C. Pronk 1 Analog computing © Kees Pronk .

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Analog computing

© Kees Pronk

http://vitrinemuseum.ewi.tudelft.nl

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Digital vs. Analog

• 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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Early examples

• Early examples of analog computing mechanisms are:

• The slide rule

• An Astrolab (such as this one in Franeker)

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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.

• We want to calculate the y-value in real-time!

y

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Some physics:

• 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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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

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Physics - 3

• The complete schematic:

• ÿ ∫ ý ∫ y

s

d

- (d ý + sy)

1 / m1 / m - (d ý + sy)

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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)

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Amplifier with gain - A

Rf

A

R1inout

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).

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Summing amplifier with gain -A

Rf

A

R1in1

out

The amplification of this circuit is Vout / Vin1 = - Rf / R1 and Vout / Vin2 = -Rf / R2,

or,

Vout = Vin1 . – (Rf / R1) + Vin2 . – (Rf / R2)

R2in2

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Integrator circuitC

A

Rinout

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.

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Differentiator circuit

C

A

R

inoutVout = -RC . (d Vin / dt)

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.

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Other circuit elements

• Apart from amplifiers, integrators and differentiators there exist other elements such as: logarithmic amplifiers non-inverting amplifiers comparators switching elements.

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The EAI 680 analog computer

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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EAI computers

• 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.

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From the EAI-680

Chopper relayChopper relay

Note the large (precision) capacitor in the integrator.Note the large (precision) capacitor in the integrator.

Integrator / amplifierIntegrator / amplifier

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From the EAI-680

Switching unitSwitching unit

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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 so-called chopper-amplifiers

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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.

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Patch panel from the EAI-680

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Modern developments

• 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:

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More information?

• 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

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This museum

• The 'vitrinemuseum' shows early computer hardware as used for various labs at Delft University of Technology.

• Have a look athttp://vitrinemuseum.ewi.tudelft.nl