# Sine-cosine converter

(57) Abstract:

The invention relates to measuring technique and can be used in information systems. The purpose of the invention is to improve the accuracy of measurement while maintaining high performance. The Converter contains amplifiers with adjustable gain, the block extracting the square root of the difference between known and unknown square values, the block extracting the square root of the sum of known and unknown square values. 1 Il. The invention relates to measuring technique and can be used in various information systems as a functional Converter when you want to simultaneously determine the value of sinX and cosX with high speed and low error conversion in the range of argument values from 0 to 4.Known sine-cosine converters time-pulse type, which, although having a low error in conversion of about 0.1% in the interval from 0 to /4, but have low performance.For example, the well-known sine-cosine frequency Converter comprising a shaper rectangular pulses, the differentiation block, block sandercoe performance.A device for computing functions sine and cosine, containing two out phase-sensitive rectifier and connected in series time-pulse Converter, the pulse shaper, the integrating amplifier and the amplifier-limiter as well as a generator of sinusoidal oscillations.This device has an error due to drift of the integrator, and most importantly has a low performance.Known sine-cosine Converter comprising multipliers, adders, reference voltage that determines the scale of the transformation. A device for providing low error conversion uses a fairly complex function approximation, which can be represented as follows:sin(/2)X [1,574 X 0,361 X

^{2}< / BR>

0,21265 X

^{3}]/[1 0,2097 X + 0,2097 X

^{2})

cos( /2)X [1 0,2136 X 0,9991 X

^{2}+

+ 0,21265 X

^{3}]/[1 0,2097 X + 0,2097 X

^{2})

The device can have a high performance, low methodological error, however, the device will be very difficult to implement, limited dynamic range due to the presence of second and third degree if the argument and will have quite a lot of instrumental error, as pogreshnost the CLASS="ptx2">Closest to the invention on a common technical solution is a sine-cosine Converter comprising two amplifiers with adjustable transmission ratios, inputs are combined and connected to the input of the Converter, and the outputs are the first and second outputs of the Converter, allowing for changes of the argument from 0 to /4 approximating function for values of sinX, cosX when using multiple breakpoints, applying the reference voltage and the diodes in the feedback circuit of each amplifier.The aim of the invention is to improve the accuracy of measurement while maintaining high performance.For this sine-cosine Converter comprising first and second amplifiers with adjustable transmission ratios, the outputs of which are the respective outputs of the Converter, whose input is connected to the input of the first amplifier with adjustable gain, inputs of the block to extract the square root of the difference between known and unknown square units and a unit for extracting the square root of the sum of known and unknown square values and the inputs of these two blocks volume is based and of the square of the unknown quantities is connected to the input of the second amplifier with adjustable gain, the control inputs of the first and second amplifiers with adjustable transmission ratios combined and connected to the output unit for extracting the square root of the sum of known and unknown square values.The essence of the invention lies in the fact that with limited argument value, for example H/4, the approximation can be carried out with the help of functions with high accuracy, specifying the following approximate equality

sinX-X - /

(1)

cosX //

(2) where X is the value of the argument, where 0 X 0,7854;

A, a, with coefficients chosen from the condition of minimization of the approximation error.The drawing shows a structural diagram of the sine-cosine Converter.It contains the amplifiers 1 and 2 with adjustable transmission ratios; unit 3 for extracting the square root of the difference between known and unknown square values; unit 3 for extracting the square root of the sum of known and unknown square values.Blocks in the sine-cosine Converter is connected as follows. The input of the first amplifier 1 with an adjustable gain, the input unit 3 for extracting the square root of the difference between known and square Pitney values are combined and connected to the input of the Converter.The output unit 3 for extracting the square root of the difference between known and unknown square units connected to the input of the second amplifier 2 with adjustable gain. Control inputs of the amplifiers 1 and 2 have been combined and connected to the output unit 4 to extract the square root of the sum of known and unknown square values. The output of the amplifier 1 and amplifier 2 with adjustable transmission ratios are, respectively, the first and second outputs of the Converter.Sine-cosine Converter operates as follows.Input voltage U

_{x}corresponding to the value of the argument X, is fed to the input of the first amplifier 1 with an adjustable gain, the input unit 3 for extracting the square root of the difference between known and unknown square values, and the input unit 4 to extract the square root of the sum of known and unknown square values.Consider first, how do you get a voltage proportional to the values of the function cosX. Each of these units 3 and 4 includes a reference voltage sources U

_{op}that are connected to the respective reference inputs of blocks 2 and 3.The output of block 3U

_{3}that depends on the voltage U

_{x}and equals U

_{3}= . This voltage U

_{2}fed to the input of amplifier 2 with adjustable gain whose value is

_{2}is determined by the voltage U

_{3}coming to its control input from the output of block 4 to extract the square root of the sum of known and unknown square values. This voltage U

_{4}well U

_{4}= .The voltage source of the reference voltage U

_{op}choose such that when the value of the input voltage U

_{x}0 output unit 3 for extracting the square root of the difference between known and unknown square values would receive the voltage U

_{op}equal to the value cosXcos0 1.The voltage U

_{3}from the output unit 3 for extracting the square root of the difference between known and unknown square value is fed to the input of the amplifier 2 with adjustable gain, a value of K

