Operational amplifiers as analogue computers

In addition to their use in measuring amplifiers, OPVs are also used in analogue computers. This may no longer seem relevant in the age of high-performance processors, but it does have advantages. For example, operational amplifiers can significantly reduce calculation time. This is particularly useful in applications where only one arithmetic operation (multiplication, addition, etc.) is to be performed, but where virtually no latency is permitted. This is still often the case in control engineering today.

The following skills are to be acquired within the scope of this chapter:

The following section presents an example that shows how an analogue computer can be constructed using the basic operational amplifier circuits given in the table.

Beispiel AnalogrechnerBeispiel Analogrechner A circuit is to be designed that implements the following function: \begin {equation} U_{\textnormal {A}} = \int U_{\textnormal {E1}} dt +x \cdot U_{\textnormal {E1}} - 2\cdot U_{\textnormal {E2}} \end {equation}

Solution First, the equation must be broken down into two sub-problems that can be solved using operational amplifier circuits.

The first sub-problem is the integration of the input signal \(U_{E1}\). To do this, an integrator circuit should first be used. The second sub-problem is the addition of the signals. A summing amplifier can be used for this. The desired behaviour can therefore be achieved by combining an integrator circuit and a summing amplifier. Is it possible to select x=0 with this circuit?

\begin {equation} U_{\textnormal {A}} = \underbrace {\left [ -\frac {1}{R_1 \cdot C} \int _{0}^{t} U_{\textnormal {E1}}~dt -\frac {R_2}{R_1} \cdot U_{\textnormal {E1}} \right ]}_{Formel~des~Integrators} \underbrace {\cdot \left (-\frac {R_5}{R_3}\right )-\frac {R_5}{R_4}\cdot U_{\textnormal {E2}}}_{Formel~des~Summierers} \end {equation} This can now be transformed as follows \begin {equation} U_{\textnormal {A}} = \underbrace {\frac {R_5}{R_1 \cdot R_3 \cdot C}}_{\stackrel {!}{=}1} \int _{0}^{t} U_{\textnormal {E1}}~dt + \underbrace {\frac {R_2 R_5}{R_1 R_3}}_{\stackrel {!}{=}x} U_{\textnormal {E1}} -\underbrace {\frac {R_5}{R_4}}_{\stackrel {!}{=}2} \cdot U_{\textnormal {E2}} \end {equation}

As can be seen from the formula, the component values now only need to be selected so that the correct pre-factors are obtained. A choice of x=0 is only possible if the resistor \(R_2\) is omitted. In this case, the result is an „ideal“, which, however, is not usually constructed in reality.