In the little analog computer example shown last month (April 14, p. 24), if we wanted to change the mass of the "car," we could change the feedback capacitance for A4. But it's inconvenient to adjust the value of capacitors or change around a large number of them. So instead, let's apply a pot to the input resistor.
Instead of the 100-kΩ resistor going from the summing point of A4 to the output of A3, we could have a 50-kΩ resistor going to the tap of a 50-kΩ pot, driven by A3. Or, we could have a 10-kΩ resistor going to the tap of the pot. This pot could be a 0.1% linear potentiometer—a 50-kΩ, 10-turn pot—with a turns-counting dial. These pots can still be bought for about $20, plus $20 for the dial, from Vishay-Spectrol. Now you could turn the gain up an octave, or down one or two octaves, making the "car" lighter or heavier. Similar gain adjustments could be applied to the paths for + and − damping factors at A6. (But I just used dumb rheostats.)
You've probably noticed that the pot setting, when the pot's wiper is loaded with a fixed resistor, will cause a nonlinear effect. To get 100% of the input conductance, you might set the pot to 100%. But to get 50% of the maximum gain, you'd typically set 63% on the pot. To get 25% or 29% of full-scale gain, the makers of analog computers—almost all of them—had special procedures for "pot setting" to some odd rotation value so the user could get the desired gain. Or, they could measure the actual gain as a function of an observed setting (sketch A). You'd turn the pot and measure the voltage at "VPOT."
George Philbrick didn't like that. He had coefficients that could be dialed in with sets of sort-of "BCD" conductances, using 12-position rotary switches. So if you didn't want 100 kΩ (10 micromhos), you could set the dials for 8 micromhos, or 9 or 11 or 22. Or 9.9 or 9.8 or 9.7, or 7.7 or 6.6 or 5.5. Or any gain coefficient between +1% and +1000%, or −1% to −1000%, or to zero. This was a very neat and NOT nonlinear gain function, even if it was kind of "digital."
George didn't let his computers just use binary-coded input conductances. That would take four precision resistors for each decade of gain-setting. He used ternary gain schemes. For example, if you wanted to change from an input conductance of 1 micromho, to double that gain from −1 to −2, he would connect in [3 micromhos −1 micromho]. To accomplish this, he would put in a 333.3-kΩ resistor to one summing point and a 1.000-MΩ resistor to a precision current inverter to give a net conductance of 2.0 micromhos. Each decade needed just three resistors, such as 1 MΩ, 333.33 kΩ, 166.67 kΩ; then, 10 MΩ, 3.333 MΩ, 1.666 MΩ; and so forth (sketch B).
This meant that every computing function, whether summer or integrator, needed two good precision op amps per channel—one for the function, and one for the current inverter. But that's okay, because many functions needed to accept + and − inputs or provide + and − gains. The Philbrick "K5-U" computers had this feature from 1958 to 1968. The company implemented a good number of accurate summing resistors, but no tweaking of "precision pots" was ever necessary.
Comments invited! rap@galaxy.nsc.com —or: Mail Stop D2597A, National Semiconductor P.O. Box 58090, Santa Clara, CA 95052-8090
I am a chemist turned chemical engineer. I never kept going to become an EE, but certainly have brushed up against analog computers. Built my own 3-integrator versions out of op amps in the 70's. When I went to grad school in 1980, I discovered a couple of small analog computers in the chemical engineering control theory laboratory (taught by Peter Rony of BugBook fame). I simulated chemical reaction kinetics, and despite the low order of accuracy (1%), I really appreciated the direct connection between the rate constant "pot" and the immediate display of the results. I often wish that I had a peripheral for my computer that would connect a knob to a parameter in my digital simulations. I once saw that the MIT Project Whirlwind computer had such pots. Just this week, a computational chemist down the hall wished he had a knob attached to his Mathematica simulations of reaction rates. The processors are probably now capable of the speed/accuracy combination of the analog computers, but everyone seems to insist on ultimate accuracy at the expense of understanding behavior!
Kip Mercure -August 30, 2003
I really like to have the ability to have the articles in pdf format. The html usually prints poorly. It usually prints with stuff other than the article of interest. I know that you have to pay the bills, but I don't want all the "free" adds when I print.
Michael Bolt -August 08, 2003
I completely agree with the comment from Gerald Wood; it is an enormous step back that we cannot have the .pdf files.
The layout of html pages is often horrible and not easy to read. Pictures are even worse. Progress comes at a price...
Peter Haak -May 22, 2003
Dear Editor, If it is no longer possible to use the pdf format, why not to embedd the schematics in the html file? It will be much more readable. My best regards to The Great Bob Pease and to all ED staff.
Sergio Tassinari -May 22, 2003
You might have mentioned to Mr. Wood that selecting 'Printer Friendly' format seems to automatically provide the diagrams for printout.
My request is for a listing and availability of all Mr. Pease's historical columns for those who have only recently been introduced to their charm.
Robert Schwebel -May 21, 2003
I like the articles relating to analog electronics and how they could be interfaced to the digital systems. They help me understand more about OP AMPs and how I could apply them to my experiments and to my Electronics Workbench software.
John McCullough -May 21, 2003
I like the article -- I like all of Robert's stuff. What I do not like is the new format. Please give us the PDFs with the diagrams already embedded.
EDITOR RESPONSE: Sorry, it is no longer possible to obtain online articles as pdf files. Our new website takes advantage of the superior search capabilities of html files, making html the only available format.
Gerald Wood -May 18, 2003
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