An analog or analog computer is a form of computer that uses aspects of continuously changing physical phenomena such as electrical, mechanical, or hydraulic numbers to model problems that are being solved. In contrast, digital computers represent symbolically different amounts, as their numerical values ​​change. As analog computers do not use discrete values, but rather continuous values, unreliable processes are repeated with exact equality, as they can with Turing machines. Unlike digital signal processing, analog computers do not experience quantization disruptions, but are limited by analog sound.
Analog computers are widely used in scientific and industrial applications where digital computers at that time did not have sufficient performance. An analog computer can have a very wide range of complexities. The slide rules and nomograms are the simplest, while the naval control computer controls and large digital/analog hybrid computers are among the most complicated. Systems for process control and protective relays using analog computing to perform control and protection functions.
The advent of digital computing has made the analog computers simpler obsolete since the 1950s and 1960s, although analog computers are still used in certain applications, such as flight computers in airplanes, and for teaching control systems at universities. More complex applications, such as synthetic aperture radar, remained analogue computing domains until the 1980s, as digital computers were inadequate for the task.
Video Analog computer
Settings
Setting up an analog computer required the scale factor to be selected, along with the initial conditions - that is, the initial value. Another important thing is to create the necessary interconnection network between the computational elements. Sometimes it is necessary to rethink the problem structure so that the computer will function satisfactorily. No variables are allowed to exceed computer limits, and differentiation should be avoided, usually by rearranging "network" interconnects, using integrators in different meanings.
Running an analog analog computer, assuming a satisfactory setting, starts with a computer held with some fixed variable at its initial value. Moving the switch releases the hold and allows the problem to run. In some cases, the computer can, after a certain time interval, repeatedly return to its original state to reset the problem, and run it again.
Maps Analog computer
Analogue time line
Precursors
This is a list of examples of early computing devices that are considered to be modern computer precursors. Some of them may even have been dubbed as 'computers' by the press, though they may fail to adapt to modern definitions.
The south-pointed train, found in ancient China during the first millennium BC, can be considered the earliest analog computer. It is a mechanical wheeled vehicle used to distinguish the direction of the southern cardinal.
The Antikythera mechanism is an orrery and is claimed to be the earliest analog computer analogue, according to Derek J. de Solla Price. It was designed to calculate the position of astronomy. It was discovered in 1901 in the ruins of Antikythera on the Greek island of Antikythera, between Kythera and Crete, and has dates to around 100 BC. A device of a level of complexity comparable to the Antikythera mechanism will not reappear until a thousand years later.
Many mechanical tools for calculation and measurement are made for astronomical and navigational use. Planisphere is a star chart created by Ab? Ray ?? n al-B? R? N? at the beginning of the 11th century. Astrolabs were created in the Hellenistic world of the 1st or 2nd century BC and are often associated with Hipparchus. The combination of planisphere and dioptra, astrolabe is effectively an analog computer capable of working on some kind of problem in spherical astronomy. The astrolabe that combines computer calendars and gears was invented by Abi Bakr of Isfahan, Persia in 1235. Ab? Rayh? N al-B? R? N? creating the first mechanically directed lunisolar astrolabe calendar, the longest fixed knowledge processing machine with gears and gears, around <1000 years. The clock of the castle, the mechanical clock of electric power invented by Al-Jazari in 1206, was the first programmable analog computer.
This sector, a computational instrument used to solve proportional problems, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found applications in cannons, surveys and navigation.
Planimeter is a manual instrument to calculate the area of ​​a closed figure by tracing it with mechanical connection.
The slide rule was found around 1620-1630, shortly after the publication of the concept of logarithms. This is a hand operated analogue computer for multiplication and division. As the development of slide rules develops, added scales are provided reciprocity, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular triggers and hyperbolic and other functions. Aviation is one of the few areas where slide rules are still widely used, especially for solving the problem of time spacings on light aircraft.
The tidal prediction engine invented by Sir William Thomson in 1872 is useful for navigation in shallow waters. It uses a pulley and cable system to automatically calculate the predicted tidal level for a certain time period in a particular location.
