RU2037831C1 - Method of measuring phase relations between two sinusoidal signals - Google Patents

Abstract

FIELD: measurement technology. SUBSTANCE: after values of signals are divided one by another, the difference may be determined for phase delay or phase excel of signal-dividend relatively the signal-divisor at specific relations of signal-quotient at time moments t₁, t₂. These time moments differ from medium part of time interval to be described and being equal to half-period of signal-divisor. EFFECT: measurement technology. 2 cl, 3 dwg

Description

The invention relates to measuring equipment, in particular to methods for determining the difference in the lead and phase lag of 90 ^about one signal relative to another signal of the same frequency, and is intended for predominant use in precision devices of the low-frequency range, while the signal amplitudes can vary significantly from each other and vary widely
Known methods for determining the phase shift of 90 ^about when measuring the phase difference [1, 2, 3] These methods are characterized by considerable complexity due to the large number of operations, which include the formation of additional pulses at certain points in time, comparing time intervals, introducing modulation coefficients, correlation and etc. Furthermore considerable complexity of these methods arises error in determining the phase shift ⁹⁰ at a small amplitude at least one of the signals, and this error becomes significant at subsonic frequencies, when decreasing the rate of change signal value and the response time of the threshold device becomes ambiguous, especially at small amplitudes ( or the amplitude of at least one of the signals).

A known method [4] in accordance with which the studied signals are multiplied and recorded the resulting voltage having a constant component, and then determine the phase shift of 90 ^about when the constant component becomes equal to zero.

 This method is characterized by disadvantages at infra-low frequencies and small signal amplitudes due to the need to isolate the dc component with high accuracy. In addition, the method does not distinguish whether it is ahead or out of phase with one signal relative to another.

Simpler oscillographic methods are known for determining the phase shift when measuring the phase difference using Lissajous figures, for example [5] which is closest to the claimed method. The method is based on the deflection plates of the oscilloscope and the slope of the figures in the form of an ellipse on the screen of the oscilloscope is judged that is ahead or behind in phase by ⁹⁰ ° one with respect to another signal.

Definition of the phase shift 90 ^of the Lissajous figures due to the finite resolution of the oscilloscope capabilities defined beamwidth, is difficult. Moreover, with a small value of the amplitude of at least one of the signals, the studied voltages are recorded in the nonlinear section of the deflecting voltage. In addition, the error in the registration of the studied signals with an oscilloscope increases in the infra-low frequency range due to the difficulties of quantitative measurements.

 The aim of the invention is to improve the accuracy of measurement.

The goal of the method for determining the phase relationship 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, is achieved by the fact that the values of one signal under study are divided by the values of the other, the signal-private signal is recorded, at least two signal-private values on a time interval located within half of any period of the divider signal and not exceeding the duration of this half one, and the values of the signal-private are selected at time t ₁ and t ₂ equally spaced in time relative to the middle of the considered half-period of the signal-divider, and distinguish advance or phase lag of 90 ^about between the signals of the dividend and the divider by the value of the sign of the signal-private, taken at a certain time, when the selected values of the signal-private inside the studied half-period of the signal-divider have different signs, and the modules of these values of the signal-private do not differ by an amount greater than the error of the selected toda comparison. A specific time for the sign value of the signal-private is chosen at time t ₁ .

The essence of the invention lies in the fact that, having performed the simplest action on the studied signals, dividing the values by each other, it is possible to unambiguously determine ^{whether the} signal-divisible signal is divisible or ahead in phase by 90 ° from the signal-divider by the value of the sign of the signals-private taken at a certain time at certain ratios of the selected signals-private at time t ₁ and t ₂ equally spaced from the middle of the considered half-period of the divider signal.

When dividing two sinusoidal signals of the same frequency, the signal-private is a function of time:
f (t) [A sin (ωt + F ₁ )] / [B sin (ωt + F ₂ )] (1) where B sin (ωt + F ₂ ) ≠ 0;
F ₁ and F _{2 the} initial phases of the two studied signals;
A and B are the amplitudes of the studied vibrations.

