# Computer Analog back in time

After several requests from many quarters I decided to publish an article on the computers (computers) analog.

I will try in this paper to dispel the rumor that they are very complex, certainly not simple, but, only because they require a different mental approach by digital computers.

Essentially we have only two types of computers at the base of all future developments, the analog derived from slide rules already used in 1600

And the digital one which is derived from the abacus

In the past to solve a difficult problem with the electronic calculation you could choose between an analog computer, a digital computer, or both together in a hybrid configuration.

For a very complex math involving differential equations and other messy calculations, analog computer was unbeatable. Being able to solve differential instances almost instantly.

With analog computers was normal to make parallel computations, many parts of a problem could be solved simultaneously, accelerating the solution.

This made the simulation of large and complex fast and practical physical systems.

In the past, digital computers were very slow, while he is able to be programmed to do calculations and other higher mathematical algorithms, they were essentially impractical for simulations.

When digital computers grew in speed it was clear that they would compete with analog computers.

Today, almost every digital computer, from large mainframes to smaller PC, performs calculations and other higher mathematics in a flash and with unmatched precision.

The analog could no longer compete and have simply disappeared. Just like many other electronic technologies, these impressive machines had their lifecycle.

However, It was and still is a cool technology. Analog computers were constants and variables with analog voltage levels proportional. These are then processed by various electronic circuits that perform mathematical operations in analog form.

The key processing circuit was the operational amplifier.

The op amp can be easily reconfigured to perform a wide range of mathematical operations, sum / subtraction, multiplication / division, integration and differentiation and many more. The op amp can also be configured to perform logarithmic and trigonometric operations with special feedback circuits nonlinear.

Per program an analog computer was enough to simply write the equations you wanted to solve, convert them into a block diagram, then they cablavano the various calculation elements together to form the individual blocks on a large panel.

## Example of mathematical resolution

Let us assume, for example, of having to solve an equation of the type

$LARGE&space;Afrac{d^{2}V_{o}}{dt^{2}}+&space;Bfrac{dV_{o}}{dt}+CV_{o}=V_{i}$

Dove $LARGE&space;LARGE&space;A$, $LARGE&space;LARGE&space;LARGE&space;B$ e $LARGE&space;LARGE&space;LARGE&space;C$ are constants and $LARGE&space;V_{o}$ e $LARGE&space;V_{i}$ are time-varying voltages that may be analog corresponding functions of time.

You can solve the equation that describes the physical system by adopting the following procedure:

• isolating the derivative of higher order equation; it then takes the form
• $LARGE&space;LARGE&space;LARGE&space;frac{d^{2}V_{o}}{dt^{2}}=&space;+&space;frac{V_{i}}{A}-&space;frac{B}{A}&space;frac{d&space;V_{o}}{dt}-frac{C}{A}V_{o}$
• the terms are added to the second member in an adder to the operational amplifier according to the scheme below, then the output will be equal to $LARGE&space;LARGE&space;frac{d^{2}V_{o}}{dt^{2}}$
• subsequently integrates this output as many times as is necessary to get the problem of variable, ie twice
• then realizes a feedback loop which returns to the inputs of the adder values $LARGE&space;LARGE&space;LARGE&space;frac{dV_{o}}{dt}$ e $LARGE&space;LARGE&space;LARGE&space;-V_{o}$ and if fixes the amplitude with the input potentiometers.
• It then applies the voltage to the other input of the adder. The value $LARGE&space;LARGE&space;LARGE&space;LARGE&space;frac{-dV_{o}}{dt}$ It is obtained by exchanging sign $LARGE&space;LARGE&space;LARGE&space;LARGE&space;LARGE&space;frac{dV_{o}}{dt}$with another operational inverter

Most of the problems have been solved realizing simulation circuits, Also large complex systems involving chemical processes or space travel.

In the face of those who say that an analog computer is complicated to program.

With analog components, calculation precision was not so great compared to what you could get with a digital computer, but it was good enough for most jobs.

Many really hard problems have been solved this way. These computers gave answers to the calculation that you could not find yourself on paper for lack of a suitable solution.

The math software available today easily solve complex problems, impossible until the seventies of the last century.

One such system simulated the first Apollo mission to the moon at NASA in Houston.

A large digital system simulated the long flight from Earth to the Moon while a pair of analogue computers simulating fast dynamic of the Apollo spacecraft in the initial and final conditions.

The ADC and DAC interfaces allowed to the analog and digital cameras to exchange data. Can you imagine that complex equations can be simulated with a hybridity .

Hybrid systems were also used for aerospace and petrochemical companies. A similar system was used by Bell Helicopter in Fort Worth where they simulated their helicopter projects.

Most of these analog computers were the iterative one in which they were used fast supplements and the problem was solved and repeatedly scaled back many times per second.

This could display the graphical results on an oscilloscope. By allowing dynamic interaction of the solution that has permission to view the problems and optimize designs.

# First operational valve

The first operational amplifiers were the K2-W constituted with two vacuum tubes 12AX7.

