Archangelsky functional converter

 

(57) Abstract:

Usage: in measurement technology, in particular in devices for determining the argument vector. Objective: improving the accuracy of measurement while maintaining the high performance and ease of implementation. The inventive 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 measuring technique and can be used to determine the argument vector, and also in various devices as a function Converter to calculate the inverse trigonometric functions of the form arctgX with high speed and high precision in the interval changes of values from 0 to 1.0.

A device for determining the argument of the vector containing the logarithmic function generators, power summation and subtraction of the voltage, the memory block, the block nonlinear correction, switches, and flow calibration. Its work is based on the approximation argument functions, logarithmic functions, orthogonal components.

However, this device is quite SL is etnicheskogo Converter, containing two resistors with zeropressure conductivity, resistor to zeropressure resistance and an operational amplifier.

The device has a small truncation error of approximation taken a mathematical expression

arctgx= (A1x+A3x3)/Babout+x2), where the coefficients a1, A3Bo must be determined with very high accuracy (less than 0.02%).

This Converter requires the use of complex digital devices, which in combination with the analog signals irrational.

Known trigonometric functional converters time-pulse action based on the formation time intervals using a harmonic reference signal, similar to the device in which to obtain the output signal corresponding to the argument vector, proportional to the value arctgX use two balanced modulator, an adder and a comparator.

Such a device is quite simple in execution, but has low speed.

Know another device for trigonometric transformations, containing adders and block division on a logarithmic utilities output device. It solves implicitly the following relationship:

arctgX=Uo=(P/2)(X1,2125)/[1+(X1,2125)]

The device is quite simple to implement, has low performance when using diodes in the feedback circuit of the logarithmic amplifiers, this type of approximation gives a large error 0.7aboutto change interval argument from 0 to 1.0.

You can implement more complex mathematical relationship using amplifiers, multiplier-divider device and summation blocks. In this case, the device will have a high performance, low methodological error, but the device will be very difficult to perform and have quite a lot of instrumental error, because error several nonlinear devices will determine the overall error.

Closest to the invention is Archangelsky functional Converter comprising an amplifier with an adjustable gain, allowing for changes of the argument from 0 to 1.0 approximating function when using multiple breakpoints, applying the reference voltage and the diodes in the feedback circuit of the amplifier is high performance.

For this Archangelsky functional Converter comprising an amplifier with an adjustable gain, the input and the output of which is connected to the input and output of the Converter, respectively, inputs of a unit for extracting the square root of the sum of known and unknown square values, the input connected to the input of the Converter, and the output with the control input of the amplifier with adjustable gain.

The essence of the invention lies in the fact that with limited argument value, for example 0 X 1.0, the approximation can be done with a simple function with high precision, specifying the following approximate equation:

arctgX=X/f(x) for 0 X 1.0, (1) where X is the value of the argument;

f(x) for f(x) 1.0 at > (aX);

And while the coefficients chosen from the condition of minimization of the approximation error.

The drawing shows a structural diagram Arkhangelskoe functional Converter.

Archangelsky functional Converter comprises an amplifier 1 with an adjustable ratio transmission unit 2 to extract the square root of the sum of known and unknown square values.

Blocks in the Converter is connected to the Chi and block 2 to extract the square root of the sum of known and unknown square values, the output of the latter is connected to the control input of the amplifier 1 with an adjustable gear ratio. The output of the amplifier 1 with an adjustable ratio transmission connected to the output of Arkhangelskoe functional Converter.

Archangelsky functional Converter operates as follows.

Input voltage Uxcorresponding to the value of the argument X, is fed to the inputs of the amplifier 1 with an adjustable ratio transmission 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 U2that depends on the voltage Ux. This voltage U2controls the gain of the controlled amplifier 1. Unit 2 is composed of a reference voltage Uop. The value of Uopin unit 2 is chosen of such size that when the control voltage U2=Uopthe transfer coefficient K1managed amplifier 1 TO a1=1,0. The voltage U2the output of block 2 to extract the square root of the sum of known and unknown square values can be represented in following what I value; the factor a is chosen in accordance with a minimum value of error executing equality (1).

This voltage U2is supplied to the control input of the amplifier 1 with an adjustable gear ratio. The transmission coefficient of this controlled amplifier 1 is inversely proportional to the control voltage U2that varies in accordance with the expression (2), so the output voltage U1can be written as follows:

U1=Uo=Ux/f(x), where f(x) (3)

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

U1= Uo= arctan X X/ Ux/. (4)

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

q[X/]-arctan X} for 0 X 1,0

For example, when A=1.0 and a=0,783 depending on 0 X 1.0 error q, expressed as a percentage, will change from q=0 to q=0,14o. All errors in this case are values with the same signs, therefore, offset by using a constant multiplier half the maximum error for the output voltage of the amplifier 1 with adjustable gain, obtain the truncation error of the transformation is equal to the value of q/2. Thus, we get the final Metodicheskie instrumental error, which will not exceed the truncation error, if the error of the controlled amplifier 1 is not more than 0.16 per cent which is the error of 0.07aboutfrom the maximum value at 45about. It is not difficult to perform, because the gain controlled amplifier should be changed only in the range from 1.0 to 0.87. 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 0.16 per cent need to provide a small range of variation of the argument (aUx<0,8 U<SUB>op

Another advantage of the proposed device is the ability to change the input signals in a large dynamic range, which is achieved using devices with a transfer rate of not more than one. When implementing more complex functions to keep the gear ratio is not greater than one difficult.

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

ARCHANGELSKY FUNCTIONAL CONVERTER comprising an amplifier with an adjustable gain, an information input and output of which are connected respectively is the square root of the sum of known and unknown square values, the inlet of which is connected to the information input of the Converter, and the output connected with the control input of the amplifier with adjustable gain.

 

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