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 X2< / BR>
0,21265 X3]/[1 0,2097 X + 0,2097 X2)

cos( /2)X [1 0,2136 X 0,9991 X2+

+ 0,21265 X3]/[1 0,2097 X + 0,2097 X2)

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 Uxcorresponding 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 Uopthat are connected to the respective reference inputs of blocks 2 and 3.

The output of block 3U3that depends on the voltage Uxand equals U3= . This voltage U2fed to the input of amplifier 2 with adjustable gain whose value is2is determined by the voltage U3coming 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 U4well U4= .

The voltage source of the reference voltage Uopchoose such that when the value of the input voltage Ux0 output unit 3 for extracting the square root of the difference between known and unknown square values would receive the voltage Uopequal to the value cosXcos0 1.

The voltage U3from 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 K2in this case, when Ux0 must be equal TO21.

The voltage U4the output of block 4 to extract the square root of the sum of known and unknown square values equal to U4= . For the input voltage Ux0 get U3U< the amplifier 2, the transfer coefficient K2would be equal TO21.

Consequently, the amplifier 2 with adjustable gain is chosen so that when the control voltage U4Uopthe transfer ratio TO2amplifier 2 would be equal TO21 and linearly decreased with the increase of the control voltage U4.

Thus, at the output of the amplifier 2 with a variable gear ratio gain output voltage UOUT2U2that is:

U2= / for U2Uop< / 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 U2corresponding to the functions cos X and defined by the expression:

cosX=U2=UOUT2= / (4)

for 0Ux0,7854 Uop; 1,0 cosX 0,7071; UopU20,7071 Uop.

Consider, as an output voltage proportional to the values of the functions sin x Input voltage Uxcorresponding 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 U4that depends on the voltage Ux. This voltage U4controls the gain of the amplifier 1 with an adjustable coefficient. The value of Uopin 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 U4Uopthe transfer ratio TO1managed amplifier 1 is equal to the unit. The voltage U4the 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:

U4= for U4Uopif (cUx) Uop, (5)

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

The voltage U4is 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 U4that varies in accordance with the expression (5), so the output voltage U1can be written as follows:

U1=UOUT1=Ux/

(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 q1for relation (1) can be obtained from the following expression:

q1=[X/]-sin X}/sinX 0 for X 0,7854

For example, when And 1.0 and 0,6156 depending on 0X0,7854 error q1will change from q 0 to q 0,34% of All errors in this case have a negative value, therefore, increasing the voltage U1the 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 q2for the relation (2) can be obtained from the following expression:

q2= / cosX]/cosX 0 for X 0,7854

For example, if the selected values And 1.0; and 0,788; 0,6156 error q2have 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 q2the 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 0Ux0,7854 Uopthe error of q10,17% and q20,08% 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 Uop0.6 Uopand in block 4 to extract the square root of the sum of known and unknown square values 0,6156*0,7854 Uop0.5 Uop. 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 TO1and K2, i.e., the transmission ratios TO1and K2change 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.

 

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