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problems encountered when building an analog computer for simulating 2nd order diff eq

CR7

Mar 18, 2015
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Mar 18, 2015
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I plan to build an analog circuit to solve diff eq of the form x''+bx'+cx=f(t), where b and c are positive.

1. Ignoring the value for each component and focus on the whole connection. Is the circuit actually correct? Since I've used a few inverted integrator and inverted summers, I'm not really sure if the circuit is doing what I want to do, and if the sign for the coefficients b and c are correct.

2. What frequency range and values for the resistors and capacitors should I use? I heard that if the frequency is too low, the input current offset will make the output voltage drift to the rail of the op-amp, is it true? (actually I don't really know what this means). And I should keep the product of R and C equal to one, don't I?

thanks
 

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hevans1944

Hop - AC8NS
Jun 21, 2012
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Welcome to Electronics Point! And congratulations on your decision to explore the fascinating world of analog computers.

There is still a lot of interest in this "obsolete" technology which can perform real-time simulations of complex physical systems. Unfortunately, my last relevant experience with analog computers involved the GEDA (Goodyear Electronic Differential Analyzer) circa 1968 or thereabouts. This was a fascinating vacuum-tube based analog computer that was becoming obsolete by the time I was exposed to it. Lots of deka-pots to set co-efficients to four significant figures, tons of relays to setup initial conditions, a huge removable patch-board (several were available for "off-line programming") and ±100 V op-amps. This contraption could simulate, in real time, the flight of an aircraft, recording data on multiple channels of a high-speed oscillographic light-beam galvanometer recorder. Pretty damned impressive for a young technician who had just finished a four-year tour with the U.S. Air Force and now worked for a prestigious local research institute with lots of contracts at Wright-Patterson AFB and around the country. IIRC, the Air Force was investigating whether the GEDA could be retrofitted with solid-state op-amps for better performance. The answer: maybe, but not at a cost they were willing to pay.

I don't see any major errors in your simulation. However, real-world op-amps have two things that will kill an analog computer simulation using real op-amps: input offset voltage and input offset current. Ideally, both of these are zero; in actuality they never are. This is especially important with op-amp integrators because an integrator accumulates the offset errors on the integrating capacitor and will eventually drive the op-amp output to one of the power supply rails. That is why there is always a "reset" switch to discharge the integrating capacitor prior to beginning a simulation. There are other issues, too, regarding how to setup initial conditions, that must be established prior to beginning a simulation. Homogenous linear differential equations are easy to setup and solve. It is the simulation and solving of non-linear partial differential equations in real time where a good analog computer really shines. Good luck with that.

I would like to send you to a blog about someone who is currently building a very sophisticated analog computer. It would be well worth your time to read how his project started more than two years ago and where it is today. Follow this link to adventure and endless wonder!

73 de AC8NS
Hop
 
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LvW

Apr 12, 2014
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Apr 12, 2014
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Three comments from my side:

1.) I think, you must not care about offset voltages/currents because this is a problem for "self-standing" integrators only. However, in your case, both integrating blocks have an overall dc feedback (acting like ohmic resistors parallel to the integrating capacitors). Hence, no parallel resistors are necessary.

2.) I think, in general the design is able to realize the given diff. equation - however, you could save some opamps (inverters) if you would use integrator blocks able to integrate the difference between two input signals. Such circuits can be found using the keyword "BTC integrator" (BTC: Balanced Time Constants)

3.) Here is an even better method for reducing the number of opamps (from five to three): As a first stage you can use a differential amplifier (two feedback signals connected to both opamp inputs). In this case, no additional inverters are necessary. The resulting circuit is a very popular biquadratic (universal) filter structure: The KHN topology (Kerwin, Huelsman, Newcomb)
 
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Peter McNair

Mar 26, 2015
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Mar 26, 2015
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I agree - the world of analogue computers is a fascinating one! After seeing one way back in 1976 (Science Museum, London), I have got around to building my own...

http://analog-ontology.blogspot.co.uk/

What's interesting to me is that the popularity of analog computers appears to start to die out shortly after the invention of the very thing which would be useful in making analog computers: the integrated circuit op amp (1965, µA709)...
 
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