Analog computer

An analog(ue) computer are shit as a form of computer that uses electrical or mechanical phenomena to model the problem being solved by using one kind of physical quantity to represent another. The central concept among all analog computers can be better understood by examining the definition of an analogy. The similarities of an analogy define the salient characteristics of the comparison. But the differences in an analogy are important too. Modeling a real physical system in a computer is called simulation.

Polish Analog computer ELWAT.

However, the difference between these systems is what makes analog computing useful. Consider a simple mass-spring system. To construct the physical system would require buying the springs and masses, 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. 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 dynamic range. They are also limited by noise levels.

There is a lack of understanding about electrical systems that sometimes leades 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 binary electrical pulse 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 is limited by the (necessarily finite) number of symbols which may be used in the calculation itself.

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 applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation).

Some examples:

• the abacus is a hand-operated digital computer (but not binary; it is biquinary)
• the slide rule is a hand-operated analog computer
• early gun directors used mechanical analog computers to direct gunnery fire

How analog computers work

Computations are often performed, in analog computers, 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 an 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, 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, reactance, resistance, and variable current (e.g., Zener) 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 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).

Analog computer components

Analog computers often have a complicated framework, but they have, at their core, a set of key electrical components which perform the calculations, which the operator manipulates through the computer's framework:

• 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 and parasitic effects 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 processes 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 has been working on research using Extended Analog Computers. At the Harvard Robotics Laboratory, analog computation is a research topic.

Practical analog computers

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

• nomogram
• Moniac computer
• astrolabe
• operational amplifier
• planimeter
• mechanical integrator
• Torquetum
• Tide predictors
• Water integrator
• Target Data Computer
• Norden bombsight
• Hydraulic model of UK economy
• the Antikythera mechanism
• and the slide rule

Analog synthesizers can also be viewed as a form of analog computer, and their technology was originally based on electronic analog computer technology.

Idealized analog computers

Computer theorists often refer to idealized analog computers as real computers (so called 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. Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real number problems.

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 0716719398.

See also

• signal (information theory)
• signal (computing)
• set theory
• computability theory
• differential equation
• dynamical system
• chaos theory
• slide rule

External links

• 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