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--- en:analogrechner:rg14-mini [2023-05-29 23:05] – created rainer
+++ en:analogrechner:rg14-mini [2025-02-24 22:23] (current) – References title rainer
@@ Line 1: / Line 1: @@
-====== Affordable Flexible Analog Computer RG14 ======
+For a PDF version: {{:analogrechner:affordable_flexible_analog_computer_rg14-mini.pdf|}}
+<nimla>
+Affordable Flexible Analog Computer RG14-Mini
-The description is currently available as PDF:
+Autor: Rainer Glaschick, Paderborn\<br>rainer@glaschick.de
+Datum: 2018-02-02 2023-05-26
-{{:analogrechner:affordable_flexible_analog_computer_rg14-mini.pdf|}}
+. Introduction
+==========
+As classical analog computers are no longer produced, there is a lack of affordable new ones,
+with the exception of [https://the-analog-thing.org/ The Analog Thing].
+The latter, however, sticks to the classical model with all its inconveniences.
+My new design is close to the classcial design, with some small, but for my opinion significant  changes:
+. The computing elements are plugged into the connection board, thus it is possible to archive calculations.
+. As the computing elements are pluggable, the configuration can be adapted; there is no other limit for the computing elements than the number of slols.
+. Computing elements have a current input as primary input, thus avoiding a lack of input menans.
+. Potentiometeres deliver a current, not a voltage; thus can be calibrated in advance.
+. Digitally set potentimeters allow quick and precise setup.
+. The modules can be configured with jumpers for various functions.
+. Integrators have a very quick initialisation circuit and can thus be used as track-and-hold
+. Initial conditions for integrators can be set with potentiometers on the module, but also via a current input.
+. The adder has options to function as (inverting) adder, precision rectifier or comparator; no free wiring of components is required.
+. Potentiometers have a (digital) switch than can disable the output;
+so more than one signal can be switched directly,
+and no switches are necessary on calculating modules.
+. Power supply is only (precise) 30V DC. Calculations use &plusmn;10V.
+. A module is small: 100mm x 14mm and can be made on perfboard with 2.54mm spacing.
+. Connections use a common and affordable prototype plugboard.
+. Repetitive operation not yet provided
+This project was designed to verify the design of the modules;
+an advanced version without plugboard, but with digitally controllable
+options and connection is under test.
+More information could be found at [https://rclab.de/en/analogrechner/inhalt].
+Construction
+======
+The following picture shows a plugboard with 10 places,
+using 7 modules to generate triangle curves:
+[img:analogrechner/./DreieckgeneratorRG14.jpg:80%]
+Each module is 100mm x 14mm; the raster, as defined by the plugboard,
+is 600mil = 15.24mm.
+This kind of plugboard can be sepearated in the middle connection part
+and two power busses.
+On the top is a double power bus bar (+15V upper, red; -15V lower, blue);
+in the middle the ground line (blue, lower)  and the signal to set
+initial conditions (red upper).
+The modules are, from left to right:
+- Potentiometer KL as linear potentiomenter (special)
+- Integrator with intial value 0.8
+- Potentiometer KG with two for coarse / fine, output switch unused
+- Adder configured as commparator
+- Potentiometer KS; digitally settable from 0.00 to 9.90 digitally
+and additonally a fine setting upto 0.10
+- Adder
+- Power adapter with switch for initial / run mode
+The common term "Potentiometer" was used for the settable voltage-to-current converter;
+it will be called "factor connector" or "factor" hereafter.
+The active calculating elements are called "functor" as
+they realise a function like addition, integration etc.
+The symbols used in the following schematics are variations
+of the normally used ones:
+[img:analogrechner/./DreieckgeneratorRG14.svg]
+A circle denotes a factor with voltage input and current output.
+There is an inversion bullet at the input, followed by a ground symbol
+to denote that the functor has a virtual ground at the input.
+The numbers below are the slot numbers, and the numbers near the in-
+and outputs are the pin numbers of the 5-pin connector.
+If a switch is used, the half circle on a box is used as for 'F2'
+in slot 5.
+Due to the current input, more factor connectors are required
+than normally.
+Although more expensive than a potentiometer, the overall gain
+in useablity and the fact that there are never to few inputs
+justifies this expense.
