English translation
Operating Instructions for the Telefunken Electronic Analog Computer RA 463/2
This document is an English translation of the original German (Deutsch) Bedienungsanleitung for the Telefunken RA 463/2 electronic analog computer.
I. General Characteristics
The RA 463/2 analog computer is a fully electronic device for repetitive computation. Computation speeds can be continuously varied between 0.1 and 112 seconds. After the computation interval has elapsed, the computation is automatically repeated. The computing system contains both linear and non-linear computing units with high component accuracy, which are implemented in plug-in modules along with auxiliary devices. The modular assembly makes it possible to combine various large devices into one system. The system consists of a display cabinet and one or more computing cabinets.
Programming the device is performed reliably and clearly using short patch cords. Program changes can be made with the machine switched on, making the procedure very convenient and quick. For qualitative and accurate quantitative evaluation of computation results, a specially developed dual-beam display device is available. Connection of an electromechanical recorder is also possible.
II. Commissioning
In the display cabinet of the analog computer is the switching panel, which contains the mains switch and the mains fuse of the computer. The left switch and the left fuse are for the preamplifier circuits, the right switch provides the mains voltage for the anode supplies. The display device has its own mains switch.
Commissioning of the computer proceeds as follows: Switch on the preamplifier voltage using the “Vorheizen” (Preheat) switch. After a warm-up time of approximately one minute, switch on the anode supply voltage. The overload indicator lamps of the computing units light up; when they go out, the computer is ready for computation. The display device is switched on last.
Shutdown of the computer follows in reverse order: first the display device, then the anode voltage, and finally the preamplifier voltage.
III. Calibration Instructions
When computations of high accuracy are to be performed, it is advisable to calibrate the display device and the computing units used beforehand.
The mains devices are set to the prescribed supply voltage, the display device adjusted to correct deflection amplification, and the undeflected electron beam aligned to the center of the screen. All other calibrations serve to correct the zero-point error in the DC amplifiers contained in the computing units.
Calibration work is most conveniently carried out in the following order after the system has been running for approximately half an hour:
- Calibration of the mains devices for supply voltage
- Calibration of the display device
- Calibration of the computing units
The main function switch of the computer is at the “Zeitgeber” (timer) position during all calibration work. All computing units, except computing amplifiers II and the display device, may be loaded during calibration.
1. Calibration of the Mains Devices for Supply Voltage
Test switch in switch panel position 0, sensitivity switch depressed. The reading should be within ±2 scale divisions of the center. For larger deviations, connect the ±100 V mains device’s precision instrument and set the supply voltage by means of the calibration potentiometer on the front panel of the ±100 V mains device to 100 V ± 0.5 V.
Test switch in switch panel position I. Adjust the first +200 V and −200 V mains devices by means of the calibration potentiometer on the front panel to the smallest reading on the control instrument by pressing the sensitivity switch. Further, calibrate the +200 V and −200 V mains devices by switching the test switch through positions II, III, IV, etc.
2. Calibration of the Display Device
To compensate for the geometric error of the cathode ray tubes, the undeflected electron beams are centered: Switch S₁ and S₂ to position 0, switches S₃ and S₄ and all inputs off. Press the half-tone key, increase brightness until light spots are just visible. Use the zero potentiometer to center the light spot precisely in the center of the screen. Deviations are corrected with the corresponding potentiometer V.
It is then necessary to verify whether the light spots of S₁ and S₂ still sit exactly at the scale center. If necessary, repeat the amplification calibration and the scale center calibration alternately several times.
3. Calibration of the Computing Units
All computing units contain DC amplifiers whose zero points are adjustable. This is done by setting the zero potentiometers so that the output voltage of the amplifier at zero input becomes a minimum.
For measuring the output voltage, the compensation measuring device included in the timer is available. This allows measurement of the machine unit of + or −100 V in three decades, with each decade subdividing the tastatur value by 10 with high accuracy. Note that a key must always be pressed in each test column (e.g., 0.0.5 or 7.0.0).
The output voltage of the compensation keyboard depends — according to the polarity of the keys pressed on the keyboard — on the positive or negative side of the voltage bridge. The built-in null instrument shows the bridge balance; its sensitivity can be increased by pressing the black key.
For zero calibration of the DC amplifiers, enter 0.0.0 in the compensation measuring device, and connect the output of the amplifier being calibrated to one of the input terminals of the measuring device. The individual inputs are activated by pressing the corresponding white keys. For special cases requiring attention during calibration of some computing units, reference is made in the following sections.
a) Computing Amplifier I, VRe 463/2
Function switch in position Σ or f. Connect one of the outputs to the compensation measuring device. Enter 0.0.0 and calibrate using the zero potentiometer on the front panel of the computing amplifier.
b) Computing Amplifier II, VRe 463/2
Computing amplifier unloaded. Connect one of the outputs to the compensation measuring device. Enter 0.0.0 and calibrate using the zero potentiometer on the front panel of the computing amplifier.
c) Multiplier, MRe 463/2
The computing amplifier contained in the multiplier is calibrated in the same way as computing amplifiers I and II at the minimum zero point. Function switch of the multiplier in position 0. Connect one of the outputs to the compensation measuring device. Enter 0.0.0 and calibrate using the zero potentiometer on the front panel of the multiplier.
