Back to homepage
Analog computer 1
Introduction
Analog computer is a type of computer that works with continuously
changing variables, as opposed to digital computer that uses discrete
values. Digital computers are almost always electronic or
electromechanical devices, while analog types can use any continous
variable: voltage, water flow,
air pressure, length (slide rule) and other.
Finished analog computer.
While first modern computers were analog electromechanical differential
analyzers in the 1930s, soon thereafter they were faced with
competition from electronic digital computers. By 1960s, pace of
miniaturization of digital components meant that digital computers
became less expensive than analog ones, while being able to produce
exact answers, a must for many human endeavors. Analog computers
continued in use for simulation of complex physical processes, but even
here they were eventually superseded by simulations run on digital
computers.
Having said that, they were (and still are) excellent tools for
simulation of real world. One gets much better understanding of certain
phenomena by being able to directly change the variables and see the
outcome immediately.
Article
Recently I stumbled upon an article
about
very
simple
analog
computer in a 1961 scanned Popular
Electronics magazine. This pushed me to make a copy along similar
lines. Only components needed are three potentiometers, battery/ or
AC/DC adapter/ or step-down transformer, and voltmeter/ or
galvanometer/ or headphones. Digital
voltmeter will do just fine, and most people have that. Analog meter is
fine, but it is rarely seen nowadays.
My pots one and
three (R1, R3) have value
of 250
Ohms, and second one (R2) 25 kiloOhms. Potentiometer
values are not critical, BUT second potentiometer R2 must be much
larger in value than the first one, to reduce voltage divider R1
loading. With value 100x greater, loading error is approximately 1%.
With R2 only 10x greater than R1, loading error is around 10%.
Supply voltage is not
critical, it can be anything from 1 to 10 volts, DC or AC.
If you use headphones instead of a voltmeter to detect nulls, you must
use some AC voltage source instead of DC (for example 120 Vac/6 Vac
transformer). In that case, headphone buzzing will disappear once your
solution pot R3 is set to proper solution. If you use DC with
headphones you won't hear anything anywhere on the scale - computer
won't work.
Schematic
I made a schematic based on the original article. R1 is pot used for
setting the first variable, R2 is used for second variable, and R3 is
the "result" potentiometer. If R1 pot is set to 0.5 (50%) of its
maximum value, this means that one half of the supply voltage shows
between R1 pot wiper and ground. If R2 is now set to 0.2 (20%) of its
maximum value, its
output (wiper-ground voltage) will show only 0.5*0.2=0.1 (10%) of
supply voltage. We have
effectively created a voltage multiplier.
When wiper of R3 is set to the same setting (10% maximum resistance
from ground to wiper), voltages at wipers of pots R2 and R3 will be the
same, and voltmeter will read zero. Voltmeter will read a nonzero value
(error voltage) for any other setting of R3. In this manner, R3 can be
used, when calibrated, to show multiplied (already scaled) voltage
value at wiper of R2.
Build
A quarter inch thick wooden tile was drilled
for three potentiometer shafts. After inserting the pots and securing
them, knobs were put in place and plastic tie-wraps were put around the
knobs to serve as scale pointers. I had some issues with knobs that I
have selected, so I decided to
replace them with wooden blocks (from 2x4s) into which I have put some
small nails for pointers. They were drilled with holes somewhat smaller
than pot shafts, so they fit snugly when forced onto them.
Board backside.
Round scales were traced out on cereal box cardboard and cut out. They
were glued to the wooden faceplate.
Next, without making connections between the pots themselves, you need
to calibrate the scales. To do this, first mark minimum and maximum pot
positions (for regular pots around 300 degrees are swept). Measure
total maximum pot resistance (let's say 250 Ohms). Connect your ohmeter
between grounded pot terminal (pick one side tab) and pot wiper
(central tab), and slowly increase resistance until you reach 1/10th of
maximum pot resistance (in my case 25 Ohms). Mark this point with
longer line and label 10. Next move to 2/10ths of max. resistance
position and mark this point with next long line and label 20. Proceed
until all tenths are marked. If you wish, you can also mark 5/100,
15/100, 25/100 spots, you will obtain better precision. Same process
was repeated for other two pots, except that labels for third pot had
increments of 1000 and maximum value of 10000. After finishing
calibration, connections
were made according to article schematics. Alternative method of
calibration for third pot (that in hindsight appears to be somewhat
more
precise) is to set two multipliers R1 and R2, calculate their product
on calculator, and mark that result on third scale. It does feel like a
bit of cheating though :)
Fine... But what does
it do?
Multiplication, division, squaring of numbers, and finds the square
root of given number. Maximum result is 10000, and variables 1 and 2
have a maximum value of 100. Suitable scaling can be used, so if you
add
three zeros to variables 1, 2 and result, maximum result is now 10 000
000 000. If variables 1 and 2 are numbers very different in size,
precision
will suffer. Average precision in optimal middle-to-high R3 scale range
is 2-3%,
but falls off rapidly towards the low end of the scale.
Multiplication
Just set dials 1 and 2 to desired values for multiplication, for
example 70 and 80. Now turn dial 3 (result) until you can read exactly
0 volts on your voltmeter. Read multiplied result from scale three.
Multiplication/Division.
Division
Set number to be divided on scale 3. Set number to divide with on scale
2. Turn dial of scale 1 until voltmeter reads zero. Then read result
from scale 1.
Squaring
Set number to be squared on dial 1. Set that same number on scale 2.
Turn dial 3 until voltmeter reads zero. Read result from scale 3.
Square root
Set number for which the square root is to be found on scale three. Now
turn dials 1 and 2 until both are set on the same numbers, and
voltmeter reads zero (this takes some practice). Number on scale 1 (or
2) is the square root of the number shown on scale 3.
Useful links
An
introduction
to
analog
computer
-
in
Popular
Electronics
magazine, 1961
Analog computer
- Wikipedia page
Back to homepage