A differential analyzer, a mechanical analog computer designed to solve differential equations with integration, uses a wheel-and-disc mechanism to perform integration. In 1876 James Thomson had discussed the possibility of constructing the calculator, but he was hindered by the limited output torque of a spherical-and-disc integrator. In a differential analyzer, the output of one integrator pushes the next integrator input, or graph output. The torque booster is a progress that allows these machines to work. Beginning in the 1920s, Vannevar Bush and others developed a mechanical differential analyzer.
Modern era
Dumaresq is a mechanical calculating device discovered around 1902 by Lieutenant John Dumaresq of the Royal Navy. It is an analog computer that deals with the vital variables of fire control problems for the movement of the vessel itself and of the target vessel. It is often used with other devices, such as the Vickers range clock to generate range and deflection data so that the sights of the ship's guns can continue to be established. A number of versions of Dumaresq result from increased complexity as developments occur.
In 1912, Arthur Pollen had developed an electrically driven mechanical analogue computer for fire control systems, based on a differential analyzer. It was used by the Russian Imperial Navy in World War I.
Beginning in 1929, AC network analysis was built to solve the calculation problems associated with power systems that were too large to be solved by numerical methods at the time. This is basically a scale model of the electrical properties of a full-size system. Because network analysis can handle problems that are too large for analytical methods or hand calculations, they are also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzes were built in the late 1950s.
World War II weapons directors, weapon data computers, and bomb scenes using mechanical analog computers. In 1942, Helmut HÃÆ'¶lzer built an electronic analog computer entirely in the PeenemÃÆ'¼nde Army Research Center. V-2 rocket trajectory Mechanical analog computers are very important in the control of firearms in World War II, the Korean War, and the Vietnam War past; they are made in significant quantities.
FERMIAC is an analog computer invented by physicist Enrico Fermi in 1947 to assist in his study of neutron transport. Project Cyclone is an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon is an analog computer developed by RCA in 1952. It consists of over 4000 electron tubes and uses 100 dial and 6000 plug-in connectors to the program. MONIAC ​​Computer is a hydraulic model of the national economy first introduced in 1949.
Computer Engineering Associates was released out of Caltech in 1950 to provide commercial services using "Analogy Direct Electrical Analog Computers" ("the largest and most impressive general purpose analysis facility for field problem solutions") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi.
Educational analog computers describe analogue calculation principles. The Heathkit EC-1, $ 199 educational analog computer, created by Heath Company, USA c. 1960. It was programmed using a patch cable connecting nine operational amplifiers and other components. General Electric also marketed an "educational" analog computer kit with a simple design in the early 1960s consisting of two tone transistor generators and three wired potentiometers such that the oscillator frequency was eliminated when the potentiometer disk was positioned by hand to satisfy the equation. The relative resistance of the potentiometer is then equivalent to the equation formula solved. Multiplication or division can be done depending on the dial considered the input and which is the output. Limited accuracy and resolution and simple slide rules are more accurate; However, the unit shows the basic principle.
In industrial process control, thousands of analogue loop controllers are used to adjust the temperature, flow, pressure, or other process conditions automatically. This control technology ranges from pure mechanical integrators, through vacuum tubes and solid-state devices, to analogue control emulation by microprocessors.
Electronic analog computer
The similarities between linear mechanical components, such as springs and dashpots, and electrical components, such as capacitors, inductors, and resistors are conspicuous in terms of mathematics. They can be modeled using equations of the same form.
However, the difference between these systems is what makes analog computing useful. If one considers a simple mass spring system, building a physical system would require making or modifying springs and masses. This will be followed by attaching them to each other and an appropriate anchor, collecting test equipment with the right input range, and finally, performing the measurements. In more complicated cases, such as suspensions for race cars, experimental construction, modification, and testing are very complicated and expensive.
Electric equivalents can be built with some operational amplifiers (op amps) and some passive linear components; all measurements can be taken directly with the oscilloscope. In the circuit, (simulation) 'spring stiffness', for example, can be changed by adjusting the capacitor parameters. Electrical systems are analogous to physical systems, hence the name, but cheaper to make, generally safer, and usually easier to modify.
As well, electronic circuits can usually operate at higher frequencies than simulated systems. This allows the simulation to run faster than real time (which can, in some cases, be hours, weeks, or longer). Experienced users of electronic analog computers say they offer relatively familiar control and understanding of the problem, relative to digital simulations.
