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PowerPedia:Analog computer

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. The Norden bombsight was a highly sophisticated optical/mechanical analog computer used by the United States Army Air Force during There was an error working with the wiki: Code[21], the There was an error working with the wiki: Code[22], and the There was an error working with the wiki: Code[23] to aid the pilot of a There was an error working with the wiki: Code[24] aircraft in dropping There was an error working with the wiki: Code[25]s accurately.]]

An analog computer (spelled analogue in British English) is a form of There was an error working with the wiki: Code[1], There was an error working with the wiki: Code[2] or There was an error working with the wiki: Code[26] phenomena to model the problem being solved. More generally an analog computer uses one kind of physical quantity to represent the behaviour of another physical system, or mathematical function. Modeling a real physical system in a computer is called There was an error working with the wiki: Code[27].

History

The There was an error working with the wiki: Code[28] 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 about 100-150 BC. The findings suggest that Greek technology was far more advanced than previously thought. No other civilisation is known to have created anything as complicated for over a thousand years.

Timeline of analog computers

The There was an error working with the wiki: Code[29] 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 There was an error working with the wiki: Code[30], 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.

There was an error working with the wiki: Code[31] era There was an error working with the wiki: Code[32]s and There was an error working with the wiki: Code[33]s used mechanical analog computers.

There was an error working with the wiki: Code[34] electronic analog computer c 1950 was a very adaptable machine, that could be configured to solve a range of problems.

The There was an error working with the wiki: Code[35] was a hydraulic model of a national economy built in the early 1950s

There was an error working with the wiki: Code[3] An educational analog computer made by the Heath Company , USA c 1960.

There was an error working with the wiki: Code[4] "Orion quantum computing system", the worlds first working There was an error working with the wiki: Code[36] operates as an analog computer.

Electronic analog computers

The similarity between linear mechanical components, such as There was an error working with the wiki: Code[5]s and There was an error working with the wiki: Code[37]s, and electrical components, such as Capacitors, There was an error working with the wiki: Code[38]s, and There was an error working with the wiki: Code[39]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 amplifiers (There was an error working with the wiki: Code[40]s) and some passive linear components all measurements can be taken directly with an There was an error working with the wiki: Code[41]. In the circuit, the (simulated) 'mass of the spring' can be changed by adjusting a There was an error working with the wiki: Code[42]. 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. The all-electronic analog computer is also extremely fast, since a calculation is completed at the rate at which a signal traverses the circuit, which is generally an appreciable fraction of the speed of light.

The drawback of the mechanical-electrical analogy is that electronics are limited by the range over which the variables may vary. This is called There was an error working with the wiki: Code[6].

These electric circuits can also easily perform other simulations. For example, Voltage can simulate There was an error working with the wiki: Code[43] and Amperes can simulate water flow in terms of There was an error working with the wiki: Code[44]s 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 There was an error working with the wiki: Code[45] 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 computers

There is an intermediate device, a There was an error working with the wiki: Code[7] applications requiring such a combination (e.g., a high frequency There was an error working with the wiki: Code[46] or a weather system computation).

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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 There was an error working with the wiki: Code[8]) Other calculations are performed similarly, using There was an error working with the wiki: Code[47]s and specially designed circuits for other tasks.

The use of electrical properties in analog computers means that calculations are normally performed in There was an error working with the wiki: Code[48] (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.

There was an error working with the wiki: Code[9], and variable current (e.g., Zener diode) diodes. Generally, a nonlinear function is simulated by a nonlinear waveform whose shape varies with voltage (or current). For example, as voltage increases, the total There was an error working with the wiki: Code[10] 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 There was an error working with the wiki: Code[11] 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:

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The core mathematical operations used in an electric analog computer are:

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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

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 There was an error working with the wiki: Code[16], There was an error working with the wiki: Code[17] 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 There was an error working with the wiki: Code[56].

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 There was an error working with the wiki: Code[18] to There was an error working with the wiki: Code[57]s. Thus, from these points of view, the wind tunnel data gathering is either an Experiment or a There was an error working with the wiki: Code[57].

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, There was an error working with the wiki: Code[59] from Indiana University, Bloomington, Indiana has been working on research using Extended Analog Computers. At the There was an error working with the wiki: Code[60], analog computation is a research topic.

Practical examples

These are examples of analog computers that have been constructed or practically used:

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There was an error working with the wiki: Code[76]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 There was an error working with the wiki: Code[77]s (because they operate on the set of There was an error working with the wiki: Code[78]s). Digital computers, by contrast, must first There was an error working with the wiki: Code[79] the signal into a finite number of values, and so can only work with the There was an error working with the wiki: Code[80] set (or, with an approximation of irrational numbers).

These idealized analog computers may in theory solve problems that are There was an error working with the wiki: Code[19] 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 also

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Other computers

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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 0-7167-1939-8.

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

Start-up demos quantum computer By Michael Kanellos Staff Writer, CNET News.com, Published: February 14, 2007 Accessed 16 Feb 07. "Ultimately, D-Wave's computer is an analog computer, according to Alexey Andreev, a venture capitalist at Harris & Harris and an investor in D-Wave. Answers to programs run on the computer come in the form of a physical simulation. Answers to problems in digital computers are essentially mathematical solutions."

External links

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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