Analog Computer - Electronic Analog Computers

Electronic Analog Computers

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.