Application Examples for Analog Computers — Example 1: Special Circuit Configurations for the Telefunken RAT 700

This is an English translation of the original German-language document (Anwendungsbeispiele fur Analogrechner, Beispiel 1, 15. Oktober 1963).

Some Special Circuit Configurations When Using the Telefunken Analog Computer RAT 700

In the following, a few special circuit options for the Telefunken RAT 700 analog computer will be described, enabling the user to implement individual or special operations. These circuits show possibilities for using the computing elements; in many cases they can be very useful.

1. Differentiation Using a Differentiating Computing Element

In the application of the analog computer, differentiation is the circuit with the most concerns (see Section 2.3 of the “Rechentechnik fur Analogrechner” manual). The disadvantage is that it strongly amplifies high-frequency disturbances. It is therefore always necessary when using a differentiating element to apply a low-pass filter with components R₀ and C (see Figure 1). This limits the useful bandwidth. Figure 1 shows the circuit. The transfer function for the differentiating element is given by:

Y(s)/X(s) = -s·τ₁ / (1 + s·τ₀) … (1)

where τ₁ = C·R₁ and τ₀ = C·R₀.

The cutoff frequency of the low-pass filter is:

f₀ = 1/(2π·C·R₀) … (2)

For this circuit, a capacitor C is available in the summer/integrator to provide the differentiating feedback. The individual integrating capacitors, each with a fixed end (at one end), are always available to the differentiating element. The number of usable integration capacitors, depending on the capacitance k₀, is determined; in practice it is generally possible to use k₀ = 1 or k₀ = 10. The denominator of this transfer function can be simplified so that for the end frequencies (D ≤ f ≤ 1) the approximation:

Y ≈ -(1/k)·(dx/dt)*

is valid for D values of the integrator k = 1 or 10. Figure 2 shows the programming of the differentiation circuit with the elements of the RAT 700.

The differentiating computing element requires a capacitor C in the summer/integrator section. The individual integration capacitors are connected with one end (always free). The number of available integration capacitors can be selected at the capacitance value k₀. In practice, a value of k₀ = “1” or k₀ = “10” is set. The connection of this potentiometer via a “shorting plug” connects the outputs of the free end to positions 5, 10, 11, or 16 (white sockets).

Figure 2 shows the programming of the differentiation circuit from Figure 1 using the elements of the RAT 700.

Figure 3 shows the connections on the patch panel (Steckfeld) for the differentiation circuit from Figure 2.

2. Special Possibilities of the Parabolic Multiplier

Very interesting possibilities are offered by the parabolic multiplier, which allows the computation of the function:

Yₐ = Yₑ² / 2 … (4a)

or in another form:

Yₐ = (sign Yₑ) · |Yₑ|²/2 … (4b)

To implement equation (4), one applies the input variable to both the +x and −x terminals, and connects the +y and −y terminals to ground.

The function of equation (4) has direct meaning, for example, in control systems with quadratic dependence of the controller. It can also be used for squaring, when the sign of the input variable does not change.

For Yₑ ≤ 0: Yₐ = Yₑ²/2 For Yₑ ≥ 0: Yₐ = −Yₑ²/2

Particularly interesting is the circuit shown in Figure 5 for forming the square root.

This delivers the quantity:

Yₐ = Yₑ / √|Yₑ| … (5a)

or in other notation:

Yₐ = (sign Yₑ) · √|Yₑ| … (5b)

With this circuit, the radicand may have any sign; we obtain, depending on the sign, the positive or negative branch of √|Yₑ|.

This function also plays a major role in engineering.

Finally, this operation can also be implemented with only one amplifier and the multiplier network. Figure 6 shows how this is to be patched.

The red output sockets in the connection field of the multiplier network now become the input of the circuit. On one of these sockets, a potentiometer with value α = 0.5 is connected as the radicand. By means of a shorting plug, as in the normal application of the multiplier, the two G sockets are connected to each other. The +x and −x sockets of the multiplier network are connected to the amplifier output, and the +y and −y sockets are connected to ground. For stability, the usual capacitance of about 300 pF is connected between the output and summing point of the amplifier.

Figure 5 — Circuit for computing the function of equation (5): square root circuit using multiplier and two amplifiers.

Figure 6a — Symbolic representation of the square root circuit using one computing amplifier and the multiplier network (without its own follower amplifier). The rectangle represents the multiplier network without the downstream amplifier. The output sockets of this network are used as input here.

Figure 6b — Connections on the patch panel for the circuit of Figure 6a.

[Translation covers all 7 pages of the original document.]