Demonstration Analog Computer (DIY)

This document is an English translation of the original German-language text by F. Vogel (2009).

Demonstration Analog Computer

F. Vogel — 06.05.2009

1. Overview

This miniature analog computer is intended for demonstrating electronic analog computing technology as it was used from approximately 1950 to approximately 1980, before being rapidly displaced by digital computers. The device allows the solution of simple, typical examples from the field of analog computing. The number of computing components in the device has been matched to these example problems.

The demonstration computer is realized with standard operational amplifiers in BiFET technology, with an input impedance of 10¹² Ohms, an open-loop gain of > 3×10⁵, and a typical offset voltage of 5 mV. The computing voltage, or machine unit, is ±10 Volts. Resistors that influence computing accuracy are selected to ±0.05% tolerance. The time constants of the integrators have a tolerance of ±1%. The computer is housed in an aluminum enclosure measuring 188 × 120 × 77 mm. The front panel contains the operating controls and the programming field. Power is supplied by an external plug-in power supply of 9 V DC / 1200 mA.

Available computing components:

2 Integrators
3 Summers
1 Open amplifier / inverter
4 Coefficient potentiometers
1 Multiplier unit
1 Diode function generator for the sine function

Auxiliary equipment:

Reference voltage sources for +10.00 V and −10.00 V
Display meter with LED polarity indicator
12-position address selector switch
Overload indicator
Triangle-wave generator with ±10 V output
±15 V power supply unit

2. Operating Controls and Programming Field

The front panel layout includes:

Operating controls:

Power switch
Display meter
Address selector switch
Overload indicator
Polarity indicator
Display meter switch
Toggle switch for potentiometers K3 / K4
Integrator control
External input for display meter

Programming field:

A — Coefficient potentiometers
B — Integrators
C — Summers
D — Open amplifier / inverter
E — Multiplier unit
F — Function generator for sine function
G — Reference voltages
H — Ground point for potentiometers K3 / K4
J — External input for display meter
K — Triangle-wave generator

3. Computing Components

3.1 Summer

y = −(x₁ + x₂ + 10·x₃)

Each of the three summers has two variable inputs with a weighting factor of 1 and one variable input with a weighting factor of 10. The achievable static computing error is ±0.1%.

3.2 Integrator

y = −∫₀ᵗ (x₁ + 10·x₂) dt − IC

Each of the two integrators has one variable input with a weighting factor of 1 (time constant: 1 s) and one input with a weighting factor of 10 (time constant: 0.1 s). An additional IC input is provided for setting an initial condition.

Three operating states can be selected with a switch:

RUN: Input signals are integrated.
HOLD: Integration is paused and the last output voltages are stored. (Voltage droop due to capacitor discharge is approximately 6 mV per minute.)
IC: The inverted voltages of the IC inputs appear at the integrator outputs. After switching from IC to RUN, integration begins from these initial values.

A repetitive integrator control is not provided for this simple demonstration computer.

3.3 Open Amplifier / Inverter

The open amplifier has a nearly infinite gain (> 300,000). In addition to the two summing inputs x₁ and x₂, the summing junction of the amplifier is also accessible as a separate input x₃. If summing input x₂ is connected to the output, the amplifier operates as a normal inverter with transfer function: y = −x₁.

3.4 Coefficient Potentiometers

y = k·x, 0 ≤ k ≤ 1

The four coefficient potentiometers are 10-turn potentiometers with a lockable graduated scale. For precise coefficient adjustment, the +10.00 V reference voltage and an external digital voltmeter are used.

3.5 Multiplier Unit

The multiplier unit is designed for bipolar input voltages in the range −10 V to +10 V (corresponding to a variable range: −1 ≤ x₁, x₂ ≤ +1). It operates on the translinear principle, achieving very high computing accuracy.

By appropriate connection of its five inputs X, Y1, Y2, Z1, Z2, four computing functions can be selected:

Function	Variable Range	Static Error
Multiplication	−1 ≤ x₁ ≤ +1; −1 ≤ x₂ ≤ +1	Error ≤ 0.2%
Division	−1 ≤ x₁ ≤ +1; 0 ≤ x₂ ≤ +1	Error ≤ 0.3%
Squaring	−1 ≤ x ≤ +1	Error ≤ 0.2%
Square root	0 ≤ x ≤ +1	Error ≤ 0.2%

3.6 Diode Function Generator for Sine Function

The sine function is approximated using a diode function generator with eleven line segments. The breakpoints are defined by selected Zener diodes. The function generator is designed for an input variable in the range −1 ≤ x ≤ +1. The maximum deviation of the approximated curve from the mathematical sine function is less than 0.5%.

3.7 Reference Voltage Sources

Two highly stable reference voltages are integrated in the analog computer, which can be calibrated to +10.00 V and −10.00 V using adjustment controls.

3.8 Display Meter with LED Polarity Indicator

The display range of the meter is ±10 V (±1 machine unit). It has accuracy class 2.5 and therefore falls well short of the accuracy of the computing components. However, it is very suitable for purely qualitative demonstrations or for trend indication of a variable. For precise static measurements, the analog computer has a parallel output for an external digital voltmeter connectable via sockets on the rear of the enclosure. When measuring with a digital voltmeter or oscilloscope, the built-in display meter can be switched off.

3.9 Address Selector Switch

A 12-position address selector switch connects the outputs of the computing components and the coefficient potentiometers directly to the display meter or DVM. In switch position 12, the display meter is connected to an input socket on the programming field.

3.10 Overload Indicator

Brief overloads of computing components cannot be detected with a digital voltmeter. The analog computer therefore has an overload indicator at the output of the address selector switch, which monitors the currently selected computing component. The switching thresholds of the monitoring circuit are set to ±10.3 V (±1.03 machine units). If the monitored variable exceeds these limits, the overload condition is signaled by a red LED.

3.11 Triangle-Wave Generator (1.5 Hz to 75 Hz)

For supplying defined, linearly time-dependent variables, a triangle-wave generator is integrated in the analog computer. The generator delivers an output voltage of ±10 V. A multi-turn adjustment control varies the generator frequency in the range 1.5 Hz to 75 Hz. The adjustment control is accessible on the right side of the enclosure.

3.12 Power Supply Unit

The analog computer is powered by an external DC power supply of 9 V DC / 1.2 A. The total power requirement of the computer is approximately 1.8 W. The required operating voltages of ±15 V for the computing components are generated by a DC/DC converter. The output voltages of the converter are stabilized to ±0.5%.

3.13 Computer Accessories

DC power supply 9 V DC / 1.2 A
Branch cables
Button cables (for step-function generation)
Patch cables (two lengths)
Diode cables (with two series-connected diodes; junction accessible via separate connector)

4. Programming

The individual components are connected with patch cables, available in two different lengths. For branching in computing circuits, dual sockets are provided at all computing-component outputs. Additional patch cables are also designed as branch cables. A special cable has a pushbutton and serves to generate a step function. Another special cable integrates two series-connected diodes; the junction point is accessible via a separate plug contact (yellow). This diode arrangement is used for implementing discontinuous computing functions.

5. Mechanical Construction

The analog computer is housed in an aluminum enclosure measuring 188 × 120 × 77 mm. All operating controls and the programming field are on the front panel. The rear panel contains sockets for the DC power supply and for an external digital voltmeter. All computer components including the power supply are mounted on a single PCB. The computer board is double-sided and measures 105 × 88 mm.

[Translation covers the first 9 pages (complete document); the original is 9 pages total.]