Simple Analogue Computer
This instrument is capable of
carrying out the arithmetical
operations of multiplication and
division with reasonable accuracy.
The evaluation of powers and roots
with log. scales may also be achieved.
LTHOUGH popularly associated with formidable
A arrays of electronic instruments capable of
- incredibly complex calculations, computers in one
form or another have been with us for a very long
time. We have only to recall the familiar abacus or
bead bar of our childhood to realise that our acquain-
tance with computers started at a very early age.
Modern computers are of two major types: the
digital, which depend on the way we use numbers,
and the analogue, in which numbers are represented
by physical quantities such as length and current.
A simple example of a digital computer is the abacus
while a good example of the analogue computer is
the slide rule,
Although elaborate computers are beyond the scope
of the average constructor, quite simple instruments
can be made using everyday components. The simple
analogue computer described in this article was con-
structed by the author for classroom demonstration
purposes. Although no originality is claimed for
the design it was felt that a description of the instru-
ment would be of interest to other constructors,
particularly those engaged in teaching.
BASIC CIRCUIT
The computer is based on the familiar Wheatstone
bridge network shown in Fig. 1. Such a network is
commonly employed in the determination of an
unknown resistance. When the bridge is balanced,
for example, when the current through the galvano-
meter is zero, the following well known relationship
holds,
RI x R4= R2 x R3
or transposing,
RI _ R3
R2°° R4
YW
. BYt
ala
Fig. 1. Basic Wheatstone bridge network on which the
computer is based
Generally, Rl and R2 form a calibrated resistance
wire system, while R3 is a resistor of known value.
R4 is the unknown resistor. When the system is
balanced, the ratio R1:R2 is determined, and hence
R4 can be calculated. By a reversal of this procedure,
the operations of multiplication and division can be
carried out.
If the resistors constituting the arms of the bridge
are made variable and are accurately calibrated, the
two arithmetical operations are easily performed.
To multiply two numbers, R4 is set to some power of
ten, the multiplicand set on R2 and the multiplier on
R3. The bridge is balanced with R1 and the answer
automatically read off on the R1 scale. To perform
the operation of division, R4 is again set to a power
of ten, while the numerator and denominator are set
on Ri and R2 respectively. The bridge is balanced
with R3 and the answer taken from this scale. For
both arithmetical operations it is of course necessary
to find the decimal point by inspection.
The scope of the bridge can be further extended by
providing logarithmic scales for R3 and R4. Powers
and roots may then be evaluated. This application
will be discussed at a later stage.
PRACTICAL CONSIDERATIONS
In common with all other analogue computers the
accuracy is limited by the precision of the components
employed in the circuit. The author found that
ordinary wire wound variable resistors of the type
normally employed in radio work were of sufficient
precision to enable quite a high degree of accuracy
to be achieved.
In the original design the bridge was energised by a
battery, the balance point being indicated by a sensitive
galvanometer. However, since it was highly likely
that the instrument would be subjected to somewhat
indelicate handling, the fragile galvanometer was
replaced by headphones and a simple but robust
transistor audio oscillator used to energise the bridge.
CONSTRUCTIONAL DETAILS
The computer is mounted on an aluminium panel,
the relevant drilling and mounting details being given
in Fig. 3. Four 34in diameter discs cut from stiff
white cardboard, and on which are described 24in
diameter circles, are used as dials.
The audio oscillator is mounted on a 6in x 4in
etched wiring board as shown in Figs. 4 and 5. An
alternative method using Veroboard may also be
used by those constructors who wish to avoid the
use of chemicals. For comprehensive examples of
this method the reader is referred to the April 1965
issue of PRACTICAL ELECTRONICS.
ETCHED WIRING BOARD
The copper laminate is polished with metal polish
and then washed in warm soapy water. After rinsing
and drying, the circuit pattern shown in Fig. 4 is drawn
out with cellulose paint of the car “touch up” type.
The paint is allowed to dry for approximately 30
minutes and the laminate immersed in a 30 per cent
w.v. solution of ferric chloride. This solution is
prepared either by dissolving 75gm of the anhydrous
salt or 92gm of the hydrated salt in 200ml of water
containing 3ml of concentrated hydrochloric acid.
The resulting solution is made up to 250ml. For
complete dissolution of the unwanted copper a reaction
time of roughly 30 minutes at 40 degrees C is required.
The etching is done by gentle agitation of the solution.
The prepared board is washed with water to remove
all traces of the iron salt and the cellulose paint removed
by swabbing with cotton wool soaked in acetone or
other suitable solvents.
Fig. 2. Circuit of the simple com~ kQ
puter. Additional resistors for
calibration (R5-RI0) are not
R4
shown here but are explained
later in Figs. 6, 7, and 10
AT
kn c
| .25uF
R3
47
vai vR2
se TR2 1k 1k
°
PHONES
4 9°
VR3 vR4
4k
Au
CIRCUIT DESCRIPTION
The circuit diagram of the computer is given in
Fig. 2. Four 1,000 ohm wire wound potentiometers
(VR1i-4) form the arms of the bridge. The transistor
oscillator is of the Hartley type. Oscillation is main-
tained by feedback in the correct sense through the
primary of the audio transformer Tl. Although the
output of the oscillator may be taken via C2 from the
emitter of TR1, an additional stage of amplification
may be found advantageous, particularly where noisy
background levels are encountered.
