Cosine converter

 

(57) Abstract:

Application: the device can be used as functional Converter to calculate values of the function cos X when the value of the argument 0X(/4). The purpose of the invention: reduction of the instrumental error of the measurements. The inventive approximation carried out with the help of linear and nonlinear functions, which allows you to apply simple approximating function, implemented using a small number of links. The Converter includes an adder block allocation maximum, the block extracting the square root of the difference between known and unknown square value and the voltage reference. Positive effect: the device has a small number of links, which helps to reduce the instrumental error, while maintaining high performance, low methodological error of no more than 0.3%. 1 Il.

The invention relates to measuring technique and can be used for cosine conversion with high speed, low error and simple implementation in the interval of values from 0 to 4.

Known sine-cosine converters time-pulse type, which have low performance.

For example, the well-known cosine frequency Converter [2] contains the shaper rectangular pulses, the differentiation block, the delay unit, managed key block of memory.

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

Know another device for calculating trigonometric functions [3] contains 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.

Such a device for measuring values of cos X is the error due to drift of the integrator, and most importantly has a low performance.

Known cosine Converter [4] contains the multipliers, adders, reference voltage that determines the scale of the transformation.

The device uses a fairly complex function approximation, which can be represented as follows for angles from 0 to /2:

< / BR>
The device has high performance, but it has quite a lot of instrumental error, which consists of pogreshnostyami Converter [5] contains the multipliers, the adders and the voltage reference for scaling conversion when changing the argument from 0 to 4. The Converter implements similar [4] approximating function for a simplified scheme, however, disadvantages [4] is saved.

The aim of the invention is to reduce the instrumental error of the signals at the ease of implementing and maintaining a high performance.

The essence of the invention lies in the fact that with limited argument value, for example 0X/4, the approximation can be performed with high accuracy simpler function than proposed in the prototype, specifying the following approximate equation:

(1)

cos X C-KX for 0,610,7854

where X is the value of the argument;

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

Goal cosine Converter containing an adder, a first input which is the input of the Converter is achieved by the fact that it introduced the power allocation of the maximum and the block extracting the square root of the difference between known and unknown square values, the first input connected to the input of the inverter, a second input of the adder unit root extraction of quadrangularis, the outputs of the adder and the block extracting the square root of the difference between known and unknown square units connected to the inputs of block allocation maximum, the output of which is the output of the Converter.

The drawing shows a structural diagram of the cosine of the Converter.

It includes

the adder 1;

unit 1 extracting the square root of the difference between known and unknown square values;

unit 3 selection maximum.

Blocks in cosine Converter is connected as follows. The input of the Converter is connected with the first inputs of the adder 1 and unit 2 extract the square root of the difference between known and unknown square values. The source of the reference voltage Uopconnected with the second inputs of the adder 1 and the block extracting the square root of the difference between known and unknown square values. The output of the adder 1 is connected to the first input unit 3 selection of the maximum, and the output unit 2 to extract the square root of the difference between known and unknown square values connected with the second input unit 3 selection of the maximum, the yield of the latter is connected to the output of cosine Converter.

Cosine is converted into the steps on the first inputs of the adder 1 and unit 2 extract the square root of the difference between known and unknown square values. The voltage Uopfrom the source of the reference voltage supplied to the second inputs of the adder 1 and unit 2 extract the square root of the difference between known and unknown square values. At the output of the adder 1 are the voltage U1, which decreases with the increase of the input voltage Ux. The output of block 2 to extract the square root of the difference between known and unknown square units receive the voltage U2, which is dependent on the voltage Ux. These voltages U1 and U2 are received at first and second inputs of unit 3 selection of the maximum, respectively. The voltage source of the reference voltage Uopchoose such size that when the value of the input voltage Ux=0 at the output of block 2 extract the square root of the difference between known and unknown square values would receive the voltage Uopequal to the value of cosX=cosO=1. The voltage U2 at the output of block 2 extract the square root of the difference between known and unknown square values can be represented in the following form:

(2)

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

The voltage U1 at the output of the adder 1 can be written as pogreshnosti complete equality (1).

The voltages U1 and U2 are received at first and second inputs of unit 3 selection of the maximum, respectively. If you select A=0,94; C=1,215; K=to 0.645 output unit 3 selection high gain voltage equal U3=Uothat for 0Ux0,7854 Uophas the following values:

for 0Ux0,61 Uop< / BR>
(4)

for 0,61 UopUx0,7854 Uop< / BR>
cosX=U3=1,215 UopTO 0.645 Ux.

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

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

< / BR>
for 0X0,61;

q2=[cos X (1,215-To 0.645 X)]/cos X

for 0,610,7854.

For example, if A=0,94; C=1,215; K=to 0.645 error does not exceed the values q1=0,31% and q2=0,29% to 0X0,7854.

The ease of implementation provides a small amount of instrumental error, which will not exceed the truncation error. This is achieved by the fact that when the input voltage 0Ux0,61 Uoperror q1 is determined by the error block 2 extract the square root of the difference between known and unknown square values. To ensure accuracy of less than 0.3% it's easy for specified ratios of input voltages.

When the input voltages 0,61 UopU

The device is implemented using a conventional links, known in the literature:

the adder 1 [6a]

unit 2 extract the square root of the difference between known and unknown square values [7]

unit 3 selection max [6b]

Cosine Converter comprising an adder, a first input which is the input of the Converter, characterized in that it introduced the power allocation of the maximum and the block extracting the square root of the difference between known and unknown square values, the first input connected to the input of the inverter, a second input of the adder unit extracting the square root of the difference between known and unknown square units connected to the reference input reference voltage of the Converter, the outputs of the adder and the block extracting the square root of the difference between known and unknown square units connected to the inputs of block allocation maximum, the output of which is the output of the Converter.

 

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