+While normally of no concern, it might be good to know that
+the output voltage range is &plusmn;10V and the input current range
+is &plusmn;50µa for the numbers &plusmn;1.
+.1 Functors (calculating elements)
++++++++++++++++
+The active calculation elements called "functors" provide an output
+voltage as a function of the input current (including time).
+The five pins on the plugboard are used as follows:
+. Voltage input for the factor 1 (i.e. 200k&Omega;)
+. Primary current input (&plusmn;50µA)
+. Defined per module
+. Defined per module
+. Voltage output
+Pins 3 and 4 may be analog in- or outputs, or digital signals;
+the latter sinking 1mA to ground (from positive supply) if true.
+Pin 1 is always a factor 1 voltage input to save factor modules
+if the factor is 1 as is often the case.
+.1.1 Adder
+---------
+By jumper on the board, the adder can be configured as:
+- plain adder
+- limiter (rectifier) positive
+- limiter (rectifier) negative
+- comparator
+- zeroing amplifier (open amplifier)
+The circuit:
+[img:analogrechner/./Summierer.svg:90%]
+The 5 pins are used as follows:
+. Voltage input factor 1
+. Current input
+. Digital output if < 0 when configured as comparator
+. Digital output if > 0 when configured as comparator
+. Voltage output.
+The limiters are precision rectifiers that limit the output
+to positive or negative values (after inverted) with factor 1,
+i.e. a current of +25µA gives -5V for the negative and 0V for the positive
+version
+As they are normal adders otherwise, an extra input current can be used
+to shift the input discriminating value; the output is always either positive
+or negative (including zero).
+If configured as a comparator, pins 3 and 4 are digital outputs
+if the input current is less or greater zero,
+i.e. the output has maximum positive  or negative voltage.
+They might be used to switch factors on or off.
+The comparator has a small hysteresis of 1&permil; to avoid oscillations.
+Pins 3 and 4 should not be used otherwise.
+The zeroing (open) amplifer has already a small capacitor in the feedback
+path.
+Integrator
+-----------
+The integrator can be configured for 1/sec or 100/sec only:
+[img:analogrechner/./Integrierer.svg:90%]
+The 5 pins are used as follows:
+. Voltage input factor 1
+. Current input
+. Current input for external initial value
+. Digital input for use as track-and-store
+. Voltage output.
+The initial value can be set by a (vertical) potentiometer with
+% accuracy. The polarity is selected by a jumper.
+Additionally, a current at input 3 can be used for the initial value.
+Then, the potentiometer should be set to zero.
+If the polarity would be included in the potentiometer,
+a switch would be necessary to deactivate it, and the accuray halved.
+Setting the intial value uses a -- not so common -- quick scheme,
+where the capacitor is charged from the op amp output to ground,
+thus the charge time is defined by the output impedance of the op amp.
+It requires two additional switches, but allows the
+circuit to be used as a track-and-store device.
+(An example has not yet been found).
+Initialisation time is less than 10ms for the 1/sec range.
+The integration capacitor is composed of two capacitors
+that may be selected to achieve 1% accuracy.
+The proposed op-amp TL051 has a low offset voltage of at most 1.5mV,
+which is small enough for most applications.
+The drift is less than 1.5% in 100sec
+in the 1/sec range with one connector connected and zero input.
+The better available AD820 has 0.8mV offset and thus half the drift.
+Using the AD820 for the integrators and the TL051 elsewhere is a
+good compromise that avoids soldering calibration resistors.
+If a TL071 or TL081 is used, the offset voltage is less than 15mV,
+and the offset should be corrected during manufacturing by soldering
+extra resistors.
+Multiplier
+--------------
+The Gilbert-cell based AD633 is used for the multiplication
+of two numbers.
+Pin usage is special:
+. Factor 1 voltage input for pin 2
+. Current input for multiplicand or divisor
+. Current input for multiplicator or dividend
+. Factor 1 voltage input for pin 3
+. Output
+May be configured for multiplication, division, squaring and
+square root.
+The sign of one operand and thus of the output may be inverted
+by configuration.
+Circuit:
+[img:analogrechner/./Multiplizierer.svg:90%]
+Factor connectors
++++++++++++++
+A factor connector converts a voltage to a current to (virtual) ground
+with a setable factor.
