analog computer

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A page from the Bombardier's Information File (BIF) that describes the components and controls of the Norden bombsight. The Norden bombsight was a highly sophisticated optical/mechanical analog computer used by the United States Army Air Force during World War II, the Korean War, and the Vietnam War to aid the pilot of a bomber aircraft in dropping bombs accurately.

An analog computer (spelled analogue in British English) is a form of computer that uses continuous physical phenomena such as electrical,^[1] mechanical, or hydraulic quantities to model the problem being solved.

Timeline of analog computers

• The Antikythera mechanism is believed to be the earliest known mechanical analog computer.^[2] 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 a level of complexity comparable to that of 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 BC 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.^[3]

• Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe,^[4] an early fixed-wired knowledge processing machine^[5] with a gear train and gear-wheels,^[6] circa 1000 AD.

• The Planisphere was a star chart astrolabe also invented by Abū Rayhān al-Bīrūnī in the early 11th century.^[7][8]

• 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,^[9] is considered to be the first programmable analog computer.^[10] 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,^[11][12] 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.^[10]

• An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan in 1235.^[13]

A slide rule

• 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.^{[citation needed]}

• 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.^{[citation needed]}

• World War II era gun Director (military), Gun Data Computers, and bomb sights used mechanical analog computers.^{[citation needed]}

• The MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.^{[citation needed]}

• 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.^[14][15]

• Heathkit EC-1, an educational analog computer made by the Heath Company, USA c. 1960.^{[citation needed]}

• translates physical variables by performing arithmetic and logical procecsse on discrete alphanumric data.

Electronic analog computers

Polish analog computer AKAT-1.

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 electric current can simulate rate of 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.

Analog digital hybrid computers

There is an intermediate device, a 'hybrid' computer, in which an analog output is convert into standard digits. The information then can be sent into a standard digital computer for further computation. Because of their ease of use and because of technological breakthroughs in digital computers in the early 70s, the analog-digital hybrids were replacing the analog-only systems. Hybrid computers are used to obtain a very accurate but not very mathematically precise 'seed' value, using an analog computer front-end, which value is then fed into a digital computer iterative process to achieve the final desired degree of precision. With a three or four digit precision, highly accurate numerical seed, the total computation time necessary to reach the desired precision is dramatically reduced, since many fewer digital iterations are required (and the analog computer reaches its result almost instantaneously). 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).

Polish Analog computer ELWAT.

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 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 (in the case of purely arithmetic operations), 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).

Components

A 1960 Newmark analogue computer, made up of five units. This computer was used to solve differential equations and is currently housed at the Cambridge Museum of Technology.

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:

• 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 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

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.

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, 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

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

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

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. In theory, ambient noise is limited by 'quantum noise' (caused by the quantum movements of ions). Ambient noise may be severely reduced— but never to zero— by using cryogenically cooled parametric amplifiers). Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real number problems.^{[citation needed]}

See also

Wikimedia Commons has media related to: Analog computers

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

Other types of computers:

• DNA computer
• Molecular computer
• Quantum computer
• Wetware computer
• Digital computer

People associated with analog computer development:

• George A. Philbrick

Notes

References

• 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.

• Jackson, Albert S., "Analog Computation", McGraw-Hill Book Company, 1960, ASIN: B0006AW3BS, ISBN 59-11934.

External links

• Large collection of electronic analog computers with lots of pictures and documentation
• Simulation of a car suspension system with an electronic analog computer
• Introduction to Analog-/Hybrid-Computing (pdf)
• Example programs for Analog Computers (pdf)
• 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
• 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
• The Enns Power Network Computer - an analog computer for the analysis of electric power systems (advertisement from 1955)