 The function f (t) is a periodic discontinuous function and in appearance resembles the functions of tangents or cotangents.

In the case of F ₁ > F ₂ , F ₂ 0, expression (1) can be written as follows for K> 0, 0≅F _o ≅π / 2 and K <0, π / 2 <F _o ≅π:
f (t) K [cos F _o + sin F _o ctg (2 π t / T)] (2) where T 2 π / ω; KA / B;
F _o the phase difference between the studied signals.

In the case of F ₂ > F ₁ , F ₁ 0 can be written for K> 0, -π / 2≅F _o ≅0 and К <0, -π≅F _o <-π / 2
f (t)
K1 / [cos F _o + sin F _o ctg (2 π t / T)] (3)
Putting F _o 270 ^about or F _o 90 ^about (for the case when the divisible signal is 90 ^o ahead of the phase divider signal), have the following meanings: sin F _o 0; cos F _o 1. Substituting these values in expression (2), get
f (t) K [ctg (2 π t / T)] (4)
Putting F _o 270 ^о or F _o -90 ^о (for the case when the divisible signal is 90 ^{o out} of phase with the divider signal), they have the following values: sinF _o -1, cosF _o 0. Substituting them into expression (3 ) receive
f (t) -K [tg (2 π t / T)] (5)
Therefore, when the signal-divisible is 90 ^o phase ahead ^{of the} signal-divider, a signal-private corresponding to the function f (t) is obtained in the form of cotangent multiplied by the coefficient K, i.e. the function f (t), symmetric with respect to the time t _o located in the middle of the half-period under consideration, when f (t _o ) 0.

When the dividend signal lags in phase by ⁹⁰ by divider signal obtained quotient signal corresponding to the function f (t) as a tangent function. Therefore, a function f (t) is obtained that is symmetric with respect to the time t _o corresponding to the middle of the half-period under consideration. The coefficient K determines only the slope of the function f (t).

Once the dividend signal leads the signal-divider ^90, record signal to the quotient in the form of cotangent function, and when the signal is divisible behind the divider signal ⁹⁰ to RESIDENCE tangent function, so advance or retard in phase by ⁹⁰ ° is determined by the value of the sign of the signal-private, selected at a certain point in time t ₁ , which can be selected at the beginning of the half-period under consideration or at the end of it. The choice of time at time t _{1 is} preferable, since at this moment of time, the value of the signal-private is recorded and stored.

Determine the value of q, showing the relative increment in percent of the functions of expression (4) for small deviations from the phase shifts of 90 ^about between the studied signals as
q (a ₁ / a ₂ ) 100% (6) where a ₁ K cos F _o + Ksin F _o ctg (2 π t / T)
K ctg (2 π t / T);
a ₂ K ctg (2 π t / Т).

After simplification, expression (6) takes the form
lql [cos F _o / ctg (2 π t / T)] +
+ sin F _o 1} 100% (7)
As seen from the expression (7), the value q is independent of the K factor, and depends only on the value of phase shift deviation from ^about 90 and the value ctg (2 π t / T), i.e. from the values of time t ₁ and t ₂ . The value of sin F _o -1 with small deviations from 90 ^about tends to zero (for example, the following ratio sin 89.90.9999985 is true). Therefore, the increment of the function f (t) is determined by the value of the first term enclosed in square brackets in expression (7), increasing with increasing value of the deviation of the phase shift from 90 ^about .

The effect of the choice of time instants t ₁ and t _{2 is} evaluated. The cotangent is defined in the interval 0 <t <π, its modulus reaches values of several tens or more at t close to zero or π, i.e. at the edges of the considered interval of the divider signal; therefore, the q value in these regions tends to zero. With the value of lctg (2 π t / T) l 1, which will be with the values of t ₁ T / 8 and t ₂ 3T / 8, the quantity lql cosF _o . For example, with small deviations of 0.1 ^about the phase shift 90 ^about have the following meanings:
cos 89.9 0.001745 and lql 0.1745%
Therefore, if we take the values of the signals-private, having different signs at times t ₁ , t ₂ closer to the middle of the considered interval, then the increments lql increase for a fixed value of F _o .

