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en:analogrechner:rg14-mini [2023-05-29 23:05] – created raineren:analogrechner:rg14-mini [2025-02-24 22:23] (current) – References title rainer
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-====== 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|}}+ 
 + 
 +1. 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: 
 + 
 +1. The computing elements are plugged into the connection board, thus it is possible to archive calculations. 
 +2. 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. 
 +3. Computing elements have a current input as primary input, thus avoiding a lack of input menans. 
 +4. Potentiometeres deliver a current, not a voltage; thus can be calibrated in advance. 
 +5. Digitally set potentimeters allow quick and precise setup. 
 +6. The modules can be configured with jumpers for various functions. 
 +6. Integrators have a very quick initialisation circuit and can thus be used as track-and-hold 
 +7. Initial conditions for integrators can be set with potentiometers on the module, but also via a current input. 
 +8. The adder has options to function as (inverting) adder, precision rectifier or comparator; no free wiring of components is required. 
 +9. 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. 
 +10. Power supply is only (precise) 30V DC. Calculations use &plusmn;10V. 
 +11. A module is small: 100mm x 14mm and can be made on perfboard with 2.54mm spacing. 
 +13. Connections use a common and affordable prototype plugboard. 
 +14. 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.  
 + 
 +1.1 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: 
 +1. Voltage input for the factor 1 (i.e. 200k&Omega;) 
 +2. Primary current input (&plusmn;50µA) 
 +3. Defined per module 
 +4. Defined per module 
 +5. 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.  
 + 
 + 
 +1.1.1 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: 
 + 
 +1. Voltage input factor 1 
 +2. Current input 
 +3. Digital output if < 0 when configured as comparator 
 +4. Digital output if > 0 when configured as comparator 
 +5. 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: 
 + 
 +1. Voltage input factor 1 
 +2. Current input 
 +3. Current input for external initial value 
 +4. Digital input for use as track-and-store 
 +5. Voltage output. 
 + 
 +The initial value can be set by a (vertical) potentiometer with 
 +5% 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: 
 +1. Factor 1 voltage input for pin 2 
 +2. Current input for multiplicand or divisor 
 +3. Current input for multiplicator or dividend 
 +4. Factor 1 voltage input for pin 3 
 +5. 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. 
 + 
 + 
 +1.1.1 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: 
 +1. Voltage input 
 +2. Digital input to switch off (if active low) 
 +3. Not used 
 +4. Current output from the switch 
 +5. 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: 
 +1. Voltage input first factor 
 +2. Voltage input second factor  
 +3. Current output second factor upto 0.1 
 +4. Current output second factor upto 1.0 
 +5. 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: 
 +1. Voltage input 
 +2. Input for &plusmn;1 
 +3. Current output upto 0.1 
 +4. Current output in conjunction with pin 2 
 +5. 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: 
 +1. +15V 
 +2. +10V calibrated 
 +3. GND 
 +4. -10V calibrated 
 +5: -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. 
 + 
 + 
 +1.1 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; }  
 +</nimla>

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