+The simplest version uses a potentiometer (e.g. 10k&Omega;) with
+a resistor (200&k&Omega;) from the tap to the output.
+The largest linearity error by this resistor is 0.75% for a factor
+of 0.67
+(see [http://rclab.de/analogrechner/potentiometerbelastung]).
+Because the output is always connected to a virtual ground,
+the factor is independent of the number of connected connectors,
+thus it is not necessary to adjust the potentiometer depending
+on the circuit used;
+a fixed scale can be used.
+This means that it is no longer possible to determine the actual
+setting by probing the output with a voltmeter.
+.1.1 Standard factor connector KS
+----------------
+The standard version of a factor connector
+not only allows factors larger than 1 (upto 10.0),
+The upper digits are set digitally (from 0.1 upto 9.9),
+plus a potentiometer for the lower digits (from 0.00 to 0.10).
+As the latter has 5% accuracy, but only a weight of a tenth,
+the overall accuracy is still better than 1%.
+The circuit used is:
+[img:analogrechner/KopplerStandard.svg:90%]
+This connector has an analog switch to switch the output on or off,
+controlled by a digital input, e.g. from a comparator.
+Pin usage:
+. Voltage input
+. Digital input to switch off (if active low)
+. Not used
+. Current output from the switch
+. Current output unswitched
+Pin 5 must be left open if pin 4 is used, as otherwise
+the current node would be shorted.
+The preferred BCD switches for manual change without tool
+are fairly expensive;
+thus, BCD switches for screw driver operation can be used
+alternatively.
+Double factor: KD
+-----------------
+The double factor has two (not switchable) factor connector in one module
+to save slot space:
+[img:analogrechner/KopplerDoppelt.svg:90%]
+The fist factor connector has one digital switch for 0.0 to 9.0,
+and one potentiometer for 0.0 to 1.0,
+thus the accuracy is about 5%.
+A variant uses the switched factor 0.0 to 0.9 and
+the analog part from 0.0 to 0.1, thus has 0.5% accuracy.
+The second factor is just a potentiometer upto 1.0 with 5% accuracy,
+and can be supplied with the constant 1.0 from the power supply.
+It has also a second output with factor 0.1, thus from 0.0 to 0.1.
+Pin usage:
+. Voltage input first factor
+. Voltage input second factor
+. Current output second factor upto 0.1
+. Current output second factor upto 1.0
+. Current output first factor.
+Pin 2 must be left open, if the constand 1.0 is supplied;
+and pin 3 must be left open, if pin 4 is used.
+Linear variant KL
+----------------
+Instead of a common potentiometer, a linear potentiometer is used:
+[img:analogrechner/KopplerLinearpoti.svg:40%]
+Pin assignment:
+. Voltage input
+. Input for &plusmn;1
+. Current output upto 0.1
+. Current output in conjunction with pin 2
+. Current output except
+Normally, pin 1 and pin 5 provide a common potentiometer,
+with an extra output on pin 3 for small factors;
+could be used together with pin 5.
+If pin 1 is connected to +1 and pin 2 to -1,
+pin 4 supplies a constant between -1 und +1.
+Coarse-fine connector  KG
+-----------------
+Another connector with a switch adss the values of two potentiomenters,
+one in the range 0.0 to 1.0 and the other one in the range 0.0 to 0.1:
+[img:analogrechner/KopplerGrobFein.svg:50%]
+In general, both potentiometers should be used alternatively,
+i.e. the other one set to zero.
+Adding a small value to a large one is, however, less useful
+than originally assumed, as the accuracy of the first one is 5%
+and thus half of the value to be addend with the second one.
+This module has more historical than actual value.
+Power connector
++++++++++
+A module is always used as a power supply.
+It is normally provided with 30V DC , and internally
+generates a ground line for &plusmn;15V as well as
+precise &plusmn;1 voltages (10V):
+[img:analogrechner/PowerSingle-TH.svg:90%]
+At the 5-pin connector, it supplies:
+. +15V
+. +10V calibrated
+. GND
+. -10V calibrated
+: -15V
+The integrators derive the initial value from &plusmn;15V,
+as well as some factor connectors.
+These are thus dependent on the accuracy of the supply;
+but are anyhow not precise.
+Construction
+===========
+There are several ways to make a module, with different
+levels of required skills and base material.
