An Introduction to Analog Computers
December 1961 Popular Electronics

December 1961 Popular Electronics Table of Contents Wax nostalgic about and learn from the history of early electronics. See articles from Popular Electronics, published October 1954 - April 1985. All copyrights are hereby acknowledged.

Analog computers are said to be the oldest form of computer, but I maintain digital computers predated analog computers by millennia. That's right, our ancient forebears certainly counted using their fingers and toes (aka digits) for addition and subtraction long before anyone assembled a mechanism for performing mathematical operations. Astronomers were some of the most prolific inventors of analog computers for determining the positions of planets, moons, comets, and even longitude and latitude upon the face of the Earth. Charles Babbage made one of the most famous mechanical computers - the Babbage Difference Engine. Probably the most widely used analog computer is one form or another of a slide rule. I say one form or another because many of the cardboard type calculators are forms of slide rules. One type of analog computer we use in the RF business everyday is a frequency mixer, which takes two numbers (frequencies) and produces the sum and difference. This 1961 issue of Popular Electronics magazine reports on a couple low cost analog computers available at the time, including the three-dial Edmonds Analog Computer that appeared in advertisement in many technical magazines of the day.

An Introduction to Analog Computers

Now you can take your first step into the fascinating world of electronic brains

By Julian M. Sienkiewicz, Managing Editor

For centuries man has been utilizing simple analog devices to solve mathematical problems by analogy. In other words, numbers are converted into something else which can be worked with more easily than the numbers themselves. One everyday example is the slide rule, which converts numbers into distances, then reconverts the summed distances into numbers, providing a solution. Anyone who has multiplied two numbers on a slide rule will testify to its operating ease, rapid solution, and remarkable accuracy.

This article will go one step beyond the slide rule and describe a direct-reading analog computer which will solve simple addition and multiplication problems, extract roots, and perform trigonometric operations. So simple is this computer that it could be called an "electronic slide rule."

Voltage Analog. An ordinary potentiometer will help us see how a number can be converted into a voltage analog. Figure 1 shows a simple circuit of a potentiometer, R1, connected in series with a battery, B1. Rotating the dial pointer on the shaft of R1 causes the potentiometer wiper to "pick off" a voltage proportional to the dial setting.

In Fig. 1, the dial is calibrated from zero to one and the voltage supplied by the battery is 1.0 volt. Thus, in this particular instance, the dial setting indicates the voltage at the wiper of the potentiometer. A voltmeter connected at the output terminals of this circuit will indicate the setting of the dial  -0.36 volt would mean that the dial is set at 0.36 unit. The voltage is an analog voltage, since it may represent a dial quantity of 0.36 acre, quart, or even light year.

Multiplying. In Fig. 1, a voltage analog for the number 0.36 was developed at the wiper of R1. It can also be said that the supply voltage across R1 was multiplied by 0.36. Thus, 1.0 volt times 0.36 will be 0.36 volt. If a voltage other than 1.0 volt were supplied by B1 in Fig. 1, we would be multiplying the supply voltage by the dial setting.

This apparent ability of potentiometers to multiply can best be seen in Fig. 2. Battery B1 supplies 1.0 volt across potentiometer R1. Dial A is set at 0.36 so that analog voltage A developed at the wiper of R1 (0.36 volt) is applied across potentiometer R2. Dial B is set at 0.50 so that the voltage at the wiper of R2 will be only 0.50 times the voltage across R2, or simply 0.36 x 0.50. The voltage developed at the wiper of R2 is appropriately called analog voltage A-B, and voltmeter M1 will indicate this voltage to be 0.18 - the product of 0.36 and 0.50.

Loading Error. Looking again at Fig. 2, you will note that the value of potentiometer R1 is 50 ohms, whereas potentiometer R2 is a 1000-ohm unit. The reason for this is quite simple, provided you down-gear your thinking from analog computers to simple d.c. networks. Figure 3(A) corresponds to Fig. 2 when the wiper of R1 is set at 0.50 or mid-position. Hence, R1a in Fig. 3(A) represents the "top half" of R1 in Fig. 2 (the portion between terminals 1 and 2). Likewise, R1b represents the "bottom half" of R1 (the portion between terminals 2 and 3). We know from the dial setting that analog voltage A should be 0.50 volt. However, let's see what analog voltage A actually is in Fig. 3(A).

First, since R1b and R2 are in parallel, their combined resistance is approximately 24.4 ohms. Using Ohm's law, we find that the voltage drop across R1b (in parallel with R2) is approximately 0.49 volt. This means that R2 in Fig. 2 will tend to lower the true value of analog voltage A and introduce a small error. In the case cited, the error is only 2% - not much for this simple computer circuit.

In Fig. 3(B) , the value of R2 was selected as 50 ohms solely to illustrate the loading effect of R2 on R1b. In this instance, the combined resistance of R1b and R2 is approximately 17 ohms. Again resorting to Ohm's law, we find analog voltage A developed across R1b and R2 to be approximately 0.40 volt. Compared to the desired analog voltage of 0.50, the loading effect of a 50-ohm potentiometer will introduce an error of 20% - an excessive amount for most purposes.

