RU1831687C - Method for measurement of phase shift of two sinusoidal signals - Google Patents

Abstract

Usage: measurement technique, phase shift detection 90 ° between oscillations of the same frequency. Summary of the invention: having performed the simplest action on the signals under study, dividing their values by each other, the phase shift of 90 ° is uniquely determined between these signals, by the absence of a difference between the modules of the selected bipolar signal-private values at times ti and t2 within the half-period of the divider signal, equally spaced in time from the middle of the half-period under consideration. 3 ill.

Description

The invention relates to the field of measurement technology, and in particular to methods for determining the phase ratios of two sinusoidal signals, in particular to methods for determining a phase shift of 90 degrees of voltage or current signals 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 and vary widely.

The purpose of the invention is to improve the accuracy of determining the 90 ° phase shift of two sinusoidal signals.

When dividing two sinusoidal signals of the same frequency, the signal-to-frequency is a function of time: - ffrHAsK # t + F,) (wt + F2}} (1} where K is A / BvBsln (wt + Pr) gM): Fi and Fa are the phases of the two studied signals, and A and B are the amplitudes of the studied vibrations.The function f (t) will be a periodically discontinuous function, and in appearance it will resemble the function of tangents or contangents.

In the case of Fi F2, expression (1) can be written similarly to (6) as follows for,, / 2 and. " P

 f (t) K cosF0 + sinFoCtg (2m / T), (2)

where l / w FO is the phase difference between the studied signals. And in the case, Fi 0. can be entered for, - ЛУ2Ј Fo 0 и.-Лг. P0 $ .- l / 2 (6):

f (t) K (t / fcosFo + sin Foctg (2lg / T)} (3)

Putting Fo -270 ° or Fo 90 ° (the first variant of a phase shift of 90 degrees between two sinusoidal signals), we will have the following values: sin F0 0;

00 Сл

ON 00

Xi

with

cos Fo 1. Substituted these values in the expression (2) and (3), we obtain, respectively:

f (t) (27rt / T) f (t) (2jrt / T)

(4) (5)

Putting Fo 270 ° or F0 -90 ° (the second possible phase shift of 90 degrees between two sinusoidal signals) we will have the following values: sinF0 -1, cosFo 0. Substituting them in expressions (2) and (3), we obtain, respectively:

f (t) (27rt / T) f (t) (27rt / T)

Therefore, in the case of a phase shift of 90 degrees, we obtain the function f (t) in the form of a tangent or contangent function. multiplied by the coefficients K or -K, that is, we will have a function f (t) symmetric with respect to the time t (0) corresponding to the middle of the half-period under consideration. The coefficient - ± K will only determine the slope of the function f (t).

We define a quantity q showing the relative increment in percent of the functions of expressions (4), (6), for small deviations from the phase shifts of 90 degrees between the signals under study, as

/ q / (a1 / a2) 100%.

where ai K cosFo + K sinF0 ctg (2 L: ctg x x (2 t / T);

32 Kctg (2 jrt / t)

After simplification of the expression (8) takes the form:

/ q / {cosF0 / ctg (2 lt / T) +

+ sinF0-1} 100% (9)

As can be seen from (9), the quantity q does not depend on the coefficient ± K, but depends only on the value of the deviations of the phase shifts from 90 degrees and depends on the value of ctg (2 l t / T), i.e., on the value of the time ti. The value (sinFo-1) tends to zero for small deviations from 90 degrees (e.g. sin 89.9 ° 0.9999985). Therefore, the increment of the function f (t) will be determined by the value of the first term enclosed in square brackets in expression (9), increasing with increasing value of the phase shift deviation from 90 degrees. Let us estimate the influence of the choice of time instants tt. The cotangent is defined on the interval G; its modulus reaches values of several tens or more at t close to

zero or P, i.e., at the edges x of the considered divider signal interval, therefore, the q value in these regions tends to zero. With the value of lctg (2 t / T) | 1 that

5 will be at ti T / 8 and t2 3T / 8, I q I cos F0. For example, for small deviations of 0.1 degrees from a phase shift of 90 degrees, we have the following values: cos 89.9 0.001745, and Iql 0.1745%.

10 Therefore, if we take the values of the signals-quotient having different signs at these time instants, their modules will differ by almost 0.35%, and if we choose the instants of time ti and t2 closer to

15 in the middle of the interval under consideration, the increments Iql will increase for a fixed value of F0.

