# Analog computer

An **analog/analogue computer** is a form of computer that uses electronic 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.

For example, the similarity between linear mechanical components (springs, dashpots) and electrical components (capacitors, inductors, resistors) is striking in terms of mathematics.
They can be modeled using equations that are of the same form. 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 spring and mass, attaching them
to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking measurements. The electrical equivalent can be constructed with a
few operational amplifiers (Op amps) and some passive linear components; all measurements can be taken with an oscilloscope. In the circuit, the mass of the spring can be changed by adjusting potentiometers. 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 drawbacks of the mechanical-electrical analogy is that electronics are limited in the range over which the variables may, well, vary. This is called dynamic range. They are also limited by noise levels.

There is a lack of understanding about electrical systems that gives the terms *analog* and *digital* confusing and somewhat dubious meanings. Analog systems are understood only as continuous, time variant electrical systems. From the above discussion, it should be obvious that this is not correct. It is most likely an outgrowth of language from a time when the electrical-mechanical analogy was the most common type of analog computer. The popular understanding of *digital* is not very specific but definitely linked to consumer electronics and personal computers. In fact, digital has a technical definition. In the context of circuits, it refers to the advantage of binary circuits in terms of signal-to-noise ratio.

There is an intermediate group, hybrid computers, in which a digital computer is used to control and organize inputs and outputs to and from attached analog devices; for instance analog devices might be used to help generate initial values for iterations, or the analog computer might be used to solve a non-analytic differential equation problem.

Some examples:

- the abacus is a hand-operated digital computer
- the slide rule is a hand-operated analog computer
- early gun directors used mechanical analog computers to direct gunnery fire

## Contents

## 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 a current resistance *x*+*y* milliamperes. Other calculations are performed similarly, using operational amplifiers and other circuits for other tasks.

The use of electrical properties in analog computers means that certain calculations on a computer are performed in real time, without calculation delays as on 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 sum of a voltage waveform, usually by means of a capacitor, which accumulates charge over time.

Nonlinear functions and calculations can be constructed to a given amount of accuracy by creating a diode function generator: a set of diodes and resistors of varying values. As voltage increases, the total resistance summed changes 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 were all described by A.K. Dewdney (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

## 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 impedances 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 calculations. 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).

These idealized computers can *in theory* solve problems that are inextricable on digital computers; however, as mentioned, in reality analog computers are far from attaining this ideal, because of noise minimization 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

## External links

- Lecture 20: Analog vs Digital
*(in a series of lectures on "History of computing and information technology")* - Doug Cowards's Analog Computer Museum
- Jonathan W. Mills's Analog Notebook
- Indiana University Extended Analog Computer
- Harvard Robotics Laboratory Analog Computation

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