RU2000580C1 - Method for determining phase correlation of two sine-wave signals - Google Patents

Abstract

Usage: measuring technique, determination of the phase and phase imbalance of two harmonic vibrations ./ of one frequency. Summary of the invention: having performed the simplest action on the signals under study — dividing their values by each other, they determine the phase and antiphase conditions when the modulus of the extreme value of the signal-partial at the half-period of the divider signal does not differ from the module of any other value of the signal-private within the considered half-period an amount greater than the error of the comparison method. 3 ill.

Description

The invention relates to measuring technique, and in particular to methods for determining phase ratios, in particular to methods for determining the in-phase and antiphase characteristics of two sinusoidal voltage signals or currents of the same frequency, and is intended for predominant use in precision devices of the low-frequency range, when the signal amplitudes can significantly vary among themselves and vary widely.

Various methods are known for determining the phase ratios of two sinusoidal signals when measuring their phase difference. These methods are characterized by considerable complexity due to the large number of operations consisting in the formation of additional pulses at certain points in time, comparing time intervals, introducing modulation coefficients, correlation, etc. In addition to the considerable complexity of these methods, an error of determination

in-phase and out-of-phase with a small amplitude of at least one of the signals, especially in the infra-low-frequency range of measurements, this error becomes significant due to the fact that at the low-frequency frequencies the signal change rate is significantly reduced and the response time of threshold devices becomes ambiguous, and this ambiguity is even more increases at small amplitudes (or the amplitudes of at least one of the signals).

Simpler oscillographic methods are known for determining the phase ratios of two sinusoidal signals. These methods are based on the use of deflecting plates of the oscilloscope, when the sign of the phase difference of the signals under investigation is judged by the determined position of the beam mark on the oscilloscope screen.

In the method, the test signals are supplied each to its own pair of deflecting plates. Determination of in-phase and out-of-phase by Lissajous figures due to finite section

with

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the decisive ability of the oscilloscope, determined by the beam width, is difficult, moreover, with a small value of the amplitude of at least one of the signals for recording the studied voltages, it will be carried out in a nonlinear section of the deflecting voltage. In addition, the error in the registration of the studied signals with an oscilloscope increases in the low-frequency range due to the difficulties of quantitative measurements.

The closest technical solution to the claimed one is the method in which the signals under investigation are supplied to the CRT deflecting plates, peak-like pulses are formed from one of the signals and also fed to the CRT deflecting plates. An amplitude mark is formed on the oscilloscope screen, by the position of which the signal parameters can be judged on the ordinate axis.

This method has the same drawbacks that are known, that is, at infra-low frequencies and at small signal amplitudes, the error in determining the parameters of the signals increases significantly. In addition, this method does not allow to determine the synphaenic and antiphase signals,

The aim of the invention is to enhance the functionality.

The goal in the method of determining the phase ratio of two sinusoidal signals, according to which the studied signals interact, and the phase ratio is judged by a qualitative assessment of the results of this interaction, is achieved by the fact that the values of one signal under study are divided by the values of the other, the signal quotient, select at least two values of the signal-quotient on a time interval located within half of any period of the divider signal and not exceeding the duration of this half a period, one of the signal-private values being chosen extreme, and the phase and antiphase of the dividend and divider signals are determined by the absence of differences between the extreme value of the signal-private and any other value inside the studied half-period of the signal-divider.

When dividing two sinusoidal signals of the same frequency, the signal-to-frequency is a function of time

f (t) Asln (ewt + Fi) /

/ In sin (ait + F2),

(1)

where B sin (ai + F2); Fi and F2 are the phases of the two studied signals;

A and B are the amplitudes of the studied vibrations.

The function f (t) will be a periodic discontinuous function, and in appearance resembles the functions of tangents or cotangents,

In the case, expression (1) can be written as follows for K 0.0 Fo / 2 and K 0, / 2 Fo l

fifteen

f (t) K cos Fo + sln Ft std (2 g / T),

(2)

where T - 2 / W FO is the phase difference between the studied vibrations.

And in the case, you can enter for K 0, - / 2 F0 0 and

, - FO - / 2

25

f (t) K 1 / cosFo + slnFo ctg (2 t / T)

(3)

Having set (the condition of in phase), we will have the values sin cos F0 ° 1. Substituted these values in expressions (2) and (3), we obtain, respectively:

f (t) K + K (0 / tg wt) hK (4)

f (t) K / HOctg (2 t / T)) K (5)

Setting F0 ± 180 (antiphase condition), we have the values slnF0 0; 4Q cosF0 -1 Substituting them in expressions (2) and (3), we obtain respectively.