Similarly, the increment for the tangent function is determined from expressions (5) and (7)

20 according to the formula:

Iq (az-a4) 100%,

(YU)

where az K {1 / cosF0 + sinF0 ctg (2 L t / T)} 25a4 Ktg (2jrt / T)

The expression az can be represented as follows:

azK tg (2 L t / T) (2 L t / t) cos F0 + 30 + sin F0

Then expression (10) after transformations will have the following form:

35

lql {cos Fo + + ctg (27Tt / T)} 100%

(eleven)

If I ctg (2 vt IT) / 1 for small deviations from 90 degrees, the condition cos F0 1 will be satisfied. Therefore, from expression {11) we obtain iqj cos F0 similar to that obtained previously. And if we take the time instants q and t2 closer to the middle of the half-period of the divider signal, then

increments (q) will also increase for a fixed value of Fo.

Thus, for small deviations from the phase shifts of 90 ° of two sinusoidal signals, the values of the function f (t) cHmana of the individual will rise or fall relative to the abscissa axis, i.e., the symmetries of the function f (t) will be broken relative to the middle of the field under consideration at the period of the divider signal, and absolute

The signal values are the quotient at selected times ti and 1d. evenly spaced from the middle of the half-period under consideration will differ by an amount greater than the error of the comparison method.

A quantitative assessment of the capabilities of the proposed method was carried out by oscillographing the signals under investigation and using a computer. In the first embodiment, the device for implementing the method (Fig. 1) comprises a division unit 1 and an oscilloscope, the input of which is connected to the output of the division side 1. and is fed to the two inputs of the latter sinusoidal signals Ux (t) and Uy {t). As a division unit, a digital voltmeter B7-23 operating in the division mode and an oscilloscope of the C1-VZ type were used. The signals Ux (t) and Uy (t) had a frequency f of 0.2 Hz and an amplitude of Ux 200 and Uy of 20 mV, respectively. The phase shift between the signals was set using the phase shifting BC 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 - 2-10 mA signal was divided by 10 and 100 times, respectively.

In the second embodiment, the method was tested on an IBM PC / AT computer. Sinusoidal signals with a frequency f of 0.2 Hz or less at a sampling frequency of 200 Hz and amplitudes with arbitrary units A 2-104 and B 2-103 were simulated using a computer with phase difference values set by the operator. In accordance with the program, the computer divided the signals, and on the display screen, the operator observed the nature of the change in the function f (t) on each of the half-periods of the divider signal.

Examples of the obtained graphs with deviations from the phase shift of 90 degrees by 0.1 are shown in Fig. 2,3. The studies showed that for various combinations of the parameters of the studied oscillations in amplitude and frequency, phase shifts of 90 degrees between the signals were clearly determined at small amplitudes and at low frequencies up to deviations from the desired shifts of less than 0.01 "values frequencies of the studied signals in hundredths of a hertz.

One of the best digital phase meters F2-34 available today allows determining the phase shift of two sinusoidal signals, but guarantees the accuracy of determination to 0.2 at frequencies not lower than 1 Hz, which is much worse than the proposed

way.

The efficiency of determining 90 degree phase shifts between the studied signals in the infra-low frequency region and with a small value of at least one of the signals is achieved due to the fact that the method is not used, as in other known methods, for a number of operations that are the source of errors, namely, measurement signal crossing times

the level of the reference voltage, comparing the durations of the generated pulses and other operations that are relatively complicated with the proposed method.

The proposed method has a large

value because of its simplicity and reliability in conducting physical experiments.

Field of the invention Method for determining the phase ratio

two sinusoidal signals, according to which the studied signals interact, and the phase ratio is judged by a qualitative assessment of this interaction, characterized in that

the values of one signal under investigation are divided by the values of another, the signal-private is recorded, at least two values of the signal-private are selected over a time interval located within half of any period of the divider signal and not exceeding this half-period in duration, and the values of the signal-private are selected at time instants ti and t2 equidistant in time with respect to the middle of the half-period of the divider signal under consideration, and a 90 ° phase shift between the divider and divider signals is determined when the selected values The signal is private within the studied half-period

the divider signal have different signs, and the moduli of these values of the private signal do not differ by an amount greater than the error of the selected comparison method.

fiv & f

FIG. 2

fi & 3