Multifunctional trigonometric converter

 

(57) Abstract:

Application: the invention relates to the field of measurement technology and can be used in various functional transducers for determining the values of arcsin X with high speed, low error in some interval of values of the argument. With its help it is possible to determine also the value of the function tg X. Goal: expand functionality. The inventive approximation is carried out in the range of variation of the argument from 0 to 4 . The Converter contains a voltage reference, block 1 multiplication and unit 2 extract the square root of the sum of known and unknown square values with corresponding connections. Used, an approximate function allows you to simplify the Converter, to extend its functionality to provide a large dynamic range for the input signal, high speed, low error in conversion. 1 Il.

The invention relates to the field of automation and computer engineering and can be used in various functional converters, to determine the values arcsinX with high speed, low error function tgX.

Known anxiously converters time-pulse type [1] which, although having low error conversion (about 0.1 deg. in the interval from 0 to /4), but have low performance.

Known anxiously Converter [2] contains the amplifier, the input and the output of which is connected to the input and output, respectively, two resistors, a capacitor, three key scheme OR NOT and RC filter that calculates a function approximation for angles from 0 to 4. The device is quite simple, but great is the approximation error.

Closest to the proposed technical characteristics is the trigonometric Converter [3] contains blocks the multiplication, the adders and the source of the reference voltage with corresponding connections. The device does not allow you to use it to calculate as trigonometric, and inverse trigonometric functions.

The aim of the invention is the enhanced functionality with ease of implementation and high performance.

To do this multifunctional trigonometric Converter contains a voltage reference and the power multiplication, the output of which alsenoy values, the first input and the first input of the multiplication are combined and the input of the Converter, the output voltage reference is connected to the second input unit, extracting the square root of the sum of known and unknown square values, the output of which is connected with the second input of the multiplication.

The essence of the invention lies in the fact that with limited argument value, for example 0 < X < 0,707, the approximation can be done with a simple function with high precision, specifying the following approximate equation:

UoUxf(Ux), (1)

where Uothe output voltage;

Uxvoltage input;

f(x)=f(Ux)=

The drawing shows a structural diagram of a multifunctional trigonometric Converter. It consists of: unit 1 multiplication; block 2 extract the square root of the sum of known and unknown square values; Uopthe voltage reference.

Blocks in the Converter are connected in the following way. The input of the Converter is connected with the first inputs of block 1 of the multiplication and unit 2 extract the square root of the sum of known and unknown square values. Conclusion reference nastey values, the output of which is connected to the second input of block 1 multiplication. The output of block 1 multiplication connected to the output of a multifunctional Converter.

Unit 1 is a unit, the output of which receives a voltage proportional to the product of the two input signals at the first input of which receives an input voltage Uxand on its second input receives the voltage U2from the output of block 2 extract the square root of the sum of known and unknown square values. The output of block 1 of the multiplication, i.e., the output of the proposed Converter, receives the signal, proportional to the value of trigonometric functions, i.e., the product of the voltages Uxand U2.

Using these two blocks are interconnected, as shown in the block diagram, you can implement various trigonometric functions, for example, the following:

1) Function arcsinX. In this case we have:

arcsinX (180/) Xf(x). (2) where X is the value of the argument, where 0 < X < <0,7071;<BR> f(x)= f(x)>1.0 at

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

The Converter operates as follows. Input voltage Uxcorresponding to the value of the argument X, is atrata unknown quantities. The output of block 2 receives the voltage U2that depends on the voltage Uxand the DC voltage Uopwhich is supplied to the second input of block 2 extract the square root from the sum of the known and of the square of the unknown quantity. The voltage Uopchoose such size that when the voltage at the output of block 2 U2Uopthe voltage U1the output of block 1 of the multiplication is U1Ux. Unit 2 extract the square root of the sum of known and unknown square values can be represented in the following form:

U2= for U2>Uopif (aUx)<U<SUB>opopa known value; factor and is chosen in accordance with [1,2] This voltage U2supplied to the second input unit 1 multiplication. The output voltage U1can be written as follows:

U1=Uo=U=UxU (4) where X Ux/Uopand 0,684.

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

U1=Uo=arcsin X=X f(x)=(180/)X (5)

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

q=[(180/)X]-arcsin X, for 0<X<0,7071 (6)

For example, if A 1.0 and and 0,684 error q zavisimosti will q/2| ie 0.16 deg. Requirements to the magnitude of the error block 2 extract the square root of the sum of known and unknown square value is easy to perform, since the condition 0 < X < 0,684*0,7071.

2) Function tgX. In this case, the output of the inverter receives a signal proportional to the function tgX in accordance with a mathematical expression in the form:

Uo= U= UxU (7) where the coefficient a is selected near the unit.

The maximum error q transnova transformation can be defined by the following formula:

q= 1-{[X]/tgX} (8) where and 1; 0 < X < (/4); the expression in square brackets is a mathematical account of the proposed tangence dependence. Error values of the proposed approximation, as shown by the calculations for this transnova conversion, 1,2%

MULTIFUNCTIONAL TRIGONOMETRIC CONVERTER comprising a source of reference voltage and block multiplication, the output of which is the output of the Converter, characterized in that it introduced the block extracting the square root of the sum of known and unknown square values, the first input and the first input of the multiplying together the attraction of the square root of the sum of known and unknown square values, the output of which is connected to the second input of the multiplication.

 

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.

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

Up!