Trigonometric cascandy converter

 

(57) Abstract:

The invention relates to computer technology and can be used in the information measuring systems. The purpose of the invention is to improve the accuracy of measurement while maintaining the high performance and ease of implementation. The Converter comprises an amplifier with adjustable gain and the block extracting the square root of the sum of known and unknown square values. 1 Il.

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 determine the value of cosec X with high performance, low accuracy and ease of implementation in the interval of values from 0 to 4.

Known trigonometric Kaskaskia converters time-pulse type, which, although they have low error in conversion of about 0.1% in the interval from 0 to /4, but have low performance.

Trigonometric cascandy Converter can be obtained from the sine Converter, given their inversely proportional dependence, so, for example, known sinosic delay, managed key block of memory.

The device has a small amount of error, however, has a low performance.

Know another device to calculate trigonometric functions, using which one can obtain the dependence of the function cosec X, 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 low performance.

Known sine Converter that you can use to receive the signal corresponding to the function cosec X containing 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 for angles from 0 to /2:

sin ( /2)X [1,574 X 0,361 X2-0,21265 X3]/[1-0,2097 X + 0,2097 X2).

In this case, the device may have a high performance, low truncation error is of tapana in the argument, and will have quite a lot of instrumental error, because errors of several nonlinear devices will determine the overall error.

The closest technical solution is the trigonometric Converter formed by the amplifier, the gain of which varies in a nonlinear law, allowing for changes of the argument from 0 to /4 approximating a function close as desired. The desired non-linear function get when using multiple breakpoints, applying the reference voltage and the diodes in the feedback circuit of the amplifier.

The aim of the invention is to improve the accuracy of measurement with ease of implementation and high performance.

Goal trigonometric cosequences the Converter comprising an amplifier with an adjustable gain, the output of which is connected to the output of the Converter is achieved by the fact that the Converter is further introduced the unit to extract the square root of the sum of known and unknown square values, the input connected to the input of the Converter and control input of the amplifier with adjustable gain, the input of which is connected to the output of the block extracted for the her in that limited the argument value, for example 0 X /4, the approximation can be done with a simple function with high precision, specifying the following approximate equation:

cosec X f(x)/X for 0 X 0,7854 (1) where X is the value of the argument;

f(x) for f(x) if (aX)

A, A the coefficients are chosen from the condition of minimization of the approximation error.

The drawing shows a structural diagram of trigonometric josecanseco Converter.

It consists of the amplifier 1 with adjustable gain and block 2 to extract the square root of the sum of known and unknown square values.

Blocks in trigonometric cosequences the Converter is connected as follows. The input of the Converter is connected with the control input of the amplifier 1 with an adjustable gain and an input unit 2 for extracting the square root from the sum of the known and unknown quantities, the yield of the latter is connected to the input of the amplifier 1 with an adjustable gain. The output of the amplifier 1 with adjustable gain connected to the output of the trigonometric josecanseco Converter.

Trigonometric cosequently the Converter operates leprowse the input of the amplifier 1 with adjustable gain and the input unit 2 to extract the square root of the sum of known and unknown square values. The output of block 2 to extract the square root of the sum of known and unknown square units receive the voltage U2which is fed to the input of the amplifier 1 with adjustable gain, which is controlled by the voltage Ux. Unit 2 is composed of a reference voltage Uopwhose value is chosen of such size that when the control voltage Ux0,7854 Uopthe transfer coefficient Kymanaged amplifier 1 is equal to Ky= 1,1107. In this case, cosec X=cosec 45o1,4142, the Voltage U2the output of block 2 can be represented as follows:

U2Uop+(aUx)2for U2> Uopif (aUx)<U<SUB>op

This voltage U2to the input of the amplifier 1 with an adjustable gain, the value of which is inversely proportional to the control voltage Uxthat varies from 0 to 0,7854 Uopin accordance with the condition of the range of variation of the argument X. Therefore, the output voltage U1can be written as follows:

U1Uof(x)/Ux<">

U1Uocosec X f(x)/X X f(x)/X /X /Ux(4) where A, A coefficients chosen from the condition of minimization of the approximation error.

The approximation error of q can be obtained from the following expression:

q /X coxecX]/cosec X for 0 X 0,7854 (5)

For example, if A 1.0 and a 0,6156 when determining the cosecant depending on the argument 0 X 0,7854 error q will change from q=0 to q 0,34% of All errors in this case are positive values, hence reducing the output voltage of the device 0.17% will get methodical error of conversion, equal to the value q/2, i.e., the truncation error will be the value of 0,17%

The ease of implementation provides a small amount of instrumental error. Requirements error block 2 to extract the square root of the sum of known and unknown square value is easy to perform, since its value is not more than 0.17% of need to provide a small range of variation of the argument (aUx< <0.5 U<SUB>op

Trigonometric cascandy Converter comprising an amplifier with an adjustable gain, the output of which is the output of the Converter, characterized in that the th is connected with the control input of the amplifier with adjustable gain and with the input of the Converter, and the output is connected to the information input of the amplifier with adjustable gain.

 

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