Calibration of the squaring parabola in the individual quadrants proceeds as follows:
| Quadrant | Main switch position | Calibration via potentiometer | Output voltage |
|---|---|---|---|
| I | I | I | +100 V ± 1% |
| II | II | II | +100 V ± 1% |
| III | III | III | +100 V ± 1% |
| IV | IV | IV | −100 V ± 1% |
Measurement of the output voltage is most conveniently done with the compensation measuring device set to 9.9.9.
d) Function Generator, FGe 463/2
In the function generator, the portions of the individual diode segments of the chopper-stabilized computing amplifiers are summed. This amplifier is calibrated as follows: Set all switches S₁ to S₁₀ to position Leerstellen (blank positions), S₁₁ and S₁₂ to 0, switch S₁₃ to 1. Connect one of the outputs to the compensation measuring device. Enter 0.0.0 and calibrate using the zero potentiometer on the front panel. Then switch S₁₃ to positions 4 and 10 one after another.
IV. Computing Operations
The computing units in the RA 463/2 analog computer can perform the following computing operations:
- Multiplication by a constant factor
- Sign reversal
- Summation
- Integration
- Differentiation
- Multiplication
- Division
- Generation of an arbitrary function f(x)
- Generation of special non-linear functions (dead zone, limitation, Begrenzung)
1. Multiplication by a Constant Factor
a) Constant Factor “a” < 1
Multiplication by a factor a < 1 is performed using a potentiometer from the potentiometer field. The input quantity Uₑ is applied to the input terminal of the potentiometer. The output voltage aUₑ = Uₐ is taken from one of the two parallel output terminals. The setting of the factor a is approximately performed using the scale as a starting point. The potentiometer switch must be in the unloaded state. The switch is placed at +1. The machine voltage of +100 V is now applied at the start of the potentiometer field. The second output of the potentiometer is connected via a computing cord to the compensation measuring device. On the digital keyboard, enter the desired factor a, and with the built-in null instrument increase the sensitivity of the potentiometer. After the precise setting has been found, reset the potentiometer switch to the input position, so that the applied input quantity will be multiplied by the set factor a. At the output appears the voltage Uₐ = aUₑ.
Warning: Never grip the potentiometer while a terminal or an amplifier output is connected. There is a risk that the potentiometer will burn out.
b) Constant Factor a > 1
Multiplication by a constant factor a > 1 is carried out using computing amplifier I. The switch of computing amplifier I is placed in the Σ position. The fixed weighting factors 1, 4 and 10 of the individual inputs are thus available. Arbitrary intermediate values can be obtained by inserting a potentiometer in front of one of the inputs. Care must be taken that computing amplifier I always inverts the sign of the input quantity; if one applies the input quantity aUₑ at the input with weighting factor aₙ, the output displays the voltage Uₐ = −aₙUₑ.
2. Sign Reversal
Both types of computing amplifiers invert the sign of the input quantity. If computing amplifier I is to be used for pure sign reversal, connect an input with the weighting factor 1, and place the function switch of the amplifier in the Σ position.
3. Summation
Both types of computing amplifiers sum the input quantities whenever multiple inputs are loaded with quantities. At computing amplifier I, the weighting factors of the inputs are provided. The amplifier I forms the weighted sum of the input quantities: Uₐ = −Σaᵢuᵢ. The function switch of computing amplifier I should be in the Σ position.
4. Integration
Integration is performed using computing amplifier I. The function switch is in the ∫ position.
The integration time constant is 0.1 sec, so at an integration with weighting factors 10, 40, and 100, the computation interval of 112 sec suffices. If an integration time constant of 1 sec is desired, one must connect a capacitor of 1 µF in parallel with the capacitor at terminal G, and a terminal G must be connected to an output terminal of amplifier I. A suitable 1 µF capacitor is included in the potentiometer field.
An initial value can be specified at terminal A. As voltage source for the initial value, one uses a potentiometer from the potentiometer field, whose switch depending on the desired polarity is placed in the +1 or −1 position. The precise setting of the initial value is performed with the compensation measuring device in the loaded state as described under 1).
5. Differentiation
Differentiation is in principle possible with computing amplifier I, although it should be avoided since it is the opposite of integration from the perspective of an electronic amplifier. For differentiation purposes, the amplification of the computing amplifier must increase with increasing frequency. This is not realizable. Differentiation with the computing amplifier is only approximately feasible for this reason.