Holes are drilled at the points shown in Fig. 5. Wiring
of the board is straightforward and the customary heat
shunt precautions are observed when the transistors
and other closely clipped components are soldered in
position.
The audio frequency transformer is temporarily
connected to the appropriate points on the board and
a check made on the correct functioning of the oscil- -
lator. It may be found that the leads to the primary
of the transformer require reversal to ensure feed-
back in the correct sense.
feu
‘we Se
a ,
: =
i
| a
zs 4 ‘ L Oy
2
{
isd Salle!
os
n =
=
saat
FS
S77
w
SS
iS
Sa
a4) y
SS
<p
: sa ee i it ices r —T a; yy ree 1 ia eee ba te Ms | weg: mat
. we - == wre Ps Sep te a = ; “ << s es =a tree ae oes age ig 4
Before the completed audio oscillator is mounted VRI CALIBRATION
on the main potentiometer panel, the potentiometers ;
-are calibrated by the following procedure. Two close tolerance resistors, R9 and R10, each of
’ 1,000 ohms, are wired with VR1 and the decade
_ CALIBRATION OF BRIDGE resistance box as shown in Fig. 6. The audio oscillator
7 A careful calibration of the four potentiometers is and headphones are connected to the appropriate
aS essential if accurate results are to be obtained. Al- points. With the decade box set at 100 ohms, VR1
- though calibration is simplified if a resistance box is adjusted until the null point is observed. The dial
___ calibrated in 10 ohm and 100 ohm steps is available, of VR1 is carefully marked with pencil at this point.
__ it is possible to use close tolerance fixed resistors as Repetition of the process with the decade box set at
_ calibration standards. The construction of such a 200, 300, 400 ohm etc., followed by balancing with VR1
Ea standard is shown later in Fig. 10. gives a series of points separated by 100 ohm intervals
____ Both calibration methods will be deseribed, the up to 1,000 ohms. If the decade box is calibrated in d
___ Tesistance box method being dealt with first. 10 ohm steps intermediate points may be filled in. i
TO
RESISTANCE
BOX
Se ee i!)
: OSCILLATOR
’ Fig. 8. VR3 calibration
PRIMARY TO
PRINTED BOARD
SECONDARY TO )
a PRINTED BOARD ‘
TO AUDIO |
3 ae OUTPUT OF al
= OSCILLATOR ti ‘
it 9) PHONES st PA
TO BATTERY = re 4
; + —=# OSCILLATOR oo
a Fig. 7. VR2 calibration Fig. 9. VR4 calibration Pape:
| ae Figs. 6-8. Temporary wiring of the potentiometer panel for calibration. Fig. 9. The final wiring
AL
VR2 CALIBRATION
The decade box is disconnected and VR2 wired into
circuit as shown in Fig. 7.
VRI1 is successively set at each of the previously
determined points and VR2 balanced against each
point. In this way VR2 can be accurately calibrated
in terms of VR1.
VR3 CALIBRATION
The decade box is reintroduced and R9 and R10
deleted. VRI1 and VR2 are each set at 500 ohms and
VR3 calibrated in 10 or 100 ohm steps against the
decade box. Wiring details are shown in Fig. 8.
VR4 CALIBRATION
Prior to this final calibration the complete panel is
wired as shown in Fig. 9. The audio oscillator and
transformer may also be permanently attached.
Two 3in 4 B.A. bolts serve as stand-off supports
for the oscillator panel.
After completing the wiring VR4 is calibrated against
VR3 with VR1 and VR2 each set at 500 ohms.
CALIBRATION WITH FIXED RESISTORS
A simple calibration standard is shown in Fig. 10.
Four close tolerance resistors of 100, 200, 300 and
400 ohms respectively, are wired together as shown.
By shorting out the appropriate sections a selection
of resistance values from 100 to 1,000 ohms may be
made. Two leads which terminate in crocodile clips
are conveniently used as shorting links. Resistance
tee Pere ee eS ee
Fig. 10. Assembly and wiring of the calibration resistors.
Due to the accuracy required for these resistors, it may be.
necessary to select and measure to within | per cent
tolerance of the quoted values from resistors of the nearest
“preferred” value available
values obtained when the appropriate sections are
shorted are given in Table 1.
Calibration of the bridge using this standard is
carried out exactly as before, the standard taking
the place of the decade box.
When calibration is complete the dials may be
numbered from 0 to 10 and permanently marked with
indian ink, If the calibration has been made in 100
ohm steps the intervals may be divided into ten equal
parts. No great loss of accuracy will occur since it
was found that over small portions of the potentio-
meter tracks the resistance per unit length was constant
enough to warrant this procedure.
