Multifunctional trigonometric converter

 

(57) Abstract:

Application: the invention relates to computer technology and can be used in information-measuring systems for determining the values of tg X arc sin X with high speed, low error in some interval of values of the argument if 0 X /4 . Goal: expand functionality. The inventive Converter comprises a block 1 of division, unit 2 extract the square root of the difference between known and unknown square values with appropriate links. Used, an approximate function allows you to extend the class of response functions, to simplify the Converter, to provide a large dynamic range of input signals, while maintaining high performance and high accuracy of the transformation. 1 Il.

The invention relates to computer technology and can be used in information-measuring systems, as well as in various functional transducers to determine the values tgX or arcsinX with high performance, low accuracy, ease of implementation in some interval of values for the input signals changing in a large dynamic range is istia [1] is based on the formation time intervals using a harmonic reference signal.

It is known device [2] implements tangency functional dependency using the approximation function as a ratio of polynomials. This device comprises adders, multiplier-divider blocks and difficult to implement, simplifying approximation function leads to increased conversion error.

Closest to the proposed technical characteristics is tangential Converter [3] containing a controlled amplifier, a squarer, the adder block multiplication, two differentiator, the block division, the element of comparison with corresponding connections. The device has high performance, however, plays only a function of the tangent.

The aim of the invention is the extension of functionality.

To do this multifunctional trigonometric Converter comprising the unit, put the unit extracting the square root of the difference between known and unknown square values, the output of which is connected to the input of the divider unit whose output is the output of the Converter, the input of which is the joint entrance fissionable unit and the first input unit, extracting the square root of t is known and unknown square value is the reference input reference voltage of the Converter.

The essence of the invention lies in the fact that with limited argument value of 0 < X < /4, the approximation can be performed with high accuracy, for example, in accordance with the following expressions:

tgX X/f1(x) for 0 < X < /4, (1) where X is the value of the argument;

f1(x)= for f1(x) 1

a1the factor chosen from the condition of minimization of the error of approximation of functions of a tangent.

arcsinX X/f2(x) for 0 X /4, (2) where X is the value of the argument;

f2(x)= for f2(x) 1

a2the factor chosen from the condition of minimization of the error of approximation of functions arcsine.

The drawing shows a structural diagram of a multifunctional trigonometric Converter. It consists of: unit 1 division; block 2 extract the square root of the difference between known and unknown square values. The input of the Converter is connected with the first inputs of the unit 1 division and unit 2 extract the square root of the difference between known and unknown square values. The second input unit 2 is connected to the reference voltage Uop. The output of block 2 extract the square root of the difference between known and unknown square units connected to the second of whizbees.

Unit 1 is a unit, the output of which receives the voltage U1proportional to the ratio of two input signals at the first input of which receives an input voltage Uxand to the second input of the voltage U2from the output of block 2 extract the square root of the difference between known and unknown square values. The output of block 1 of division and, accordingly, the output of the proposed Converter receives a signal proportional to the value of trigonometric functions, i.e., the ratio of the voltages Uxand U2: UoU1Ux/U2.

Using these two blocks are interconnected, as shown in the block diagram, you can implement various trigonometric functions, for example tgX, arcsinX, and when you change the inputs of the dividend and the divisor in the unit 1 division can implement the function ctgX.

Multifunctional trigonometric Converter operates as follows.

Input voltage Uxcorresponding to the value of the argument X (X Ux/Uop), is fed to the first inputs of the unit 1 division and unit 2 extract the square root of the difference between known and unknown square values, to the second input of which the post is required in the following form:

U2==U (3) where (Uop)2known value;

the factor a is chosen in accordance with (1), (2);

X Ux/Uop.

Is the IEP choose this value so that the output voltage U1the output of block 1 of division when U2Uopit would be equal to U1(Ux/U2) (Ux/Uop) Ux.

The voltage U2supplied to the second input of the divider unit 1 division, the output of which receives the voltage U1which can be written as follows:

U1UoUx/U2, (4)

where U2=U

Consequently, the received expression in accordance with (1), (2).

With the help of two blocks, shown in the drawing, you can implement trigonometric and inverse trigonometric functions.

Function tgX. In this case, the output of the unit 1 division receive a voltage, which can be represented as follows:

Uo=Ux/=Ux/U (5) where X Ux/Uop, 0 X /4.

Error value q1this transnova transformation can be defined by the following formula:

q1=1-{[X//tgX} (6) where a10,788.

Error values as calculations show, for emaho Converter receives the signal, proportional function arcsinX in accordance with the same mathematical expression as follows:

arcsinX=Uo=Ux/=Ux/U

(7) where X Ux/Uop; a20,6156; 0 X 0,7854.

Error value q2this axioscope conversion in degrees can be determined by the following formula:

q2=(180/X/-arcsinX (8)

Error values, as shown by the calculations, are in the range of 0.08about.

Function ctgX. In this case, you should swap the inputs for signal-dividend and signal divider, and the value of the conversion error will be the same as in the case of playback functions tangent.

The device allows to implement various trigonometric functions, for example tgX; arcsinX, and when you change the inputs of the dividend and the divisor in the unit 1 division can implement the function ctgX.

The advantage of the proposed device is a small instrumental error achieved by simplifying the design while maintaining the high performance and the ability to work in a large dynamic range that is achieved by using blocks with transmission ratios close to unity.

it entered the block extracting the square root of the difference between known and unknown square values, the output of which is connected to the input of the divider unit whose output is the output of the Converter, the input of which is the joint entrance fissionable unit and the first input unit, extracting the square root of the difference between known and unknown square value, the second input unit, extracting the square root of the difference between known and unknown square value is the reference input reference voltage of the Converter.

 

Same patents:

The invention relates to measuring technique and can be used in trigonometric converters to obtain values funktsii1= arcsin x,2=arccos x, and various analog computing devices

The invention relates to computer technology and can be used in information-measuring systems, as well as in various functional converters, when you want to simultaneously determine the value of sin x and cos x with a small error in the interval of values from 0 to/2

FIELD: computer engineering; automation, data processing and measurement technology.

SUBSTANCE: proposed converter has two registers, NOT gate, angle-code-to-sine/cosine-code functional conversion unit, two digital-to-analog converters, reference voltage supply, pulse generator, counter, two capacitors, subtracting amplifier, two modulators, threshold unit, two selector switches, two buffer followers, threshold voltage supply, comparison circuit, D flip-flop, and reference code shaper; all these components enable functional control of converter during recording pulse time and supply of signal indicating normal or abnormal operation of converter to user thereby essentially raising its self-control ability and yielding profound and reliable information.

EFFECT: enhanced comprehensiveness of control and reliability of converter output data.

1 cl, 2 dwg

FIELD: computer engineering, in particular, functional transformers of angle code to sine-cosine voltages, possible use in data processing systems.

SUBSTANCE: device contains block for functional transformation of angle code to code of sine and cosine, generator of impulse pack, NOT element, registers, support voltage source, digital-analog converter, switch, capacitors, buffer repeaters, modulators, threshold block.

EFFECT: increased precision of transformation.

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FIELD: physics, computer engineering.

SUBSTANCE: invention relates to computer engineering, specifically special-purpose computers. The technical result is achieved by a device for calculating trigonometric functions, which comprises sine and cosine registers, increment registers of the same values, two converters for converting direct code into complementary code, connected, besides by connections between said units, with a clock pulse generator, a memory unit and an argument counter.

EFFECT: method of removing limitations on an argument of calculated functions in the range from 0 to + when calculating trigonometric functions.

1 dwg

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