Mounted Hardwear

I've made the front panel for the control rack. I used FrontDesigner 3.0 to do the artwork. Simple to use program - recommended. Printed the artwork out on to matte photographic paper. Two A4 sheets are needed to cover the 19 inch panel (but join is pretty much invisible). Covered the image side of the paper with a double sided acrylic adhesive film. This was then used to stick the photographic paper to the back of a piece of 0.75 mm polycarbonate sheet. Holes drilled out with a small bit thence hand reamer. Easily enough (apart from the bigger holes which, in hindsight, are best dealt with using a round file - not a big blacksmith's drill).

A bit of a long winded process, but not expensive (except in terms of my time!) - and gives a pretty durable/hard wearing front panel. By the way, the background colour is vanilla cream (#FCFBE3) and the text slate blue (#004080), font is Verdana.

|x|, x^2 and xy

Two independent absolute value circuits...input is x, output is |x|, and - for good measure - x squared (divided by ten). Plus three independent basic multiplier circuits...input is x and y and output is xy/10.

Next bit of circuitry is a divider. Then I need to build four summers and some reference voltage stuff and odds and ends, to complete the integrators rack.

In other news, front panel for control rack has been drilled and awaiting completion of artwork.

Integrator/Summer Boards

Have completed wiring up the four integrator/summer boards. Testing is a bit complicated given the various permutations into which the thing can be configured. My testing scheme is to test in groups of three integrator/summers, with two units being set to INT mode and the other one set to SUM mode. The three units are wired in series. Two of the initial conditions are set to +10 V, the other to 0 V. Correct operation yields voltages which vary as sine or cosine of time.

Have tested two of the four boards. A couple of errors on the second board - namely a missing resistor (tracked down after determining one integrator had a faulty initial condition value), and a misplaced diode. The latter gave rise to the interesting - if impossible - condition of the amplifier being simultaneously over and under loaded.

Picture shows integrator/summers numbers 3 and 4. Wiring needs a little tidying. That's waxed lacing cord (RS 303-1675) by the way...not dental floss(!).

I'll test/correct the remaining two boards. After that, I put these to one side and return to the control unit rack - front panel needs drilling, labeling and populating with its furniture. Then I can finish off the integrator rack electronics (needs dedicated summer circuits - designed, not built, and similarly multiplier circuits).

Multiple Integration

Nearing the completion of the remaining three integration boards - there'll be four of these boards in total, each with two integrators, giving eight integrators in one 4U rack. The integrators can be operated either as integrators or summers - via toggle switches on the front panel. The plan is to also have four dedicated summers and a couple of multipliers in the rack unit. Plus the control unit rack, plus a coefficient potentiometer (20 off) rack. When these three racks are finished (early(ish) next year?), I'll have a usable analog computer - then follows the really interesting construction of a special functions unit...(I have some ideas for the usual suspects (sine, cosine, tangent), plus (of course) I'd like to have all the hyperbolic functions, not to mention all those due to Messrs Bessel, Struve, Hankel et al).

Quite a lot of work piling up!

So that's why they are 'circular functions'...

It just occurred to me that if I connect the output (y) and its derivative (dy/dt) from the analog computer's solution of the second order DE (see previous post) to X and Y inputs of an oscilloscope, I should get a circle (with respect to time, t). Pretty obvious really...but pleasing nonetheless:

First Program - Solving a second order DE - part the second

Having set up Figure 8.2 from Ulmann's book (integrator capacitors 1 uF and resistors 1 M ohm), switched on the analog computer, pressed COMPUTE and it just worked! Sine and cosine clearly shown on the two meters (10 V peak to peak since the initial conditions were set to + 10 V for the first integrator and 0 V for the second integrator).



The time constant of the integrators was 1 second and so the expected time period of the sine /cosine wave is 2 time pi seconds = 6.28 seconds. And it was!

Pressing the FAST button speeds the integrators up by a factor of 1000 (i.e. the 1 uF capacitors get replaced by 1 nF capacitors). Obviously too fast for the meters, but on an oscilloscope the output looks like this:

What's interesting is that the output stays like this for several minutes - typically growing slowly in amplitude until it starts clipping (FAST mode); in the normal (6.28 second time period) mode the output tends to decay very slowly (i.e. several minutes). In both cases such longevity of the solution suggests very little leakage in those Russian military capacitors!

So there you have it - not Hello World, but the solution of a second order DE! It's early days, but I can see that programming an analog computer is completely different (and a lot more exciting) than programming a digital one! I like the way the analog computer is so direct - if you want to solve a DE then you solve a DE - not mess about with some numerical scheme which may or may not be stable.

A final thought for the moment: I feel I am entering an exclusive club of analog computer programmers :) And how cool is that?..

Next steps: finish off three more integrator boards; sort out hardware for the integrator 19 inch rack; make a proper front panel for the (now finished) control unit 19 inch rack.

First Program - Solving a second order DE - part the first

(1) Have bought a copy of the recently published  Analog Computing by Bernd Ulmann. Excellent book - I particularly like the extensive foot-noting. Essential reading!

(2) Have completed the first of the (eight) integrator boards - each of which has two integrator circuits.

Messy and not yet assembled into a 19 inch rack of integrators/summers.

Anyway, I've now got three integrator/summer units to play with - enough to solve a second order differential equation of the form d2y/dx2 + Ay = 0. This is the first programming example in Ulmann's book (page 126). 

As I say, all a bit messy, but my implementation of Figure 8.2 of Ulmann's book looks like this:

(The top board is a power supply/control board for the integrators; the middle board is my original single integrator/summer and the lower one the latest pair of integrators/summers.) As mentioned, all the integrators boards etc will end up in their own 19 inch 4U rack - I just wanted to test things out!

The boards are bussed up to the main control unit (which is pretty much completed) via a 25 way D connector, via at the moment, a 25 way break out board.