SU1377877A1 - Device for extracting a root - Google Patents

Abstract

The invention relates to analog computing and may find wide application in the design of instrumentation in measurement technology, communication devices, and automatic control systems. The purpose of the invention is to improve the accuracy of the device for extracting the root. The device is based on the operational amplifier 1 and the quadrant 4. The goal is achieved by introducing into the device circuit an auxiliary root-extracting unit 7, the input of which is connected to the output of the operational amplifier 1 and the output to the output of the device. 1 il. i cl

Description

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The invention relates to computing and can be used in analog computers to extract the square root of the signals, represented as negative polarity voltages.

The purpose of the invention is to increase accuracy.

Diagram of the device shown in the drawing.

The device for extracting the root contains an operational amplifier (OA) 1, the first 2 and the second 3 large-scale resistors, a quad 4, a third large-scale resistor 5, a rectifying diode 6, an auxiliary root-extractor unit 7.

Due to the presence of diode 6, the voltage at the input of the auxiliary root-extracting unit 7 can only be positive, therefore, as an auxiliary unit 7, it is necessary to use a root-extractor device designed for operation with a positive input signal. The scale factor of the auxiliary root-extracting unit 7 can be either positive or negative. The accuracy of the auxiliary, root extracting unit 7 can be quite low.

The device works as follows.

The input voltage X through the resistor 2 is fed to the inverting input of the shelter 1. To the same input through the resistor 3 receives a signal from the output of quadrant 4, equal to SU, where C is the scaling factor of quadrant 4, and C O, Y is the output voltage devices.

From the condition of equality of currents on the inverted input of the shelter 1 we get

(one)

,

  X

 Ri R,

where X is the voltage on the inverting

OU 1 input;

RJ is the resistance of resistor 2; R, is the resistance of the resistor 3. The output voltage Y is related to the value of X as follows

(2.)

where A is the scaling coefficient of ancillary corneous removal

unit block 7, which can be both positive and negative, K is the gain of the OU 1. The transmission coefficient of the open diode 6 is taken equal to one.

Eliminating the value of x from expressions (1) and (2), after p yes and conversions, we find

W.L. one . (3)

.

0

five

0

five

0

five

The sign of the output voltage Y is determined by the sign of the scale factor A of the auxiliary root-extracting unit 7. The minus sign in front of X indicates that the input voltage X must be negative.

Thus, the output voltage of the root retriever is directly proportional to the square root of the input signal.

Resistor 5 serves to reduce the influence of the input currents of the shelter 1 on the accuracy of the device. Diode 6 serves to increase the stability of the device.

From expression (3), we find the relative change in the output voltage Y (S LY / Y) due to the instability of the values of K and A, i.e. relative error of the device. After squaring both sides of equation (3), logarithmizing and differentiating the resulting expression, going from infinitely small quantities to finite increments, after the transformations we get

and Rg + Ri / uA „with. h ,,. R R A icCRl T Let the scale factor A of the auxiliary root-extracting unit 7 be equal to

A m

(five)

where m is an arbitrary number.

Note that for m 1, the modulus of the scale factor of the auxiliary root-extracting unit 7 is equal to the modulus of the scale factor of the device for extracting the root (see equation (3)). Expression (5) can be represented as follows:

 .

Rj, R, + R, + A2KCRj

from where

Rj + R, + A2KCR2, and expression (4) takes the form

g Ri + R, xDIK

 - T ° T

Claims (1)

Invention Formula Extraction device containing an operating force the inverting input of which is connected via the first and second scale resistors respectively to the information input of the device and the output of the quad, whose input is connected to the output of the device; By the fact that, in order to increase accuracy, an auxiliary root-extracting unit was inserted into it, the input and output of which are connected respectively to the cathode of the rectifier up and down the device.