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8. Security - check for the yellow padlock on the Analogue Computer site before you buy, and the s after http:/ /i.e. https:// = a secure site

9. Contact - got a question about Analogue Computer, or want to leave a comment then check out the sites contact page. Reputable companies have them and respond.

10. Payment - ready to pay for your Analogue Computer, then use your credit card or PayPal! Be aware of companies that don't accept them, there may be genuine reasons but given the huge amount of choice you have when buying online there is no reason at all not to buy via credit card or PayPal.

. 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 electricityUniversiteit van Amsterdam Computer Museum, (2007), machine or hydraulic phenomena to model the problem being solved. More generally an analog computer uses one kind of physical quantity to represent the behavior of another physical system, or mathematical function. Modeling a real physical system in a computer is called simulation.

Timeline of analog computers





















Electronic analog computers The similarity between linear mechanical components, such as spring (device)s 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 (physics).

These electric circuits can also easily perform other simulations. For example, voltage can simulate water pressure and amperes can simulate water flow in terms of cubic metres 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 quantization 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 hybrid computer, in which a digital computer is combined with an analog computer. Hybrid computers are used to obtain a very accurate but imprecise 'seed' value, using an analog computer front-end, which is then fed into a digital computer iterative process to achieve the final desired degree of precision. With a three or four digit, highly accurate numerical seed, the total digital computation time necessary to reach the desired precision is dramatically reduced, since many fewer iterations are required. 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 computing applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation)..

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 circuit laws) 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, 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.

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, electrical resistance, in combination with diodes (e.g., Zener diode 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 Electrical 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 #Reference below).

Components s 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:



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



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-linearity, temperature coefficient, and Microelectronics 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 figures of merit.

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 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 Process (general) to computations. Thus, from these points of view, the wind tunnel data gathering is either an experiment or a computation.

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 computer; 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

Other types of computers:

People associated with analog computer development:

Notes References



External links

. 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 electricityUniversiteit van Amsterdam Computer Museum, (2007), machine or hydraulic phenomena to model the problem being solved. More generally an analog computer uses one kind of physical quantity to represent the behavior of another physical system, or mathematical function. Modeling a real physical system in a computer is called simulation.

Timeline of analog computers





















Electronic analog computers The similarity between linear mechanical components, such as spring (device)s 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 (physics).

These electric circuits can also easily perform other simulations. For example, voltage can simulate water pressure and amperes can simulate water flow in terms of cubic metres 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 quantization 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 hybrid computer, in which a digital computer is combined with an analog computer. Hybrid computers are used to obtain a very accurate but imprecise 'seed' value, using an analog computer front-end, which is then fed into a digital computer iterative process to achieve the final desired degree of precision. With a three or four digit, highly accurate numerical seed, the total digital computation time necessary to reach the desired precision is dramatically reduced, since many fewer iterations are required. 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 computing applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation)..

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 circuit laws) 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, 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.

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, electrical resistance, in combination with diodes (e.g., Zener diode 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 Electrical 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 #Reference below).

Components s 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:



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



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-linearity, temperature coefficient, and Microelectronics 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 figures of merit.

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 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 Process (general) to computations. Thus, from these points of view, the wind tunnel data gathering is either an experiment or a computation.

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 computer; 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

Other types of computers:

People associated with analog computer development:

Notes References



External links



analogue computer from FOLDOC
analogue computer < computer, hardware > A machine or electronic circuit designed to work on numerical data represented by some physical quantity (e.g. rotation or displacement) or ...

analog from FOLDOC
analog < spelling > American spelling of analogue. (1995-11-14) Try this search on ... Analog Hardware Design Language » analogue » analogue computer

analogue computer
The Free Online Dictionary of Computing (http://foldoc.doc.ic.ac.uk/) is edited by Denis Howe < dbh@doc.ic.ac.uk >. Previous: analogue Next: Analogy Model

Analog computer - Wikipedia, the free encyclopedia
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 ...

Dictionary of Computers - analogue computer
Skip to page content | Tiscali Quicklinks. Please visit our Accessibility Page for a list of the Access Keys you can use to find your way around the site, skip directly to the main ...

Analogue Electronic Computers.
The Douglas Self Site, Analogue Electronic Computers ... Analogue computers are now wholly obsolete, but in their day they were the means of choice for solving many problems in ...

Analog Computer Basics
The modern analog computer is based on an electronic circuit known as an operational amplifier. Early operational amplifiers ("op amps" for short) used vacuum tubes, since that was ...

A great disappearing act: the electronic analogue computer
Presented at IEEE Conference on the History of Electronics, Bletchley Park, UK, 28-30 June 2004. Page 1 A great disappearing act: the electronic analogue computer Chris Bissell The ...

The Moniac A Hydromechanical Analog Computer of the 1950s
The Moniac A Hydromechanical Analog Computer of the 1950s CHRIS BISSELL HISTORICAL PERSPECTIVES « FEBRUARY 2007 « IEEE CONTROL SYSTEMS MAGAZINE 69 1066-033X/07/$25.00©2007IEEE ...

Category:Analog computer - Wikimedia Commons
Media in category "Analog computer" The following 9 files are in this category, out of 9 total.

 

Analogue Computer



 
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