The disadvantage of the electrical-mechanical analogy is that electronics are limited by ranges where variables can vary. This is called the dynamic range. They are also limited by the noise level. Digital floating-point calculations have a relatively large dynamic range.
This electrical circuit can also easily perform a variety of simulations. For example, voltage can simulate water pressure and electric current can simulate flow rate in terms of cubic meters per second. The integrator can provide the total volume of fluid accumulation, using the input current proportional to the flow rate (may vary).
An analog computer is best suited to represent the situation described by the differential equation. Sometimes, they are used when differential equations prove very difficult to solve in the traditional way.
The accuracy of analog computers is limited by its computing elements as well as the quality of internal power and electrical interconnection. The accuracy of analog computer readings is limited primarily by the accuracy of the reading equipment used, generally three or four significant numbers. The precision of digital computers is limited by word size; arbitrary precision arithmetic, while relatively slow, provides a practical level of practicality that may be required.
Many small computers dedicated to specific calculations are still part of the industry's regulatory equipment, but from the 1950s to the 1970s, general purpose analog computers were the only systems fast enough to simulate real-time dynamic systems, especially in aircraft, the military and aerospace fields.
In the 1960s, major manufacturers were Electronic Associates of Princeton, New Jersey, with 231R Analog Computer (vacuum tube, 20 integrators) and then 8800 Analog Computer (solid state operational amplifier, 64 integrators). His challenger is Applied Dynamics of Ann Arbor, Michigan.
Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency restrictions), in the 1960s attempts were made in French ANALAC computers to use alternative technologies: medium frequency carriers and non-dissipative reversible circuits.
In the 1970s every major company and administration concerned with problems in dynamics had a large analog computing center, for example:
- In the United States : NASA (Huntsville, Houston), Martin Marietta (Orlando), Lockheed, Westinghouse, Hughes Aircraft
- In Europe : CEA (French Atomic Energy Commission), MATRA, Aerospatiale, BAC (British Aircraft Company).
Analog-digital hybrid
Analog computing devices are fast, digital computing devices are more flexible and accurate, so the idea is to combine the two processes for the best efficiency. An example of a hybrid elementary device is a hybrid multiplier where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as a digital upgradeable potentiometer. This type of hybrid technique is mainly used for real-time computing that is fast dedicated when computing time is critical as signal processing for radar and generally for controllers in embedded systems.
In the early 1970s, analogue computer manufacturers tried to connect their analog computers with digital computers to benefit from both techniques. In such systems, a digital computer controls an analog computer, provides for initial setup, initiates some analog operations, and automatically feeds and collects data. Digital computers can also participate in the calculation itself using an analog-to-digital and digital-to-analog converter.
The largest hybrid computer manufacturer is Electronics Associates. Their 8900 hybrid computer model is made of a digital computer and one or more analog consoles. The system is primarily dedicated to major projects such as the Apollo and Space Shuttle programs at NASA, or Ariane in Europe, especially during the integration stages where initially everything is simulated, and real progressive components replacing their simulated parts.
Only one company was known to offer general commercial computing services on its hybrid computer, the French CISI, in the 1970s.
The best reference in this field is 100,000 running simulations for each Airbus and Concorde aircraft automatic landing system certification.
After 1980, pure digital computers grew faster and faster enough to compete with analog computers. One key to analog computer speed is their full parallel computation, but this is also a limitation. The more equations needed for a problem, the more analog components are needed, even when the problem is less important. "Programming" problem means interconnection of analog operators; even with this removable cable panel is not very versatile. Currently no more large hybrid computers, but only hybrid components.
Implementations
Mechanical analog computers
While various mechanisms have been developed throughout history, some stand out for their theoretical interests, or because they are produced in significant quantities.
Most practical mechanical analog computers of any significant complexity use rotary shafts to carry variables from one mechanism to another. Cables and pulleys are used in the Fourier synthesizer, a tidal prediction engine, which sums individual harmonic components. Another category, which is virtually unknown, uses a rotating shaft for input and output only, with shelves and precision nails. Shelves are connected to relationships that perform calculations. At least one US Navy sonar control computer in the 1950s, made by Librascope, was of this type, like the main computer in Mk. 56 Pistol Fire Control System.