_{2}in this case, when U

_{x}0 must be equal TO

_{2}1.The voltage U

_{4}the output of block 4 to extract the square root of the sum of known and unknown square values equal to U

_{4}= . For the input voltage U

_{x}0 get U

_{3}U< the amplifier 2, the transfer coefficient K

_{2}would be equal TO

_{2}1.Consequently, the amplifier 2 with adjustable gain is chosen so that when the control voltage U

_{4}U

_{op}the transfer ratio TO

_{2}amplifier 2 would be equal TO

_{2}1 and linearly decreased with the increase of the control voltage U

_{4}.Thus, at the output of the amplifier 2 with a variable gear ratio gain output voltage U

_{OUT2}U

_{2}that is:

U

_{2}= / for U

_{2}U

_{op}< / BR>

(3) where the coefficients a, C are chosen in accordance with a minimum value of the error of execution equality (1).Selecting values and 0,788; 0,6156 at the output of the amplifier 2 with adjustable gain gain voltage U

_{2}corresponding to the functions cos X and defined by the expression:

cosX=U

_{2}=U

_{OUT2}= / (4)

for 0U

_{x}0,7854 U

_{op}; 1,0 cosX 0,7071; U

_{op}U

_{2}0,7071 U

_{op}.Consider, as an output voltage proportional to the values of the functions sin x Input voltage U

_{x}corresponding to the value of the argument X, is fed to the input of the amplifier 1 with adjustable gain and the input unit 4 to extract the root RMS is varatojo from the sum of the known and unknown square units receive the voltage U

_{4}that depends on the voltage U

_{x}. This voltage U

_{4}controls the gain of the amplifier 1 with an adjustable coefficient. The value of U

_{op}in unit 4 to extract the square root of the sum of known and unknown square value is chosen of such size that when the control voltage U

_{4}U

_{op}the transfer ratio TO

_{1}managed amplifier 1 is equal to the unit. The voltage U

_{4}the output of block 4 to extract the square root of the sum of known and unknown square values can be represented in the following form:

U

_{4}= for U

_{4}U

_{op}if (cU

_{x}) U

_{op}, (5)

where the coefficient C is chosen in accordance with a minimum value of error executing equality (1).The voltage U

_{4}is supplied to the control input of the amplifier 1 with an adjustable gear ratio. The gain of the amplifier 1 is inversely proportional to the control voltage U

_{4}that varies in accordance with the expression (5), so the output voltage U

_{1}can be written as follows:

U

_{1}=U

_{OUT1}=U

_{x}/

(6)

Consequently, the received expression in accordance with the expression (1).Consequently, the received expression in accordance with expressions (1) and (2).The approximation error of q

_{1}for relation (1) can be obtained from the following expression:

q

_{1}=[X/]-sin X}/sinX 0 for X 0,7854

For example, when And 1.0 and 0,6156 depending on 0X0,7854 error q

_{1}will change from q 0 to q 0,34% of All errors in this case have a negative value, therefore, increasing the voltage U

_{1}the output of the amplifier 1 with an adjustable gear ratio: 0.17% will get methodical error of conversion values of sinX, equal to the value q/2, i.e. 0.17% of

The approximation error of q

_{2}for the relation (2) can be obtained from the following expression:

q

_{2}= / cosX]/cosX 0 for X 0,7854

For example, if the selected values And 1.0; and 0,788; 0,6156 error q

_{2}have a value not exceeding q 0.16% of all errors have the same signs, so after the introduction of the amplifier 2 with adjustable gain adjustment constant multiplier can reduce the error in q 0,16% in 2 times. Therefore, the methodological error of q

_{2}the proposed approximation of the cosine function to change the argument 0X 0,7854 will have a value of not more than 0.08%

Predlagaetvashemu error. This is achieved by the fact that when the input voltage 0U

_{x}0,7854 U

_{op}the error of q

_{1}0,17% and q

_{2}0,08% can be achieved, as used in blocks 2 and 3, to extract the square root unknown value significantly lower than the known values.For example, in unit 3 for extracting the square root of the known and unknown square values 0,788*0,7854 U

_{op}0.6 U

_{op}and in block 4 to extract the square root of the sum of known and unknown square values 0,6156*0,7854 U

_{op}0.5 U

_{op}. For this reason, error blocks 2 and 3 provide little value for these limits change unknown quantities.A small error in conversion for amplifiers 1 and 2 with adjustable transmission ratios can also be secure, as they operate in a small range of changes in the values of their coefficients of transmission TO

_{1}and K

_{2}, i.e., the transmission ratios TO

_{1}and K

_{2}change within just no more than 15% SINE-COSINE CONVERTER comprising first and second amplifiers with adjustable gain, the outputs of which are the output values of the cosine and sine inverter, the different themes, it entered the block extracting the square root of the difference between known and unknown square values and the block extracting the square root of the sum of known and unknown square values, the inputs of which are connected to the input transducer, the output of block extraction of the square root of the difference between known and unknown square units connected to the information input of the first amplifier with an adjustable gain, the output of block extraction of the square root of the sum of known and unknown square units connected to the control inputs of amplifiers with adjustable gain.

**Same patents:**

_{1}= arcsin x,

_{2}=arccos x, and various analog computing devices

**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.

2 cl, 2 dwg

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