OPERATION OF COMPUTER
TABLE | A discussion of the operations of multiplication and
division was given in the introduction to ‘this article.
Resistance Q Short Out These operations are summarised at this point.
100 3&8 MULTIPLICATION
200 1&2,6&8 Set VR4 to 1 or 10. The multiplicand is set on
300 6&8 VR2 and the multiplier on VR3. The bridge is
400 1&5 balanced with VR1 and the answer taken from this
500 3&5 scale
600 7&8
700 1&4 DIVISION
on ; ge Set VR4 to 1 or 10. The numerator is set on VR1
1.000 pane and the denominator on VR2. The bridge is balanced
: with VR3 and the answer taken from this scale.
COMPONENTS...
+ ae ow
Resistors Transformer ,
RI 220kQ 10% Interyalve type, ratio 3:1
R2 2-7kQ 10% saairiatS
R3 47kQ IO & nautebeies
R4. 4-7kO /, ransistor:
R5 1000 \% TRI, TR2 OC7I or NKT272
R6 2000 4
R7 3000 142 eee ge Switch
R8 4002 1% SI Single pole on/off
RI —-1,0000 1% 2
RIO 1.0000 1% \ see Figs. 6 and 7 Battery
Potentiometers BYI 4-5V battery
VRI, 2,3,4 1[kQ linear, wire wound
Miscellaneous
er ree paper Aluminium panel. Copper laminate board. Four
C2 0-25,F paper pointer knobs. Headphones. Terminals. P.V.C.
C3 0-25uF paper insulated connecting wire.
= SE RE er
EVALUATION OF POWERS AND ROOTS
In addition to the operations of multiplication and
_ division, further interesting evaluations may be made
if the scales of VR3 and VR4 are calibrated logarith-
- ‘mically.
If we let r; be the reading of VR3 such that log r,; =
VR3 and similarly r, the reading of VR4 so that
log r, = VR4, then at the balance point, and recalling
_ that in the basic bridge of Fig. 1, R1 x R4 = R2 x R3,
it follows that
VRI logr, = VR2 log r;
or
r.VBt = pV
or VR2/VRI
i Se 2 | gi
In other words we can determine the value of rz; to the
power VR2/VR1.
' As a simple example consider the evaluation of 34.
The required power VR2/VR1, is conveniently obtained
by setting VR2 to 8 and VRI1 to 2. VR3 is set to 3
and the bridge balanced with VR4. The answer is
taken from this scale.
Roots may be evaluated using a similar procedure.
For example, suppose we wish to find 4/27 or, what
is the same thing, 27!. VR2 is set to 1 and VRI to 3.
After setting VR3.to 27 the answer is read off the
VR4 scale.
LOGARITHMIC SCALES
The logarithmic scales are prepared as follows.
A 2t4in diameter circle is inscribed on a disc. Two
_ points are marked with pencil on the circumference
of the circle such that the length of the arc is the same
as that of the linear scales. The arc is then divided
into three equal portions which in turn are sub-
divided into tenths. This calibration represents the
logarithms of numbérs between 1 and 1,000. The
_ resistance scale may now be calibrated by inserting
the values whose logarithms correspond to the inner
7
0 40
Fig. 12 (above). Example of the linear type of scale
that will be produced when the four potentiometers
are individually calibrated as described on page 694.
This linear scale is used for multiplication and division
Fig. 11 (left). Calibration scale for VR4 drawn on a
logarithmic basis to full size. This scale is used for the
evaluation of powers and roots
scale. An illustrative example is given in Fig. 11.
This scale can conveniently be used for VR4.
The second logarithmic scale is prepared by calibrat-
ing VR3 in terms of VR4. To do this VR1I and VR2
are each set at a dial reading of 5 and VR3 then
balanced against each point of VR4 by the usual
method. Fig. 12 shows an example of this scale.
Doubtless other evaluations will suggest themselves
to the mathematically-minded constructor. Circuit
variations are also possible, for example, the audio
oscillator may be replaced by a buzzer with a cheapen-
ing in the overall cost. Asa point of interest the cost
of the instrument excluding battery and phones was
ust over £2.
Contributed Articles
The Editor will be pleased to consider for publica-
tion articles of a theoretical or practical nature. Con-
structional articles are particularly welcome, and the
projects described should be of proven design, feasible
for amateur constructors and use currently available
components. ;
Intending contributors are requested to observe the
style in our published articles with regard to com-
ponent references on circuit diagrams and the arrange-
ment of components list. ~
The text should be written on one side of the paper
only with double spacing between lines. If the manu-
script is handwritten, ruled paper should be used, and
care taken to ensure clarity, especially where figures
and signs are concerned.
Diagrams should be drawn on separate sheets and |
not incorporated in the text.
should be of high quality suitable for reproduction;
but wherever possible, negatives should be forwarded.
The Editor cannot hold himself responsible for
manuscripts, but every effort will be made to return
‘them if a stamped and addressed envelope is enclosed.
Photographic prints
Ps
Fat