Online, there is a very clear pictorial reference (OP 1140) that describes the mechanism of computer fire control. To add and subtract, differential mitre-gear precision is commonly used in some computers; Ford Instrument Mark I Fire Control Computer contains about 160 units.
Integration with respect to other variables is done by rotating disk driven by one variable. The output comes from a pickoff device (such as a wheel) positioned on a radius on the disk proportional to the second variable. (A carrier with a pair of steel balls supported by a small roll works really well.A roller, its axis parallel to the surface of the dish, gives the output.) Laying it against a pair of spheres by a spring.)
The random function of one variable is provided by cams, with settings to change the follower's movement to the rotation of the shaft.
The function of two variables is provided by three-dimensional cams. In one nice design, one variable plays the cam. A hemisphere follower moves its carrier on the pivot axis parallel to the cam's cam axis. Rotating motion is output. The second variable moves the follower along the cam axis. One practical application is ballistics in cannons.
Conversion of coordinates from polar to rectangle is done by a mechanical resolver (called a "component breaker" in a US Navy retaining control computer). Two discs on a common axis position the sliding block with a pin (fat shaft) on top of it. One disc is a facial cam, and a follower in the block in the facial cam groove set the radius. The other disk, closer to the pin, contains the straight slot on which the block moves. The input angle plays the last disc (facial cam disc, for unchanged radius, rotated with another (angle) disk, differential and some gears make this correction).
Referring to the frame mechanism, the pin location corresponds to the end of the vector represented by the input angle and magnitude. Mounted on that pin is a square block.
The output of square coordinates (both sinus and cosine, usually) comes from two perforated plates, each slot fitting in the block just mentioned. The plates move in a straight line, the movement of one plate at right angles to the other. The slot is at right angle to movement. Each plate, by itself, is like a Scotch yoke, known to the steam engine fan.
During World War II, similar mechanisms converted the square into polar coordinates, but were not very successful and eliminated in significant redesign (USN, Mk 1 to Mk 1A).
Multiplication is done by mechanism based on the same right triangle geometry. Using trigonometric terms for right triangles, especially opposite, adjacent, and oblique, adjacent sides are fixed by construction. One variable changes the magnitude of the opposite side. In many cases, these variables change the sign; the oblique side can coincide with the adjacent side (zero input), or move outside the adjacent side, representing the sign change.
Typically, a pinion-operated rack moves parallel to the opposite (trig.-defined) side positioning the slide with a slot that coincides with the hypotenuse. A pivot on the shelf lets the slide angle change freely. At the other end of the slide (angle, in trig, term), a block on a fixed pin to the frame defines the vertex between the oblique side and the adjacent side.
At any distance along the adjacent side, a perpendicular line cuts a point at a certain point. The distance between that point and the adjacent side are some fractions that are the product of the 1 distance from the vertex, and 2 the magnitude of the opposite side.
The second input variable in this type of multiplier puts the plates shift perpendicular to the adjacent side. The slot contains a block, and the block position in its slot is determined by another block right next to it. The latter glide along the side of the slant, so the two blocks are positioned at a distance from the (trig.) Side adjacent to an amount comparable to the product.
To provide the product as an output, the third element, another slotted plate, also moves parallel to (trig.) On the opposite side of the theoretical triangle. As always, the slot is perpendicular to the direction of movement. A block in its slot, spinning into the oblique block of that position.
A special type of integrator, used at the point where only moderate accuracy is needed, is based on a steel ball, not a disc. It has two inputs, one to rotate the ball, and the other to determine the axis angle of spinning the ball. The axis is always in the field that contains the axis of two moving-motion rollers, much like the mouse computer ball mechanism (in this mechanism, the pickup roller is approximately the same diameter as the sphere). The pickoff axis roller is in the right corner.
A pair of "above" rolls and "under" a pickoff plane is mounted on the rotating handle directed together. The movement is driven by angular input, and forms the spin rotating shaft. Another input rotates the "bottom" roller to make the ball rotate.
Basically, the whole mechanism, called a component integrator, is a variable speed drive with one motion input and two outputs, as well as an angular input. The angular input varies the ratio (and direction) of the coupling between the "motion" input and output corresponding to the sine and cosine of the input angle.
