Home Brew Analog Computer System

[zapta]

..... I've been working like a man possessed to design and build my own solid state hybrid digital/analog computer to modestly put virtually all of those extinct commercial offerings to shame (complexity, size, precision, etc).

I wonder why there are still commercial analog computers these days that digitals computers are so cheap and powerful.  Can you give a few examples where they have an advantage over digital?

Years ago I used to maintain an analog computer. It was a Philips unit with a CRT that used to display underwater sound wave propagation based on the vertical thermal profile of the water. I had billion of potentiometers on the front and zillions trim pots inside. Calibrating it was a nightmare and it needed 24h to stabilize before being used (it was 100% solid state).

[Dave Turner]

As a relative newcomer to the EEVblog forum I've only just come across this thread; much of the day has been lost reading it. It has brought back many of my memories, particularly as earlier this year I was forced due to circumstances to skip, almost overnight, ALL of my magazine collections of Practical Wireless, Practical Electronics etc. etc. dating from the early sixties through to the early nineties. Including those editions about  the Analogue Computer mentioned at the start of this thread. (Several thousand magazines).

In 1966 I joined the newly formed computer club at school and wrote my first "Hello World" equivalent in Algol via coding sheets and punched cards to be run on the mainframe at Keele University. Wonderful a 2 week development cycle.

To the point of this thread a book book given to me then was a source of inspiration some of which is relevant. Have a look at http://books.google.co.uk/books?id=aQ84AAAAIAAJ&printsec=frontcover&dq=cambridge+university+press+we+built+our+own+computers&hl=en&sa=X&ei=YvOUUvvPBuSV7AbwsoCIDw&ved=0CD0Q6AEwAA#v=onepage&q=cambridge%20university%20press%20we%20built%20our%20own%20computers&f=false

I may be missing something but why would you need to use the ABS() function when using integer arithmetic? I don't know whether the compiler is clever enough to recognize this or not; but if not you could save computational time.

Please keep this project going with as many updates as are reasonably possible. Under many circumstances, once set up, an Analogue computer will solve a problem faster in real time than a Digital computer. With the preponderance of digital circuitry now, this is often forgotten. (Occam's Razor)

[GK]

..... I've been working like a man possessed to design and build my own solid state hybrid digital/analog computer to modestly put virtually all of those extinct commercial offerings to shame (complexity, size, precision, etc).

I wonder why there are still commercial analog computers these days that digitals computers are so cheap and powerful.  Can you give a few examples where they have an advantage over digital?

I'm not aware of any analog computer model still being commercially made. An analog computer could still be useful in the electronics lab for the study of control theory fundamentals, and that is where their application lingered on the longest. 

[GK]

As a relative newcomer to the EEVblog forum I've only just come across this thread; much of the day has been lost reading it. It has brought back many of my memories, particularly as earlier this year I was forced due to circumstances to skip, almost overnight, ALL of my magazine collections of Practical Wireless, Practical Electronics etc. etc. dating from the early sixties through to the early nineties. Including those editions about  the Analogue Computer mentioned at the start of this thread. (Several thousand magazines).

Hi,

Thanks for the interest. Pitty you had to turf all those old magazines! Although it doesn't contain much at the moment, I have a website ( http://www.glensstuff.com ) that will eventually have a full write up and all technical details of the project. I've made a lot of progress with the construction so far, but no one section/chassis is fully complete at this time, which is why the presentation hasn't much happened yet.
 

[GK]

The article gives an explanation of the graphical method (Figure 1) for manually drawing out the character on Cartesian coordinates and then working out and plotting the X and Y waveforms required for reproduce the character. This is quite simple and straight forward enough, but the article does not then go on to explain or detail the "purely graphical" method for manually computing the Fourier components of the produced X and Y waveforms - though a reference is given: T.C. Blow, Graphical Fourier Analysis, Electronics, p194, Dec. 1947. Anyone have a stash of old copies of Electronics magazine?? I need to further compute the Fourier components for the numbers 8 and 9 and the letter A through F. Any other reference provided or insight into the technique would be appreciated!

