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C. Pronk 1
Analog computing
© Kees Pronk
http://vitrinemuseum.ewi.tudelft.nl
• Digital equipment works
 in discrete time steps, and,
 in discrete value steps.
• Analog equipment works
 with continuous time, and,
 with continous values.
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Digital vs. Analog
• Early examples of analog computing
mechanisms are:
• The slide rule
• An Astrolab
(such as this one in Franeker)
C. Pronk 3
Early examples
C. Pronk 4
Example system
• Here is a typical system consisting of
a Spring (k), a Mass (m) and a Damping (c).
• The system is excited by some force and will
move in the y-direction.
y
• We want to calculate
the y-value in real-time!
• For the mass it holds that: Fm = m . a = m . ÿ
• For the spring it holds that: Fs = m . y
• For the damper it holds that: Fd = d. ý
• For the whole system it holds that:
Fm + Fs + Fd = 0
• or
• m.ÿ+d.ý+s.y=0
• Rewriting:
• ÿ = (- 1/m) . (d . ý + s . y)
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Some physics:
C. Pronk 6
Physics - 2
• ÿ = (- 1/m) . (d . ý + s . y)
• Given the second derivative ÿ, we can calculate
ý by using an integrator:
•
ÿ
∫
ý
• and in a similar way we can calculate y from ý
•ÿ
∫
ý
∫
y
C. Pronk 7
Physics - 3
• The complete schematic:
s
•ÿ
∫
ý
∫
- (d ý + sy)
y
d
1 / m - (d ý + sy)
1/m
•
•
C. Pronk 8
Some history
Analog computing was being used before digital
computers became powerful enough to do
calculations in real-time.
Analog computers are based upon the mathematical
equivalence of electrical circuits with phenomena
which need to be studied such as
 Spring/mass/damper systems
 Control systems (closed loop systems e.g. pilot in the loop)
 Systems of differential equations (e.g. economic systems)
C. Pronk 9
Amplifier with gain - A
Rf
in
R1
A
out
Under the assumption that the amplifier gain A is very
large (and some other electronics assumptions), the
amplification of this circuit is Vout/Vin = - Rf / R1
Note: such an amplifier inverts the input signal (a
positive input signal becomes a negative output signal).
Rf
in1
in2
R1
R2
A
The amplification of this circuit is
Vout / Vin1 = - Rf / R1 and Vout / Vin2 = -Rf / R2,
or,
Vout = Vin1 . – (Rf / R1) + Vin2 . – (Rf / R2)
out
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Summing amplifier with gain -A
C. Pronk 11
Integrator circuit
C
in
R
A
out
Vout = - Vin . (t / RC)
This cicuit functions as an integrator.
The output voltage is a time-integral of the input voltage.
Such a circuit converts e.g.
speed into distance, or, acceleration into speed.
An integrator "smoothes" variations in the input voltage.
C. Pronk 12
Differentiator circuit
R
C
in
Vout = -RC . (d Vin / dt)
A
out
This circuit functions as an differentiator.
The output voltage is the time differential of the input
voltage.
Such a circuit converts e.g.
distance into speed, or, speed into acceleration.
A differentiator amplifies noise and high frequencies and
is therefore seldomly used in this pure configuration.
• Apart from amplifiers, integrators and
differentiators there exist other elements
such as:




logarithmic amplifiers
non-inverting amplifiers
comparators
switching elements.
C. Pronk 13
Other circuit elements
Such an analog computer has been used for research and labs in the
aerospace faculty at TUDelft in the "Stabilisation and Control" group.
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The EAI 680 analog computer
• Electronic Associates Inc. was an
•
•
•
important manufacturer of analog
computers.
Later on, analog computers were
combined with digital computers to form
so-called hybrid computers.
E.g. EAI 640 (digital) + EAI 680 (analog)
 EAI 690 (hybrid computer).
Still later on, when digital computers
became fast enough, analog computers
were phased out.
C. Pronk 15
EAI computers
Integrator / amplifier
Chopper relay
Note the large (precision) capacitor in the integrator.
C. Pronk 16
From the EAI-680
Switching unit
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From the EAI-680
C. Pronk 18
Some electronic facts
• In the beginning the accuacy of analog dc
•
amplifiers was not sufficient for dependable
computing.
The following requirements could not be met:




infinite open loop gain
infinite imput impedance
zero output resistance
zero temperature drift
• Therefore, the input voltage was chopped
into ac; ac amplified and rectified again in socalled chopper-amplifiers
C. Pronk 19
Programming an analog computer
An analog computer is programmed by connecting the
various input and output ports by wires.
To easily set-up an experiment, patch panels were
provided.
A patch-panel was programmed for a particular
experiment.
Patch panels could be easily exchanged.
The connections of the amplifiers and other
components are "behind" the patch panel.
C. Pronk 20
Patch panel from the EAI-680
• The same ideas of composing a circuit from
•
building blocks can be found in tools such
as Simulink and Matlab.
See
http://www.mathworks.com/
Example:
C. Pronk 21
Modern developments
•
http://www.analogmuseum.org/
•
http://www.vaxman.de/analog_computing/analog_computing.html
•
http://en.wikipedia.org/wiki/Analog_computer
•
http://technikum29.de/en/computer/analog
•
http://www.play-hookey.com/analog/setting_coefficient.html
C. Pronk 22
More information?
• The 'vitrinemuseum' shows early
computer hardware as used for various
labs at Delft University of Technology.
• Have a look at
http://vitrinemuseum.ewi.tudelft.nl
C. Pronk 23
This museum