+Perfboard
+----------------
+It is perfectly possible to use perfboard with 0.1" dot raster.
+The first modules were made this way,
+and also special modules made only once.
+Best is to use double sided (not necessay with plated holes) perfboard
+as this allows to solder on the opposite side of the components.
+This important for the connectors to the plugboard, so that the pins
+can be solderd at least on the top side, to avoid stress when drawn.
+If the copper is on the bottom, this is fine for THT devices,
+in particular for jumpers.
+But soldering the connectors on the bottom side is a bit tricky and
+requires much experience in soldering.
+Copper on top is good if there are no jumpers to solder.
+Single-sided PCB
+----------------
+Until today, all modules were made on home-etched PCB,
+as the effort to route the connections with wire is not so low,
+and as I had the circuits drawn in KiCad anyhow,
+making a PCB was little extra effort that payed off already
+with the second one.
+See the preceeding section on the selection of top or bottom copper.
+Nearly all existing ones used copper on bottom in order to hold
+THT components on the top.
+Note that the connector soldering pads were squares (instead of
+circles) to allow more copper to solder and hold.
+Lately, a factor connector with copper at top was made, with
+resistors, switch transistors and BCD coded switches for all
+three digits on top.
+Double-sidede PCB
+-----------------
+Using double sided PCB with should be used whenever affordable,
+in particular with plated-through holes.
+Such PCBs are currently under construction.
+Potentiometers
+---------------
+Standard carbon potentiomenters can be used if equipped
+with a scale that is individually calibrated.
+Because the boards are only 14mm wide, thumbwheel potentiometers
+with a scale around the circumfence are a good choice.
+While many variantes were probed, currenly the APLS RK09K111
+provides the best options, because the axis of the horizontal
+operation cylinder is 6.5 mm distance from the PCB, allowing
+to use a 3D-printed thumbwheel of 12mm diameter, thus 40mm
+circumfence and 30mm usable scale, allowing 3mm distance for 10%
+variation and thus 5% accuracy (if the scale is calibrated manually).
+.
+Examples
+========
+For some examples, a picture and schematics are shown.
+.1 Triangle generator
++++++++++++++++++++++++
+[img:analogrechner/DreieckgeneratorRG14-kl.jpg:71%]
+[img:analogrechner/DreieckgeneratorRG14.svg:80%]
+Sine generator
++++++++++++++
+[img:analogrechner/SinusRG14Gleichrichter.svg]
+Lorenz-Attractor
+++++++++++++++++
+[img:analogrechner/Lorenz-Attraktor-kl.JPG]
+[img:analogrechner/LorenzAttr_RG14-B.svg:70%]
+Moon lander
++++++++++++
+[img:analogrechner/Mondlandung-kl.JPG]
+[img:analogrechner/Mondlandung-RG14-1.svg]
+Fahrdiagraph (Train simulator)
++++++++++++++
+[img:analogrechner/Fahrdiagraph-kl.JPG]
+[img:analogrechner/Fahrdiagraph_RG14.svg:80%]
+References
+=========
+\::Ulmann
+	Bernd Ulmann: Analogrechner.
+	Oldenbourg 2010.
+\::Massen
+	R. Massen: "Stochastische Rechentechnik".
+	Carl Hanser Verlag, München 1977
+\::Hannauer
+	Georg Hannauer: "Stored Program Concept for Analog Computers".
+	EAI, Princeton N.J., 1968.
+\::BryantSTFK
+	Bryant, M.D.; Shouli Yan; Tsang, R.; Fernandez, B.; Kumar, K.K.:
+	"A Mixed Signal (Analog-Digital) Integrator Design"
+	In: IEEE Transactions on Circuits and Systems, vol.59, no.7 pp.1409-1417 (2012)
+\::CowanMT
+	Cowan, G. E R; Melville, R.C.; Tsividis, Y.: "A VLSI analog computer/digital computer accelerator".
+	IEEE Journal of Solid-State Circuits, vol. 41, no. 1, pp. 42-53 (2006)
+\ASCIIMATHML ASCIIMathML.js
+\CSS print pre, blockquote {page-break-inside: avoid; }
+\CSS print h1, h2, h3, h4 {page-break-after: avoid; }
+\CSS all pre, blockquote, code {font-family: Liberation, monospace; }
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