Soooo, there isn't anyone here skilled in the art of graphical Fourier analysis then?? Our state library doesn't have copies of the periodical Electronics dating as far back as 1947. However I am working my way around the issue and here is how far I got this evening. I now have an Excel spread sheet that will plot the waveform from the entered Fourier coefficient values (5 harmonics, sine and cosine terms). The idea is that I will draw out my characters on graph paper, as described in that article and pictured Fig.1, to work out the coordinate values for the X and Y waveforms require to reproduce the alpha or numeric character on the CRT display.

I will then enter the coordinate values for each waveform in a special reserved column in my spread sheet, which will then plot them up onto the same chart as the waveform generated by the Fourier coefficients. I will then manually alter the Fourier coefficients by trial and error until the Fourier coefficient generated waveform is a best fit to the desired waveform. At that point I will have my required Fourier coefficient values.   

[ElectroIrradiator]

Soooo, there isn't anyone here skilled in the art of graphical Fourier analysis then??

Surely you are joking? No-one is insane enough to do a Fourier analysis by hand today, as we have these things called computers. There is no magic involved in the 'graphical method', it is just a tedious manual method of doing what your spreadsheet does better and faster. Guesstimate a coefficient for your target graph by using transparent overlays/Mk. I eyeball/experience, calculate difference and scale 'error graph', rinse/repeat for higher order coefficients.

[GK]

Soooo, there isn't anyone here skilled in the art of graphical Fourier analysis then??

Surely you are joking? No-one is insane enough to do a Fourier analysis by hand today, as we have these things called computers.

Yes, I am aware of these things called computers, I am sitting in front of one right now. I had no intention of doing the Fourier analysis by hand on paper, I was simply interested in the old methods as they may give some insight into how to more speedily estimate and manually optimize the coefficients with the aid of SPICE and/or a spreadsheet.

[GK]

Well this isn't easy. Due to the complex way the Fourier components interact in the generation of a waveform, simply tweaking each coefficient one after the other and then back again for a best fit to the desired function just doesn't result in a satisfactory outcome. Attached below is my first attempt - to synthesize the X deflection waveform required to generate the figure 9. A more complex methodology for tweaking the coefficients will be required here to arrive at a satisfactory fit.
   

[zapta]

Well this isn't easy. Due to the complex way the Fourier components interact in the generation of a waveform, simply tweaking each coefficient one after the other and then back again for a best fit to the desired function just doesn't result in a satisfactory outcome.

Can you use Excel solver or other solver to find the optimal coefficients?  E.g. define some distance function and let the solver minimize it.

[GK]

I really don't know. That's well beyond my familiarity with Excel right now.

[jahonen]

I think since you have only few coefficients to determine, it could be feasible to just use discretized Fourier analysis to find out the required coefficients. That is easily done by basically multiplying the desired signal against sine and cosine terms, and then summing the results and I think that the results should be multiplied by the time step used (dt).

Regards,
Janne

[GK]

Hmmm.... I half follow, but wouldn't I need a great deal more data points for my desired waveform to do any kind of moderately accurate DFT calculation on it? At the moment the waveforms are derived from my hand-drawn figures on graph paper. The coordinate values are entered into the spreadsheet and the smoothing function of Excels chart plotter gives a smooth, continuous function. Is it in some way possible to have Excels chart plotter output "smoothed" functions with the n-th fold increase in data points to a data file rather than a chart diagram?

I think my spreadsheet as is would be perfectly adequate if only I could get my hands on that cited Dec. 1947 issue of Electronics. Those guys back in 1958 did the same Fourier synthesis with impressive/adequate accuracy with pen and paper! There is obviously some kind of (most likely quite simple and straightforward) systematic methodology required in adjusting the coefficient values to eventually arrive at the desired result. Googling for hits on "Graphical Fourier Analysis" has been less than enlightening so far. The knowledge seems to be arcane now.

 
 
   

[GK]

In case anyone wants to have a play, my spreadsheet is attached. The aim of the game is to tweak the coefficient values in orange cells B3 through K3 until the blue synthesized waveform plotted on the chart matches the desired function plotted in pink. Have fun! 

[jahonen]

I did give it a go. I think you only need so much samples so that you don't alias. Then just calculate the Fourier integrals piecewise numerically. That is the approach I did here. FFT is optimized for speed, but I don't think that is the main objective here. For best results, the angle spacing should be uniform, or the difference in angle taken into account for each interval. I did just enter a experimental number of 0.05 which I used to scale down the sums so that results were in the same ballpark you had.