The first operational commercial general purpose, It was produced by George A. Philbrick Researches Incorporated nel 1952. Called K2-W, built around two double triodes mounted together with an octal socket (8-pin) for easy installation and maintenance in the time frames of electronic equipment. What made possible only after circling for this was taken from the military secret.

The schematic diagram shows the two tubes, together to ten resistors and two capacitors, a fairly simple design but, let us remember that it was the 1952:

In case you do not know the vacuum tubes, they operate in a manner analogous to the N-channel MOSFET, they lead more current when the control grid (the dotted line) It is more positive relative to the cathode (the folded line near the bottom of the pipe symbol) and conduct less current when the control grid is less positive (or more negative) respect to the cathode. The left double triode tube operates as a differential pair, converting the differential inputs (inverting and non-inverting) in a single voltage signal amplified. Such a pilot signal of the left triode control grid of the second valve through a voltage divider (1 MΩ-2,2 MΩ). That triode amplifies and inverts the output of the differential pair to a higher voltage gain, then the amplified signal is coupled to the second triode of the same tube in a non-inverting amplifier configuration for a current amplification. The two “neon tubes” act as voltage regulators, their behavior is similar to the semiconductor zener diodes, their task is to provide a bias voltage in the coupling between the two triodes amplification.

With a double supply voltage +/- 300 volt, This op-amp allows an output hike +/- 50 volt, which it is very poor by today's standards.

The essential features were:

• of open circuit voltage gain variable from 15.000 a 20.000 (It depends on the aging of the valve)
• climb speed of 12 volt / μsec,
• maximum output current of 1 mA,
• at rest dissipation over 3 watt (excluding filaments!)

It cost the modest about 24 dollars then, more or less around 800 today's dollars.

The main problem with all these initial amplifiers was that it had to balance to obtain the DC offset for the highest precision.

Today we have excellent amplifiers, analog multipliers and other analog components of higher analysis.

Several times I asked would make sense to a modern version of an analog computer?

Maybe it could be a solution to some bad calculation problem as a research situation.

A special analog computer could be built to quickly simulate the equations and with the ability to play with the various variables and so forth. It would certainly be smaller, cheaper and more precise than the monsters of the past. The analog circuits are still inherently faster than digital so maybe it could happen.

Anyway, This is now a lost technology. With digital eqiuipaggiati fast computer with DSP for the simulation of mathematical formulas software, that needs can never have an analog computer?

What a pity.

But I guess we can say the same of many other lost electronic technologies.

## Back to the Future Analog

While I documentavo network for possible integration ideas article I came across a publication last year.

In fact, They have created an analog / hybrid computer unicycle. It is described in detail in an IEEE document :

N. Guo, Y. Huang, T. May, S. Patil, C. High, M. Seok, S. Sethumadhavan, and Y. Tsividis, “Energy-Efficient Hybrid Analog/Digital Approximate Computation in Continuous Time,” IEEE Journal of Solid-State Circuits, vol. 51, no. 7, pp. 1514-1524, July 2016 .

This is proof that perhaps the analog computers still have a place in the calculation.

The analog are particularly efficient in the calculation, making almost trivial differential equations. With an almost instant solution. Playing with variables, you can try different conditions and scenarios.

Analog computers were always fast but not always accurate. They suffered and offset drift, component tolerances and degradation, and other similar diseases of the analog circuits. Today, amplifiers and other components are extremely improved, then an analog computer with superior characteristics is achievable. The main question is: “It would be useful, with faster processors and inexpensive today?” Probably not, but you could make special versions to solve unique problems.

Professor Tsividis and his colleagues have believed in this approach by creating an analog / hybrid computing circuit on a single chip. Using CMOS 65 nm, the computer is capable of solving nonlinear differential equations to 4 ° order. Use analog blocks consist of op amp in class AB with digitally assisted calibration. The calculation accuracy is in the range from 0,5% a 5%, with resolution times from less than a microsecond to several hundred microseconds.

The article in question describes only a computer can solve equations 4 ° order, but today Tsividis and his team have a chip 16 ° order. With two of these on a card, They have created a computer 32 ° order that interfaces to a laptop via a USB port. Such a system can solve some serious problems on a desktop – a nice change from the big analog systems / hybrids of the past that filled entire rooms.

In general, analog is still a good solution for some problems. However, It does not seem likely that we'll ever see an analog / hybrid commercial computer.

However special computer could be easily constructed with modern circuits at a reasonable cost.

## The hope still never dies

According to research conducted by the University of Sannio in Benevento with funding from the US Office of Naval Research, metamaterials could be designed so as to perform a "photonic calculation" on light signals passing through them, thus laying the theoretical foundations for the analog computers of the future.

Metamaterials are artificially created materials with special electromagnetic properties, and whose macroscopic characteristics depend not only on the molecular structure but also by the geometry embodiment.

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15 replies
1. Amilcare says:

I agree with Marcello
If you thought it interesting I would not be so busy to do this article

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2. Marcello says:

I would be interested in a tutorial.
Of course not too extended, I am always fascinated by the things of the past.
How do you say : “know the past to understand the present ” .
I believe that with your knowledge would make a very good article, without detracting from that of Amilcare.
Health Marcello

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