■ FIGURE 5. Operational
(because this is a multiplication) we get
3 + 2 = 5. Using the slide rule, we get
the product as 1.188 and the power of
10 is 5 or 1.188E5, or 118,800.
Build a Mechanical
One can construct a simple slide
rule that will multiply and divide from
a couple of sheets of logarithmic graph
paper. If you have a computer,
Microsoft Excel can be used to generate a logarithmic graph as shown in
Figure 3. By laying the logarithmic
scales next to each other, we have a
rudimentary slide rule as shown in
Figure 4 for multiplication and division.
There are electronic equivalents to
the linear and logarithmic slide rules.
Many people are familiar with the
linear response from an operational
amplifier shown in Figure 5A. By using
a semiconductor diode, we have a
device that has a logarithmic relationship between the voltage applied to it
and the current flowing through. As the
applied voltage across the semiconductor diode increases linearly, the current through it increases exponentially.
By using the circuit shown in Figure 5B,
we can generate a logarithmic relationship between the input voltage and the
output voltage as shown in Figure 6.
The inherent internal resistance
causes a practical problem with using
a simple diode in the logarithmic
amplifier. The resistance is subject to
change with temperature. This diode
effect can be reduced by using an
NPN transistor as shown in Figure 5C.
The relatively high base resistance of
the transistor will be bypassed as most
of the emitter current flows through
the collector region of the transistor.
Figure 6 also shows the data
compression feature of the logarithmic
amplifier. The inputs range from 100 to
10,000 mV on the input which is compressed to 374 to 598 mV on the output scale. This data compression characteristic is especially useful where the
inputs vary over a wide range of values,
for example in a nuclear power plant
where the neutron flux can range over
many decades from when the reactor
is shut down to 1012 neutrons/cm2sec
when the reactor is operating. The
logarithmic amplifier is also useful in
compressing the input data range
before analog-to-digital conversion.
So how can we construct the
electronic equivalent of the slide rule?
Well, we can use two logarithmic
amplifiers — IC1 and IC2 — to convert
two voltages to the logarithm of the
voltages. Next, we can sum or subtract the voltage logarithms using IC3.
This is the equivalent of multiplying or
dividing the voltages. We can use an
anti-logarithmic amplifier — IC4 — to
convert the sum of the logarithmic
voltages back to voltage. Finally, since
each amplifier stage reverses the sign
of the output with respect to the sign
of the input, another amplifier — IC5 —
was added to reverse the negative
sign of the anti-logarithmic amplifier
output to make the sign of the output
positive. This analog multiplier is
shown schematically in Figure 7.
You can get the functionality of
the analog multiplier shown in Figure 7
in a single eight-pin device: the Analog
Device AN633 shown in Figure 8. The
AD633JN is a four quadrature multipli-
■ FIGURE 6. Logarithmic Amplifier
Input and Output.