Result seems to be vertically offset because I didn't immediately find DC term. I leave it for your judgement if it is any better. Less work for sure.

Regards,
Janne

[GK]

Fantastic. Thanks! I really had no idea that an DFT could be done so effectively on my crude and limited set of data points. It's > 1am and I'm new to this Fourier transformation stuff, but how does one go about computing the DC term? This was an issue in that 1958 character generator design, as the toroidal transformers with the series-connected secondaries used to sum the sin and cos terms could not of course pass the DC terms. This caused some wonkyness in the on-screen positioning of some characters relative to the others. However I won't have that issue with my DC-coupled op-amp based summers, so if I can compute the DC terms for each waveform I'll be able to generate an all over better and more accurate display.
   

[jahonen]

This calculation which takes account non-uniform spacing of sampling points could be done manually relatively easily with trapezoid rule as follows:

- Take an angle a1 and a2, with values x1 and x2. Angles must be in radians. "Sampling" interval for angle should be so dense that x1 and x2 is not aliased. Function should be periodic so that first point is equal to the last point.
- Calculate c11=sin(n*a1), c12=sin(n*a2), c13=cos(n*a1), c14=cos(n*a2), where n is desired harmonic number
- Calculate piece area with trapezoid rule as (x1*c11+x2*c12)/2*(a2-a1) repeat same for cosine term c13 and c14. a2 and a1 should be so that a2 > a1.
- Now make a1=a2 and x1=x2, get new values for a2 and x2. Repeat until all points are calculated.
- Sum all sine and cosine areas together, that (should) give sin/cos coefficients for harmonic n

DC term is just average of your data points, i.e. coefficients at zeroth harmonic.

I don't know if that explanation is of any help but that approach should work.

Regards,
Janne

[GK]

Yes, your explanation is very helpful, thanks a lot. Now that the synthesis issue is essentially overcome I can get started on bread boarding the prototype.

[GK]

Apologies in advance for the potentially daft question, but that the DC component should be the average of my data points is obvious, but how do I incorporate that computed DC term into the computation of the Fourier coefficients such that the resultant waveform synthesized from said coefficients actually incorporates the necessary DC component?


EDIT: Duh! I just realised that is of course not possible. I will have to incorporate the DC terms for each characters X and Y waveform separately into my "ROM" with a settable DC-offset for each respective coefficient summing amplifier. That's simple and straightforward enough anyhow.

   

[GK]

Well here is the result - from the hand drawn character and listed X and Y data points on graph paper, through to the eventual synthesis of the waveforms in the SPICE circuit simulation, using the Fourier coefficients generated by the Excel spreadsheet DFT.

Is that good or what?   

The unit I have designed will essential be a 16 (column) by 8 (row) character screen display. I'll post up further details when I have the prototype up and running with some squiggles drawn out on the CRT.
 

[GK]

Figure 8!

Even so the figure 8 could return a closed function by itself, the system has a blanked "retrace" interval, so closed function characters require the retrace interval tacked on as an appendage.

[GK]

2) drill with a small hole (2mm) or with a center Drill that can be purchased at any  machine tools shop.

You mean:



?

Used them many times in the tailstock on the lathe but never in a drill press. Instead of using one to drill a small diameter pilot hole (the larger twist drill will still walk to a degree), how about using a larger diameter one to drill the hole in its entirety?

Here is how the panel drilling has worked out using a 5/16 center drill for the 4mm banana sockets. 120 holes drilled so far, a couple of thousand more to go.......... If one looks really closely some wonkyness can be perceived in the hole positions, but it's about as good as I think I should expect for a manual drill-press job. 

These are the front/patch panels for the computers 30 integrators. The drilling template(s) are generated in Protel, printed and then sticky taped to the blank panels. After that it's just a tedious process of center punching and then drilling. Panels are 3mm thick, 19" relay rack by Hammond.

[GK]

Quote from: GK on November 26, 2013, 07:10:44 PM
The harmonic generator will simply consist of a 5-stage binary ripple counter to produce the fundamental and harmonic frequency components. The sine fundamental and harmonic functions are produced by filtering the squarewaves with simple resistance-tuned multiple-feedback bandpass filters and the -cosine terms for each sine function are produced by simple resistance-tuned all-pass filters acting as unity gain 90 degree phase shifters. Not stuffing around with crusty inductors or trimmer capacitors here. Unlike in the 1958 design paper with its "shock-excited" resonant circuits, oscillation will be continuous with the gating and sequencing pulses/control signals derived appropriately from the harmonic generator clock source and ripple counters.

