# Analog Computers

Analog computers and their applications

### What is an analog computer?

Simply, an analog computer is a computing device that has two distinguishing characteristics:

• 1.   Performs operations in a truly parallel manner. Meaning it can perform many calculations all at the same time.

An analog computer works in parallel. This means it can carry out multiple tasks simultaneously. A digital computer, even though it may work considerably faster, can only perform one calculation at any one instant. The only way around this in a digital computer is parallel computing, where a single machine has multiple processors. Even then, programs must often be rewritten to take advantage of this.

• 2.   And operates using continuous variables. Meaning it uses numbers that that change not in steps, but change in a smooth continuous manner.

By contrast, a digital computer can only perform sequential (one at a time) operations, and operates on discrete (noncontinuous) numbers.

### What are Electronic Analog Computers

Electronic analog computers may seem to be "simple" or "like a toy computer", in fact they are powerful tools that were used during the 1950s and 1960s to design and test systems like ICBMs, supersonic aircraft and spacecraft. But the analog computer can be used to model any physical system that can be described by mathematical formulas, even more mundane ones from modeling the effects of pollution on the fish population in a river to fine tuning the suspension on a new car design. Analog computers will not only test a fixed design but also allows variables to be quickly changed to test "what if" conditions. By scaling time as an independent variable, physical processes that happen quickly can be stretched out, and processes that happen over a long period can be shortened to make the process easier to study. And it is very easy to study variables at any point in the program while it is running to find faults in the program design.
Although the electronic analog machine is correctly termed a computer, it does not perform its computations by numerical calculations as does the calculator or the digital computer. The analog computer performs mathematical operations on CONTINUOUS variables instead of counting with digits. Positive numbers are represented by positive voltages and negative numbers are represented by negative voltages, all scaled to the computer’s working range, usually -100 volts to +100 volts (vacuum tube) or -10 volts to +10 volts (transistorized), Thus the analog computer does not subtract 20 inches from 45 inches to obtain 25 inches but, rather, it subtracts 4 volts from 9 volts to obtain 5 volts. This 5 volts the operator reads as 25 inches in accordance with his arbitrarily specified "scale factor" of 1 volt equals (or is ANALOGOUS to) 5 inches.
The electronic analog computer is basically a set of building blocks, each able to perform specific mathematical operations on direct current voltages and capable of being easily interconnected one to another. Some of the basic operations include addition, subtraction, multiplication, division, inversion, and integration. By interconnecting these building blocks, mathematical equations are modeled. BUT an analog computer is a true PARALLEL computer that can solve one or one thousand equations at the same time. In fact, similar analog computers can be easily connected together to increase their computing power. When you think about the result of many equations being solved simultaneously and becoming the input to other equations, and sometimes these solutions are then fed back or looped back into the original equations with all of the variables changing CONTINUOUSLY with time, then you can get a brief glance into the incredible power of these computers. Output is usually a voltmeter, oscilloscope, or plotter.
Many universities today like Massachusetts Institute of Technology, University of Illinois, University of Notre Dame, and Purdue University offer classes or do research using analog computers, because they realize that the last chapter of the history of analog computers has not being written. It’s an ANALOG universe and analog computers are a natural way to study and understand it.

An analog computer (spelled analogue in British English) is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities incrementally, as their numerical values change.

Mechanical analog computers were very important in gun fire control in World War II and the Korean War; they were made in significant numbers. In particular, development of transistors made electronic analog computers practical, and before digital computers had developed sufficiently, they were commonly used in science and industry.

Analog computers can have a very wide range of complexity. Slide rules and nomographs are the simplest, while naval gun fire control computers and large hybrid digital/analogue computers were among the most complicated. Digital computers have a certain minimum (and relatively great) degree of complexity that is far greater than that of the simpler analog computers. This complexity is required to execute their stored programs, and in many instances for creating output that is directly suited to human use.

Setting up an analog computer required scale factors to be chosen, along with initial conditions – that is, starting values. Another essential was creating the required network of interconnections between computing elements. Sometimes it was necessary to re-think the structure of the problem so that the computer would function satisfactorily. No variables could be allowed to exceed the computer's limits, and differentiation was to be avoided, typically by rearranging the "network" of interconnects, using integrators in a different sense.

Running an electronic analog computer, assuming a satisfactory setup, started with the computer held with some variables fixed at their initial values. Moving a switch released the holds and permitted the problem to run. In some instances, the computer could, after a certain running time interval, repeatedly return to the initial-conditions state to reset the problem, and run it again.

The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), 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 making or modifying the springs and masses. This would be followed by attaching them to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking measurements. In more complicated cases, such as suspensions for racing cars, experimental construction, modification, and testing is not so simple nor inexpensive.

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) 'stiffness of the spring', for instance, 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, generally safer, and typically much easier to modify.

As well, an electronic circuit can typically operate at higher frequencies than the system being simulated. This allows the simulation to run faster than real time (which could, in some instances, be hours, weeks, or longer). Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations.

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. Floating-point digital calculations have comparatively-huge dynamic range (Good modern handheld scientific/engineering calculators have exponents of 500.)

These electric circuits can also easily perform a wide variety of simulations. For example, voltage can simulate water pressure and electric current can simulate rate of flow in terms of cubic metres per second. (In fact, given the proper scale factors, all that is required would be a stable resistor, in that case.) Given flow rate and accumulated volume of liquid, a simple integrator provides the latter; both variables are voltages. In practice, current was rarely used in electronic analog computers, because voltage is much easier to work with.

Analog computers are especially well-suited to representing situations described by differential equations. Occasionally, they were used when a differential equation proved very difficult to solve by traditional means.

An electronic digital system uses two voltage levels to represent binary numbers. In many cases, the binary numbers are simply codes that correspond, for instance, to brightness of primary colors, or letters of the alphabet (or other symbols). The manipulation of these binary numbers is how digital computers work. The electronic analog computer, however, manipulates electrical voltages that are proportional to the magnitudes of quantities in the problem being solved.

Accuracy of an analog computer is limited by its computing elements as well as quality of the internal power and electrical interconnections. The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. Precision of a digital computer is limited by the word size; arbitrary-precision arithmetic, while relatively slow, provides any practical degree of precision that might be needed.

Related files

Handbook of Analog Computations

Introduction to Electronic Analogue Computing