FN-K + K (0 / tg wt) -K

(6)

45

f (t) 0 ctg 2 g / T -K (7)

Therefore, in the case of in-phase and out-of-phase, we obtain the function f (t) in the form of a straight line numerically equal to the value ± K, i.e. f (t) ± K. For small deviations from ideal in-phase and out-of-phase, the resulting ± K will add the value formed from the second terms enclosed in

square brackets of expressions (4) to (7), in which sinFo values are substituted for zero. Since the values of tg w t and ctg with t are considered over the interval of the half-period of the divider signal, that is, 0, the values of the terms that are added

or subtracted from the values ± K of expressions (4) - (7), they will be maximum in absolute value at the beginning and at the end of the half-period under consideration.

Thus, for small deviations from the in-phase and antiphase of the two sinusoidal signals, the values of the signal f (t) function - private at the beginning or end of each half-period under consideration will deviate from ± K. And the extreme value of the signal is private-private (maximum or minimum) in Comparison with any other in a given interval within the half-period under consideration will indicate in-phase and antiphase in the absence of differences among themselves, taking into account the error of the selected comparison method.

A quantitative assessment of the capabilities of the proposed method was carried out by oscillography of the studied signals and using a computer. In the first embodiment, the device for implementing the method (Fig. 1) comprises a division unit 1 and an oscilloscope 2, the input of which is connected to the output of the division unit 1, and the sinusoidal signals Ux (t) and Uy (t) are supplied to the two inputs of the latter. A digital voltmeter B7-23 was used as a division unit. operating in the division mode, and the oscilloscope type CI-83 is selected. The signals Ux (t) and Uy (t) had frequencies of 2 Hz and an amplitude of Ux-200 mV and mV, respectively. The phase shift between the signals was set using a phase-shifting RC circuit, and the signals themselves were formed from a sinusoidal signal from the output of the GZ-110 type generator, the output amplitude of the U-2 signal 103 mV was divided by 10 and 100 times, respectively.

In the second embodiment, the method was tested on an 18M PC-AT computer. Sinusoidal signals with a frequency of f-0.2 Hz or less at a sampling frequency of 200 Hz and amplitudes with arbitrary units xU3 and B-2-104 were modeled using a computer with phase difference values. which the operator asked. In accordance with the program, the computer divided the signals, and on the display screen, the operator observed the nature of the change in function at each of the half-periods of the divider signal.

Examples of obtained graphs of the functions f (t) for the case of 1 ° and 9 at an oscillation frequency of 0.2 Hz are presented in FIG. 2, 3. The studies performed show 5 indicators. that for various combinations of the parameters of the studied oscillations in amplitude and frequency, in-phase and antiphase were clearly determined both for small values of amplitudes and for small values of frequencies 0 up to deviations from in-phase and antiphase less than 0.01 °. and the frequency values were hundredths of a hertz.

One of the modern digital phase meters, for example, type Ф2-34, allows determining phase differences, but guarantees the possibility of determining up to values of 2 ° at frequencies not lower than 1 Hz, which is much worse in accuracy than the proposed method.

0 The effectiveness of determining the in-phase and out-of-phase in the field of infra-low-frequency oscillations and with a small value of at least one of the signals is achieved due to the fact that the method does not use, as in other known methods, a number of operations that are a source of errors, such as measurement of time points of the signal crossing the reference voltage level, comparing the durations of the generated pulses and others.

Claims (1)

SUMMARY OF THE INVENTION A method for determining the phase ratio of two sinusoidal signals, in accordance with which the studied signals interact, and the phase ratio is judged by a qualitative assessment of the results of this interaction, characterized in that the values of one studied 0 of the signal are divided by the values of the other, the signal-private is recorded, at least two values of the signal-private are selected on a time interval located within half of any period of the signal5 la divider and not exceeding this half-period in duration, one of the signal values being of the particular is chosen extreme and the phase and antiphase of the signals of the dividend and the divisor are determined by the absence of a distinction between the extreme value of the signal-private and any other value inside the studied half-cycle Nala-divider. t-t / 2 pЈ / e. Z fug. 3