# Computing Amplifier

## Computing Amplifier

in analogue computers, a composite device consisting of a DC amplifier and external components that form a feedback circuit. The computing amplifier is designed to perform certain mathematical operations on analogue quantities—for example, addition, integration, differentiation, and multiplication by constants. For this reason, the amplifier proper, without the feedback circuit, is called an operational amplifier. Various types of computing amplifiers exist, such as pneumatic, hydraulic, and magnetic amplifiers. The most common type is the electronic computing amplifier, in which voltages or currents are used as signals.

When one or more input voltages appear at the inputs of the computing amplifier (Figure 1), the currents I_{1}, …, I_{n} flow through the input resistors and are summed at the point Σ, the summing junction, at the input of the operational amplifier. Because the gain of the operational amplifier is very high, the voltage at *Σ* is practically equal to zero. For this reason, I_{1} + … + I_{n} = I_{fb}. Since, however,

*I*_{1} = *U*_{in1}/*Z*_{1}, …, *I*_{in n}/*Z _{n}*

and *I _{fb} = U_{out}/Z_{fb}*, it follows that

The ratio Z_{fb}/Z_{i} determines the mathematical operation performed on the input i. If Z_{fb}/Z_{1} = 1, then the computing amplifier performs an algebraic summation of the input voltages. If Z_{fb}/Z_{i} = k_{i}, where Z_{i} and are resistances, then the summation is performed with the simultaneous multiplication of the summands by the constants k_{i.} If impedors are included in the feedback circuit, there occurs a more complicated transformation of the input signals over time. Suppose, for example, the Z_{i} are resistors (equal to R_{i•}), and the feedback circuit is formed by a capacitor C_{fb}. Then,

that is, the sum of the input voltages is integrated with respect to time. When nonlinear resistors are used in the feedback circuits, computing amplifiers permit the performance of such nonlinear operations as raising to a power, the finding of trigonometric functions, and the multiplication of variables.

There are three principal causes of error in the performance of operations by a computing amplifier: inaccuracy of the ratings of the feedback-circuit components, instability of the components, and imperfection of the operational amplifier. The higher the gain k_{a} and the input resistance of the operational amplifier and the lower the output resistance of the operational amplifier, the smaller the error. A considerable influence on the error is had by the parasitic input current I_{p} generated by the operational amplifier, the zero shift E_{p}, and the instability in these factors—drift with time and changing temperature (*see*DRIFT, ZERO-LEVEL); noise also contributes to the error. The dynamic error of a computing amplifier will be less where the bandwidth is wider, the cutoff frequency f_{co} (at which k_{a}*~* 1) is higher, and the rise rate of U_{out} is greater.

High-quality operational amplifiers are usually built with several parallel amplification channels (Figure 2). Such operational amplifiers provide k_{a}*=* 10^{8}–10^{9}, I_{p} = 10–^{12}-10-^{10} amperes, *E*_{ρ}*=* 1–50 microvolts, and f_{co}=1–100 megahertz. Operational amplifiers with one amplification channel have k_{a}= 10^{4}-10^{6}, I_{P}= 10^{-11}-10^{-6} amperes, and f_{co} = 1–20 megahertz.

### REFERENCES

Polonnikov, D. E.*Reshaiushchie usiliteli.*Moscow, 1973.

*Proektirovanie i primenenie operatsionnykh usilitelei.*Moscow, 1974. (Translated from English.)

D. E. POLONNIKOV