Whether differentiation is possible in any particular case must be decided from case to case. The prerequisite is that the input signal does not contain high-frequency components. The differentiation with the computing amplifier is carried out as follows:
The function switch is placed in position Σ or V. In the first case, the built-in feedback resistance of 1 MΩ is used. The input quantity is applied via a capacitor of the size appropriate for the desired time constant to the input. In the second case, the function switch is placed in position V. The resistance is then connected between input G and an output; the input quantity is applied via the capacitor to terminal G.
6. Multiplication
The multiplier serves to multiply two functions x = x(t) and y = y(t). Multiplication is performed using the two-parabola method. Both variables x and y must be fed into the computing circuit with both signs; if both signs of the variables are not available in the computing circuit, 2 sign-reversing amplifiers are needed. At the output of the multiplier, the function switch is in position z = xy. The output voltage Uₐ = U₁U₂ is taken at one of the output terminals z.
7. Division
Division can be performed with the multiplier with the aid of a computing amplifier.
Block diagram for division:
[Circuit diagram showing multiplier and computing amplifier I in feedback loop to implement division: x = z/y]
The circuit generates x = z/y. Note that y must not be zero since this would make the open-loop amplifiers in the feedback path of the multiplier unstable; the output must be connected via a capacitor of approximately 50 pF to the summation point (input ∞).
8. Generation of an Arbitrary Function f(x)
The function generator makes it possible to approximate any arbitrary function f(x) by a polygon. Ten polygon segments are available for this purpose, as well as a rotation about the zero point and a translation in the ordinate direction. These polygon segments are represented by diode segments; their breakpoints and slopes can be varied individually using the switching potentiometers. The type of polygon is determined by the position of the switches (corresponding to the scale markings).
For best results in generating a function, proceed as follows:
Apply to the inputs +x and −x of the function generator the time-proportional quantities +at and −at obtained from the timer. The output of the function generator is then read on the display device. The desired function f(x) is approximated by starting from the right and left toward the center of the oscilloscope screen, fitting a polygon to the other curve segment after selecting and adjusting the desired break point in the zero point of the display device. For this purpose, it is usually most convenient to always begin with the knee point closest to the zero point.
9. Generation of Special Functions
The special function generator includes the following functions:
- 3x dead zone
- 5x limitation, of which 2x have fixed limitation at the machine units (100 V) and 2x limitation functions
- The 3 limitation systems with variable limitation through the ordinate direction use the “dead zone” system. The variation of the limitation height or the dead zone height is controlled by switching potentiometers. The assignment of the potentiometers to the ordinate values is made according to the scale markings.
For use of the special function system, one must always use computing amplifier I. The inputs +x and −x of the function generator are connected to the display device.
In the dead zone system, go to the input ∞ (Eingang∞) of computing amplifier I, whose function switch is in position Σ. The output of the computing amplifier provides the desired function.
V. Example
As an example, the circuit for the differential equation:
d²y/dt² + f(x) dy/dt + ay = 0 with initial condition y(0) = y₀
is implemented. This equation describes, for example, an oscillation with variable damping determined by f(x). To match the machine units (max. 100 V), dimensions must be converted; this leads to the dimensionless variable τ = K·t. Further, by setting K, the dimensionless variable τ can be adjusted.
The differential equation then becomes d²y/dτ² + f(x) dy/dτ + Ky = 0, y₀ = K₁.
The machine integrates T = K₁t^m, where t^m is the machine time. When K is chosen so that K/K₁ and t^m/K₁ are less than 1, then T = Xt = K₁t^m·1/K₁ = t^m.
The value K₁ at the integrators provides the time scale. K = K₁ corresponds to a real-time solution; K > K₁ corresponds to time expansion; K < K₁ corresponds to time compression on the machine.
[Circuit diagram showing implementation of the differential equation with computing amplifiers, function generator, and multiplier]
VI. Repair Instructions
For the analog computer, a 1-year warranty is given. Tubes are excluded. For this purpose, the warranty claims are already covered within the tube price included in the tube guarantee, and all damage attributable to faulty operation of the system is excluded. (See general delivery conditions for products and services of the electrical industry.)
If a defect occurs in one of the plug-in units, it should be sent in as follows:
Computing amplifiers I, computing amplifier II and multipliers should be sent to:
Telefunken G.m.b.H. Geschäftsbereich Anlagen Hochfrequenz Abt. AH/MG/V4 Ulm (Donau), Elisabethenstrasse 3
for repair. Damage occurring to the other units should be reported to the nearest Telefunken branch office, which will take appropriate steps to remedy the situation.
[Translation covers all 12 pages of the original document.]