The device for calculating trigonometric functions

 

(57) Abstract:

Usage: in the information-measuring systems for computing the values of trigonometric functions. The invention is: to improve the accuracy of conversion to calculate the trigonometric functions sin x and cos x, sec x and cosec x, tg x and ctg x use trigonometric Converter with two outputs corresponding functions operating in a limited range of variation of the argument x, for example 0 x /4. Work in a limited range of variation of the argument x can reduce the error of each of the trigonometric converters, which determine the accuracy of the transformation in the range of variation of the argument x in the range from 0 to /2. This device uses known trigonometric ratios, for example with-cosine computing sin x = cos (90o- x or cos x = sin (90o- x). The device comprises a controlled amplitude detector, trigonometric Converter switch. 1 C. p. F.-ly, 3 ill.

The invention relates to measuring technique and can be used in various information-measuring systems, when you need to determine the value of the trigonometric functions sin X and cos X, sec is consistent in principle piecewise linear approximation of the given functions. The Converter includes an operational amplifier with nonlinear elements in the feedback circuit.

The disadvantage of this device is the low accuracy of the approximation.

For example, the well-known sine-cosine Converter, in which the approximation of the given function is a ratio of polynomials of the third degree. The Converter contains several multiplier-divider blocks, a few adders and scaling elements.

The disadvantage of this device is the low accuracy of the transformation due to the significant instrumental error made by a relatively large number of blocks, performing the approximation.

Know another device for calculating trigonometric functions containing two out phase-sensitive rectifier United and consistent 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.

A device for sine-cosine transform, comprising a generator of the reference sine wave is which are the outputs of the voltage, proportional to the sine and cosine of the input signal, and the control inputs are combined and connected via the first driver to the output of the time-pulse Converter, the first input connected to the first input device, in addition, the device contains a second shaper, time-pulse dividers, pulser, the comparison element, and an operational amplifier, the reference DC voltage and the source voltage, the magnitude of which varies in time.

This device allows, in addition to voltages proportional to the sine and cosine, to generate a voltage proportional to the second input voltage, multiplied by the value of the tangent of the first voltage. However, the use of a controlled divider, the output of which is connected to the information input of the second block of the sample and hold, breaks the symmetry in the formation of voltage sine and cosine, with a controlled voltage divider cannot provide high accuracy when the input signal in a wide dynamic range, which leads to errors at the output of the second unit of sampling and storage. In addition, two independent phase shifter also violate simmetrichnym measuring errors.

The closest similar technical characteristics, is a device for trigonometric transformations that contains one United amplitude detector, an adder and trigonometric Converter, and the second input of the adder is connected to the reference voltage, and the output of the trigonometric Converter coupled to the output device.

The device uses the well-known trigonometric relation sin X cos(90o-X) or cos X sin(90o-X). As trigonometric Converter usually use sine inverter, operating in the range of change of argument of 0 < X < 90aboutusing the values of the function cos X in the extended range of variation of the argument. Similarly, we can obtain the value of the functions sin X, using the cosine Converter as the primary source trigonometric Converter.

This implementation allows you to define the desired function, and the error is determined mainly by the accuracy of the used primary trigonometric Converter. Error analysis trigonometric Converter operating with arguments 0 < X < 90

The purpose of a device for computing trigonometric functions containing trigonometric Converter and amplitude detector, whose input is connected to the input device, is achieved by the fact that it introduced additional switch, and the amplitude detector is made manageable, and the first output controlled amplitude detector connected to the input of trigonometric Converter, and a second output connected to the third control input of the switch, the first and second inputs which are connected respectively to the first and second outputs trigonometric Converter, the first and second outputs of the switch are respectively the first and second outputs of the device.

Managed amplitude detector contains an adder, a switch, a comparator, and a reference voltage source that is connected to the first input of the adder, the output of which is connected to the first input, second input of the adder and of the switch and the input of the comparator combined and connected to the input of the control of the amplitude detector, the first output of which is connected to the output of the switch, the third control input connected to the output of the comparator, and the second vile corresponding pair of trigonometric functions sin X and cos X, sec X and cosec X, tg X and ctg X with a small measurement error, use the appropriate trigonometric Converter with two outputs. For example, for calculations of the functions sin X and cos X on the first output trigonometric Converter implement the function sin X, and the second output of the function cos X, and the range of variation of the argument X is restricted to half of the quadrant (0<X< < /2), varying from 0 to Uop. The voltage Uopchoose such size that when the voltage at the input of the UI= 0 the voltage on the first and second outputs trigonometric Converter 2 were, respectively, U2-1(UI=0)= 0 and U2-2(UI=0)= Uo(max).