Although they do not complete any calculations, the electromechanical position of the servos is critical in "rotating-shaft" mechanical analog computers to provide operating torque for input of subsequent computing mechanisms, as well as driving output data transmission devices such as large torques. -transmitter sync in naval computer.
Other non-computational mechanisms include internal odometer-style counters with interpolated drum calls to indicate internal variables, and mechanical multi-turn limits stop.
Considering that accurately controlled rotational speeds in the analog-fire control computer are the basic elements of accuracy, there are motors with average speeds controlled by balance wheels, hair springs, differential jewel bearings, twin-lobe cam, and spring-contacts loaded (the frequency of the ship's AC power is not necessarily accurate, or reasonably reliable, when the computer is designed).
Electronic analog computer
An electronic analog computer typically has a front panel with multiple jacks (single contact socket) that allows patch cords (flexible cables with plugs at both ends) to create interconnects that define problem settings. In addition, there is high-precision potentiometer-resolution (variable resistor) to regulate (and, when required, various) scale factors. In addition, it is possible to be a zero-center analog pointer-type meter for simple-accuracy voltage measurement. Stable and accurate voltage sources provide a known quantity.
Typical electronic analog computers contain from a few to a hundred or more operational amplifiers ("op amps"), named because they perform mathematical operations. The op amp is a type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precision feedback components which, in operation, all but cancel the current coming from the input components. The majority of op amps in the representative settings add up amplifiers, which add and subtract analog voltages, delivering results to their output jacks. In addition, an op amp with capacitor feedback is usually included in the setting; they integrate their number of inputs with respect to time.
Integrating with regard to other variables is an almost exclusive province of mechanical analog integrators; almost never done in electronic analog computers. However, given that the problem solution does not change over 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 must be made carefully to reduce unfavorable effects. For example, in the construction of an AC power grid analysis, one of the motives for using higher frequencies for calculators (not actual power frequencies) is that higher-quality inductors can be made more easily. Many general purpose analog computers avoid full use of inductors, re-casting problems in a form that can be solved only by using resistive and capacitive elements, because high-quality capacitors are relatively easy to make.
The use of electrical properties in analog computers means that calculations are usually performed in real time (or faster), at a speed determined largely by the frequency response of operational amplifiers and other computing elements. In the history of analog computer electronics, there are several types of special high speed.
Nonlinear functions and calculations can be constructed to finite precision (three or four digits) by designing function generators - special circuits of various combinations of resistors and diodes to provide nonlinearity. Usually, when the input voltage increases, the more diodes it performs.
When compensated for temperature, the decrease in forward voltage from the transistor base-emitter junction can provide logarithmic or exponential functions that can be used effectively. The Amp Op scales the output voltage so that it can be used with the rest of the computer.
Any physical process that models some computing can be interpreted as an analog computer. Some examples, created for the purpose of illustrating analog computing concepts, include using a set of spaghetti as a sorting model number; boards, sets of nails, and rubber bands as models to find the convex hull of a series of dots; and the string is bound together as a model to find the shortest path in a network. This is all described in Dewdney (1984).
Components
Analog computers often have complex frameworks, but they have, in essence, a set of key components that perform calculations, which operators manipulate through the computer framework.
The main hydraulic components may include pipes, valves, and containers.
The main mechanical components may include rotating axles for carrying data inside the computer, differential gear distributors, disk/ball/roll integrators, cams (2-D and 3-D), mechanical and multiplier regulators, and servos torque.
Major electrical/electronic components may include:
- Precision resistors and capacitors
- operational amplifier
- Multiplier
- potentiometer
- a fixed-function generator
The core mathematical operations used in analogue electrical computers are:
- additions
- integration with respect to time
- inversion
- multiplication
- exponentiation
- logarithms
- shares
In some analog computer designs, multiplication is preferred over division. The division is done by multipliers in the feedback path of the Operational Amplifier.
Time differentiation is not often used, and in practice is avoided by redefining the problem whenever possible. It fits within the frequency domain to a high-pass filter, which means that high frequency sound is amplified; differentiation is also at risk of instability.
Limitations
In general, analog computers are limited by non-ideal effects. The analog signal consists of four basic components: DC and AC, frequency, and phase. The real limits of coverage on these characteristics limit the analog computer. Some of these limitations include operational offset amplifiers, unlimited gain, and frequency response, noise flooring, non-linearity, temperature coefficients, and parasitic effects in semiconductor devices. For commercially available electronic components, the range of input and output signal aspects is always a feasibility number.