It should be evident, then, that when two potentiometers are connected as shown in Fig. 2, the second one (R2) should be many times larger than the first one (R1). However, do not be tempted into believing a potentiometer with a very large resistance - one megohm, say - will completely solve our loading problem. Even if the resistance value of the second potentiometer is very large, a voltmeter connected across its wiper and bottom terminal will also cause a loading effect and hence introduce error. This is due to the resistance of the voltmeter itself - usually only several thousand ohms.

Galvanometer Indicator. One method of removing the loading effect of the voltmeter (M1) used in Fig. 2 is to replace it with an indicator that requires no current to indicate the analog voltage developed by a potentiometer. Such a device is the galvanometer indicator shown schematically in Fig. 4.

Close inspection of the circuit in Fig. 4 reveals that current will flow though galvanometer M1 whenever the wipers of potentiometers R2 and R3 select voltages that are not equal. This condition causes the galvanometer pointer to deflect either to the left or right of its normal "center rest" or "zero deflection" position.

Since dial B is preset to "some number" input, as described earlier, it remains for dial C to be adjusted until the voltage at the wiper of R3 equals the voltage at the wiper of R2. When this occurs, the voltage drop across the galvanometer is zero, resulting in zero current through the galvanometer and no deflection of the meter's pointer. Dial C, which is calibrated to convert the voltage picked off by R3 to numbers, indicates the correct value of analog voltage A.B. Since the electrical components M1 and R3 draw no current from R2, there is no loading on the analog circuits and no errors are introduced into the electrical computations by the galvanometer.

An important fact to note in Fig. 4 is that potentiometer R3 has a value of 50 ohms. This is permissible, since (1) R3 does not load the computer circuits when the correct answer is set on dial C and (2 ) the lower value is desired so that when an incorrect answer is selected the deflection of M1 will be large due to the large currents flowing through the galvanometer movement. This large deflection due to an incorrect answer enables the computer operator to adjust dial C accurately for a galvanometer null or zero deflection. In operation, of course, the galvanometer deflects either to the right or left of its center position, depending upon whether the wiper of R3 is positive or negative with respect to the wiper of R2.

Complete Circuit. The simple analog computer circuit shown in Fig. 5 is identical to the one used in the analog computer kit made by the Edmund Scientific Co., Barrington, N. J. (see Fig. 6 ) and is the culmination of the circuits shown in Figs. 1 through 4.

Two interesting points should be noted: the first one is that the battery voltage of B1 is 3 volts. Previously in our discussion, we used a "1-volt" battery for B1. This variance in voltage suggests that the voltage of B1 is not critical, as is actually the case.

Examine Fig. 5 carefully and note that B1 is connected across two resistive legs: the summed resistances of R1 and R2, and the resistance of R3. Galvanometer M1 is used to detect a zero voltage difference between the resistive legs exactly like its counterpart in the Wheatstone bridge. Therefore, as long as the two resistive legs receive the same voltage, its value is unimportant.

The second point to be noted in Fig. 5 is that a switch (S1) has been added. This push-button switch is nothing more than an on/off switch for reducing battery drain. It is depressed only after dials A and B have been set to desired values and dial C is being adjusted so that the galvanometer indicates a null.

Sound Null. Another good way to determine when the analog computer is tuned to a null (correct answer), is to listen for it rather than look for it. In the Edmund computer, a null can be seen when the galvanometer is not deflected. In an analog computer kit made by General Electric (see cover photo),the galvanometer has been replaced with a headset; since the headset can only detect audio signals, the computer potentiometers are powered by an audio signal generator and not by dry cells. Except for these two changes, the General Electric analog computer kit is electrically identical to the Edmund kit.

Figure 7 is a simplified schematic drawing of the G.E. analog computer circuit. To operate, the computer potentiometers are preset to fixed input quantities and the "answer" potentiometer (connected to the C dial) is rotated until the audio sound is no longer heard in the headset.

Dials. The dials for both the Edmund and General Electric kits are accurately calibrated so that many complex problems can be performed. The similarity of the dials found in each kit can be seen in Fig. 8.

The Edmund dials include a linear scale plus logarithmic and trigonometric scales, whereas the General Electric dials have in addition "squared" and reciprocal scales. Instruction manuals provided with both kits give detailed instructions on how to use these dials to solve many typical problems closely related to electrical technology and science.

A Fraction of the Field. The "ground floor" introduction to analog computers which you have just read naturally covers but a very small fraction of the total analog computer field. Besides potentiometers, meters, and switches, manufacturers of analog computers also use synchros, two and three-dimensional cams, linkages, gears, and complex electronic circuits to perform the countless specialized functions the human mind may require of a machine.

If you find the subject of analog computers interesting and this ground floor introduction just whets your appetite, you might want to visit your public or school library. Each day, more and more books on this timely subject are being placed on library shelves. Look for them, and be kind to that gent who beat you there - he may be the author of this article!

Posted September 1, 2023