When the input voltage UIUop/2the voltage on the first and Strom outputs trigonometric Converter 2, respectively, the voltage U3-1(UIUop/2)0,7071 Uo(max)and U3-2(UIUop/2)0,7071 Uo(max), i.e., the reference voltage corresponds to the maximum value of the argument value 90about/2.

Using control logic voltages U5comparator 6 at the first output controlled amplitude detector 1 when changing napryajennyh voltages Uop/2< UI< Uopallocate the voltage U1-1UopUIfrom the output of the adder 4.

The second output controlled amplitude detector 1 form the control logic voltage U1-2that control the operation of the switches 3 and 5 in accordance with the diagram of Fig.3, illustrating the operation of the device to calculate the functions sin X and cos X.

Input voltage UXBto the input of the comparator 6 and the second input of the adder 4 and the switch 5. At the output of the adder 4 receives the voltage U4Uop-UIand at the output of the comparator 6, the voltage U6coming to the third control input of the switch 5, and manage its operation in accordance with Fig.3.

When the output voltage of the comparator 6, is equal to U6logical "0" or "1" on the first output controlled amplitude detector 1, respectively, at the output of the switch 5 receives the voltage U5=U1-1equal to the input UIor the difference between the UopUI. Thus, the operation of the device should be considered for two cases: first when 0 UIUop/2second when Uop/2<U<SUB>Iop.

In the first case on pervicnokislogo Converter 2 receives the voltage U2-1corresponding values of the function sine (when changing the argument from 0 to /4), i.e., U2-1f(sinX). On the second output trigonometric Converter 2 receives the voltage U2-2corresponding to the values of cosine functions (changing the argument from 0 to /4), i.e., U2-2f(cosX). These voltage U2-1U2-2come respectively into the first and second inputs of switch 3.

For change of argument 0 X /4, i.e., when U6corresponds to a logical "0" output of the switch 3 receives a voltage from the first input and the second output of the switch 3 receives a voltage from the second input. So in this case U3-1U2-1f(sinX), U3-2U2-2f(cosX).

In the second case, when U6corresponds to a logical "1" output of the switch 3 receives a voltage from the second input and second output of the switch 3 voltage with the first logon. Therefore, in this case for argument /4 < <X /2, we can get the voltage U3-1U2-2f[cos(90o-X)] f(sinX), U3-2U2-1f [sin(90o--X)] f(cos X).

Therefore, for argument 0 X /2 on the first output device to receive the voltage U3-1f(sinX) Umaxsin X, and the second output asparagine, the respective functions of sec X and cosec X or tg X and ctg X enough instead of the sine-cosine Converter 2 to apply the appropriate trigonometric Converter operating in the range of variation of the argument from 0 to 4. In this case, uses the well-known trigonometric ratio sec X cosec (90o-X cosec X sec (90o-X, tg X ctg (90o-X) or ctg Xtg (90o-X).

The improved accuracy is due to the fact that for the calculation of trigonometric functions using two trigonometric Converter, each of which operates in a limited range of variation of the argument X, for example 0 X /4. This allows to reduce the error of each of the trigonometric converters, the errors which determine the accuracy of the transformation in the range of variation of the argument X from 0 to /2.

The device can be made on the standard elements using known electronic components.

1. The device for calculation of trigonometric functions containing trigonometric Converter and the amplitude detector, the input of which is the input device, characterized in that it introduced the switch, the amplitude detector is designed panel is d which is connected to the first output controlled amplitude detector, the second output of which is connected to the control input of the switch, the outputs of which are the outputs of the device.

2. The device under item 1, characterized in that the controlled amplitude detector contains an adder, a switch, a comparator, and a reference voltage, the output of which is connected to the first input of the adder, the output of which is connected to the first information input, a control input connected to the output of the comparator, and the output is the output of the detector, whose input is connected to the second input of the adder to the input of the comparator and the second information input of the switch.

 

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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.

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EFFECT: increased precision of transformation.

2 cl, 2 dwg

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