Similarly, the increment for the tangent function is determined from expression (5) by the formula
lql = [(a ₃ a ₄ ) / a ₄ ] 100% (8) where a ₃ K1 / [cosF _o + sinF _o ctg (2 π t / T)]
a ₄ K tg (2π ^. t / T)
The expression a ₃ can be represented as follows:
a ₃ [Ktg (2 π t / T)] / [tg (2 π t / T) cosF _o +
+ sinF _o ]
Then the expression (8) after the conversion has the following form:
lq lcosF _o / [cosF _o +
+ ctg (2 π t / T)] 100% (9)
For l ctg (2 π t / T)] 1, for small deviations from 90 ^о , the condition cosF _o << 1 is fulfilled. Therefore, from expression (9) we obtain lql cosF _o , similar to that obtained earlier. If we take the time instants t ₁ , t ₂ closer to the middle of the half-period of the divider signal, then the increments lql also increase for a fixed value of F _about .

Thus, for small deviations from the phase shifts 90 ° ^of two sinusoidal signals, the values of the function f (t) of the signal-private rise or fall relative to the abscissa, i.e. the symmetry of the function f (t) with respect to the middle of the considered half-period of the divider signal is violated, and the absolute values of the signal-private at selected time instants t ₁ , t ₂ , equally spaced from the middle of the considered half-period, 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 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, and sinusoidal signals U _x (t) and U _y (t) are supplied to the two inputs of the latter. A digital voltmeter B7-23 operating in the division mode was used as a division block, and an oscilloscope of the C1-83 type was selected. The signals U _x (t) and U _y (t) had a frequency f of 0.2 Hz and amplitudes of U _x 200 mV and U _y 20 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 U2000 mV signal was divided by 10 and 100 times, respectively.

 In the second embodiment, the method was tested using simulation 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 of A 20000 and B 2000 were modeled using a computer with the 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 for the case of F _o 90 ^about (leading) and F _o -90 ^about (phase lag) are presented in Figs. 2 and 3. Studies have shown that the phase lead by 90 ^about and the phase lag by 90 ^about clearly differed at small amplitudes at infralow frequencies in hundredths of a hertz up to deviations from quadrature shifts of less than 0.01 ^o .

One of the modern digital devices, for example, a phasometer of the type F2-34, allows you to determine the phase shift of two sinusoidal signals, but guarantees the preservation of measurement accuracy to values of F _about 0.2 ^about at frequencies not lower than 1 Hz, which is much worse than the proposed method.

The effectiveness of differences in the lead or phase lag of 90 ° ^{of the} studied sinusoidal signals 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 is not used, as in other known methods [1-3], a number of operations , which are the source of errors, such as measuring the time moments when the signals cross the reference voltage level, comparing the durations of the generated pulses and other operations that are relatively complicated compared to the proposed standard special definition.

Claims (2)

1. METHOD FOR DETERMINING THE PHASE RELATIONSHIP 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, characterized in that the values of one signal under study are divided by the values of another, the signal-private signal is recorded, and the signal is selected at least two signal-frequency values on a time interval located within half of any period of the divider signal and not exceeding the duration of this half-period, Rich value signal Private selected time instants t ₁ and t _2, equally spaced in time relative to the middle of the considered half-cycle of the signal divider, and distinguish advance or retard the phase by 90 ^o between the signals of the dividend and divisor by the value of the signal-private sign taken in a certain time, when the selected values of the signal-private inside the studied half-period of the signal of the divider have different signs, and the modules of these values of the signal-private do not differ by an amount greater than the error of the selected method comparison. 2. The method according to claim 1, characterized in that a certain time for determining the sign value of the signal-private is chosen at time T ₁ .

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