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Analog computer
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===Electronic analog computers=== [[File:Analogrechner Schaltbrett vorne.jpg|thumb|Switching board of EAI 8800 analog computer (front view)]] Electronic analog computers typically have front panels with numerous jacks (single-contact sockets) that permit patch cords (flexible wires with plugs at both ends) to create the interconnections that define the problem setup. In addition, there are precision high-resolution potentiometers (variable resistors) for setting up (and, when needed, varying) scale factors. In addition, there is usually a zero-center analog pointer-type meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide known magnitudes. Typical electronic analog computers contain anywhere from a few to a hundred or more [[operational amplifier]]s ("op amps"), named because they perform mathematical operations. Op amps are a particular type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precision feedback components that, in operation, all but cancel out the currents arriving from input components. The majority of op amps in a representative setup are summing amplifiers, which add and subtract analog voltages, providing the result at their output jacks. As well, op amps with capacitor feedback are usually included in a setup; they integrate the sum of their inputs with respect to time. Integrating with respect to another variable is the nearly exclusive province of mechanical analog integrators; it is almost never done in electronic analog computers. However, given that a problem solution does not change with time, time can serve as one of the variables. Other computing elements include analog multipliers, nonlinear function generators, and analog comparators. Electrical elements such as inductors and capacitors used in electrical analog computers had to be carefully manufactured to reduce non-ideal effects. For example, in the construction of [[Network analyzer (AC power)|AC power network analyzers]], one motive for using higher frequencies for the calculator (instead of the actual power frequency) was that higher-quality inductors could be more easily made. Many general-purpose analog computers avoided the use of inductors entirely, re-casting the problem in a form that could be solved using only resistive and capacitive elements, since high-quality capacitors are relatively easy to make. The use of electrical properties in analog computers means that calculations are normally performed in [[real-time computing|real time]] (or faster), at a speed determined mostly by the frequency response of the operational amplifiers and other computing elements. In the history of electronic analog computers, there were some special high-speed types. [[Nonlinearity|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 resistors and diodes to provide the nonlinearity. Typically, as the input voltage increases, progressively more diodes conduct. When compensated for temperature, the forward voltage drop of a transistor's base-emitter junction can provide a usably accurate logarithmic or exponential function. Op amps scale the output voltage so that it is usable with the rest of the computer. Any physical process that 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 [[Spaghetti sort|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 [[Alexander Dewdney|Dewdney]] (1984).
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