.
The term analog is used in distinction to digital computers, in which physical or mechanical phenomena are used to construct a finite-state machine which is then used to model the problem being solved. There is an intermediate group, hybrid computers, in which a digital computer is used to control and organize inputs and outputs to and from attached analogue devices; for instance analogue devices might be used to help generate initial values for iterations, or the analog computer might be used to solve a non-analytic differential equation problem.
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Some examples:
- the abacus is a hand-operated digital computer
- the slide rule is a hand-operated analog computer
- early gun directors used mechanical analog computers to direct gunnery fire
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How analog computers work
Computations are often performed, in analog computers, 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 resistance x+y milliamperes. Other calculations are performed similarly, using operational amplifiers and other circuits for other tasks.
The use of electrical properties in analog computers means that certain calculations on a computer are performed in real time, without calculation delays as on 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 sum of a voltage waveform, usually by means of a capacitor, which accumulates charge over time.
Nonlinear functions and calculations can be constructed to a given amount of accuracy by creating a diode function generator: a set of diodes and resistors of varying values. As voltage increases, the total resistance summed changes 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 were all described by A.K. Dewdney (citation below).
Analog computer components
Analog computers often have a complicated framework, but they have, at their core, a set of key electrical components which perform the calculations, which the operator manipulates through the computer's framework:
- potentiometers
- operational amplifiers
- integrators
- fixed-function generators
The core mathematical operations used in an electric analog computer are:
- summation
- inversion
- exponentiation
- logarithm
- integration (with respect to time)
- differentiation
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 and parasitic impedances within semiconductor devices, and the finite charge of an electron. Incidentally, for commercially available electronic components, range 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 calculations. 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.
Practical analog computers
These are examples of analog computers that have been constructed or practically used:
- nomogram
- astrolabe
- operational amplifier
- planimeter
- mechanical integrator
- Torquetum
- Tide predictors
- Water integrator
- Target Data Computer
- Norden bombsight
- Hydraulic model of UK economy
- the Antikythera mechanism
- and the slide rule
Analog synthesizers can also be viewed as a form of analog computer, and their technology was originally based on electronic analog computer technology.
Idealised analog computers
Computer theorists often refer to idealised analog computers as real computers (so called because they operate on the set of real numbers).
These idealised computers can in theory solve problems that are inextricable on digital computers; however, as mentioned, in reality analog computers are far from attaining this ideal, because of noise minimization problems.
Reference
- 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 0716719398.
See also
- signal (information theory)
- signal (computing)
- set theory
- computability theory
- differential equation
- dynamical system
- chaos theory
External links
- Lecture 20: Analog vs Digital (http://www.yorku.ca/sasit/sts/sts3700b/lecture20a.html) (in a series of lectures on "History of computing and information technology")
- Doug Cowards's Analog Computer Museum (http://dcoward.best.vwh.net/analog/)de:Analogrechner
es:Ordenador analógico nl:Analoge computer pl:Komputer analogowy ru:Аналоговый компьютер sv:Analogdator