Well that was a bit of an oversimplification. To generate the fundamental (20 kHz) and the 2nd through to the 5th harmonic reference frequencies something a little more complicated than a 5-stage ripple counter was of course required due to the non-integer division. Here is the circuit I knocked up on breadboard this afternoon to do the job, out of parts I had at hand.
The fundamental and the 2nd, 4th and 5th harmonics are all derived from an 8MHz master clock by digital division. The fundamental, 2nd and 4th harmonic are generated by three stages of ripple counting while the 5th harmonic comes from a separate free-running divider (IC2) locked into synchronization by the 20kHz fundamental waveform.
The trickiest part was the 3rd harmonic (60kHz), which cannot be derived from the 8MHz master clock by integer division (8M/60k = 133.33). It is no good generating the 3rd harmonic from a separate master clock (say 6MHz) as it then won't be phase coherent with the fundamental. The 3rd harmonic is generated by a PLL acting as a x3 multiplier, using the fundamental as a reference.
All generated signals have the necessary locked-in phase relationships, as all harmonics have a coincident negative going transition with the fundamental. Now I just have to knock up the tuned MFB filters that will turn the squarewaves into sinewaves (while maintaining the phase relationships), and the all-pass filters to produce the cosine reference terms. Then it will be onto assembling the Fourier character ROM..... and then the multiplexing, addressable screen location memory and deflection logic...............

Put my Type 551's "dual beams" to good use...............

[GK]

I'm doing the final machine work to the front panels now (integrators panels only), but before I can complete the job and start assembling the individual 19" cases I have to figure out a convenient way to electrically connect (when mounted in the rack) each front panel to the other.

Back in the good old days analog computers were made with big, heavy power supplies with heavy, low impedance bus bars for the ground distribution as powering racks of various analog modules from common rails inevitably meant that the signal ground and power ground return was essentially one. Big heavy bus bars for the ground with low resistance were therefore mandatory to keep interference/interaction between the modules to a minimum.
I've worked around this problem by instead incorporating a separate power supply into each rack case, to power the (standardised ten) analog modules in that same case only.
Each front panel will have a single star grounding point to which all the module grounds and the PSU ground terminate. Power supply ground return currents are therefore kept inside the case and no power supply ground return currents share the signal ground termination between rack cases. This means that the entire front (patch) panel acts as a low impedance signal ground plane (and to a lesser extent the equipment cases and the actual relay rack(s) itself.

However I don't think that I can rely upon the mounting hardware holding each chassis into the relay rack to behave as a solid earth connection between the panel and the rack itself, thus ensuring that all (grounded) chassis panels are electrically connected together. After all the panels are painted, as is the rack, and the mounting bolts screw into (otherwise loosely fitted) cage nuts.

At the moment I am considering fitting a 4mm nutsert (press fitted captive nuts) into each of the four corners of each panel, so that each chassis panel (after fitting to the rack) can be linked to the ones directly above and below it with a total of four short (a couple of cm) earth braids having a lug at each end.
That will work but its probably not the most elegant solution. I am open to alternative suggestions. The design also needs to remain modular and not all chassis panels will be 3U.

[GK]

Now I just have to knock up the tuned MFB filters that will turn the squarewaves into sinewaves (while maintaining the phase relationships), and the all-pass filters to produce the cosine reference terms. Then it will be onto assembling the Fourier character ROM..... and then the multiplexing, addressable screen location memory and deflection logic...............

First part done. Here are reference signals sin wt, sin 2wt, sin 3wt, sin 4wt and sin 5wt, as produced from the squarewaves by the MFB filters



And here is -cos wt, -cos 2wt, -cos 3wt, -cos 4wt and -cos 5wt, as produced from the sine terms by the all-pass filters.



The breadboard so far:



The circuit (repeat 5 times):

[notsob]

For your 4mm shorting - perhaps use these shorting bars - http://au.element14.com/pomona/4115/shorting-bar-for-binding-posts/dp/1538396

or this is available but I would use a bolted on link - http://www.newark.com/pomona/5145/double-banana-plug-shorting-bar/dp/94F940