Decline
In the 1950s to the 1970s, digital computers based on the first vacuum tubes, transistors, integrated circuits and then micro processors became more economical and precise. This causes most digital computers to replace analog computers. Even so, some research in analog computing is still done. Some universities are still using analog computers to teach control system theory. The American company Comdyna manufactures small analog computers. At Indiana University Bloomington, Jonathan Mills has developed Extended Analog Computer based on the sampling voltage in foam sheets. At Harvard Robotics Laboratory, analogue calculation is a research topic. Lyric Semiconductor error correction circuit using analog probabilistic signal. The slide rules are still popular among aircraft personnel.
Awakening in VLSI technology
With the development of enormous integration technology (VLSI), the Yannis Tsividis group at Columbia University has reviewed the analog/hybrid computer design in a standard CMOS process. Two VLSI chips have been developed, the 80th order (250 nm) analogue computer by Glenn Cowan in 2005 and the 4-order (65 nm) hybrid computer developed by Ning Guo in 2015, both targeting energy-efficient ODE/PDE applications. Glenn's chip contains 16 macros, where there are 25 blocks of analog computing, ie integrators, multipliers, fanouts, multiple nonlinear blocks. Ning Chip contains one macro block, where there are 26 computing blocks including integrator, multiplier, fanout, ADC, SRAM, and DAC. The arbitrary nonlinear function generator is made possible by the ADC SRAM DAC chain, where the SRAM block stores nonlinear function data. Experiments from related publications reveal that the VLSI analog/hybrid computer demonstrates about 1-2 orders of benefits in solution time and energy while achieving accuracy in 5%, indicating the promise of using analog/hybrid computing techniques in the area. computing energy-saving estimates. In 2016, the research team developed a compiler to solve differential equations using analog circuits.
A practical example
This is an example of an analog computer that has been built or practically used:
Analog (audio) synthesizers can also be viewed as analog computer forms, and their technology was originally partly based on electronic analog computer technology. The ARP 2600's Ring Modulator is actually a moderate-accuracy analog multiplier.
The Simulation Board (or Simulation Board) is an analog computer user association in the US. Now known as the Society for Modeling and International Simulation. The Simulation Board Bulletin from 1952 to 1963 was available online and showed concerns and technology at the time, and the general use of analog computers for missiles.
See also
- Analog model
- The Chaos Theory
- Differential equations
- Dynamic system
- The programmable analog circuit field
- General purpose analog computer
- Lotfernrohr 7 series WW II German bomber
- Signal (electrical engineering)
- Voskhod Spacecraft "Globus" IMP navigation instrument
- XY-writer
Note
References
- A.K. Dewdney. "On Spaghetti Computers and Other Analog Gadgets for Troubleshooting", Scientific American , 250 (6): 19-26, June 1984. Reprinted on The Armchair Universe by AK Dewdney, published by WH Freeman & amp; Company (1988), ISBNÃ, 0-7167-1939-8.
- Computer Museum Universiteit van Amsterdam. (2007). Analog Computers .
- Jackson, Albert S., "Analog Computation". London & amp; New York: McGraw-Hill, 1960. OCLCÃ, 230146450
External links
- Biruni's 8-wheel lunisolar calendar in Archeology: High technology from Ancient Greece, François Charette, Nature 444, 551-552 (November 30, 2006), doi: 10.1038/444551a
- First computer
- Large collection of electronic analog computers with multiple images, documentation and examples of implementation (some in German)
- Large collection of old analog and digital computers at Old Computer Museum
- Great disappearing action: electronic analogue computer Chris Bissell, Open University, Milton Keynes, UK Accessed February 2007
- The German computer museum with a running analog computer
- Basics of analog computers
- The analog computer beats the Turing model
- Analog Jonathan W. Mills Notes
- Harvard Robotics Laboratory Analog Computation
- The Enns Power Network Computer - an analog computer for power system analysis (ads from 1955)
- Librascope Development Company - Type LC-1 WWII Navy PV-1 "Balance Computor"
Source of the article : Wikipedia
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