RU2486529C2 - Method for joint measurement of frequency, phase and initial phase of harmonic signal - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: method includes digitisation of an analogue signal, representation of its fragment with three digital codes S₁, S₂, S₃, generated at the moments of time t₁, t₂, t₃ and used to calculate the signal frequency f according to the formula $$f=\frac{1}{2\pi \tau }\arccos \frac{S_1+S_3}{2S_2},$$

where τ - digitisation interval. At the same time the signal fragment and the appropriate three codes are selected so that the code S₂ is not zero. In process of frequency variation the same codes are used to calculate the amplitude U, the phase φ and the initial phase of the signal φ₀ in accordance with the following expressions: $$U=2\left|S_2\right|\sqrt{\frac{\left(S_2^2-S_1{S}_3\right)}{\left[4S_2^2-{\left(S_1+S_3\right)}^2\right]}},$$

$$\phi =\arccos \left(\frac{S_2}{U}\right)$$

and φ₀=φ-2πft₂, where the phase φ corresponds to the moment of time t₂.

EFFECT: accelerated measurements.

Description

The present invention relates to measuring technique and can be used to simultaneously measure the frequency, amplitude, phase and initial phase of a continuous or pulsed harmonic signal from the same minimum set of source data.

A known method of determining the frequency of the signal (RF patent for the invention No. 2117306), which consists in the fact that the signal is sampled, its spectrum is calculated, the number of the maximum spectral component is determined, its amplitude is measured, as well as the number and amplitude of the largest adjacent to it, and these initial data in the frequency calculation formula.

In this analogous method, as well as in the present invention, the signal is sampled in time and the discrete values of the signal are represented by digital codes. In addition, the initial data used to calculate the frequency carry information about the frequency and amplitude of the signal.

The disadvantage of this method is that it does not use the signal directly, but its spectrum (i.e., an additional transformation — the Fourier transform of the signal) is performed. The initial data (in this case, the amplitudes of the spectral components) are used in the frequency calculation formula, and, therefore, the errors in the measurement of the amplitudes make an additional contribution to the errors in the calculation of the frequency. In addition to metrological factors that determine the errors in the measurement of amplitudes (such as, for example, the digit capacity of a digital code), objective factors are also possible, for example, due to the fact that the found maximum spectral component may not exactly correspond to the signal frequency, and therefore its measured value will be underestimated relatively true.

There is also a method of measuring the amplitude of harmonic signals (RF patent for the invention No. 2060475), which consists in the fact that in the signal spectrum register a harmonic with a maximum amplitude, determine its frequency and use this frequency in the formula for calculating the amplitude of harmonic oscillations.

In this analogue method, as in the present invention, the same initial data are used to measure the amplitude of the signal and its frequency (in this analogue it is the spectral component with maximum amplitude).

The disadvantage of this analogue method, as well as the previous one, is that it uses not the signal, but its Fourier transform, and the use of the frequency of the spectral component with maximum amplitude in the amplitude calculation formula. Because of this, frequency measurement errors associated, for example, with the fact that the frequency of the spectral component with the maximum amplitude may not coincide with the true signal frequency, make an additional contribution to the errors in the calculation of the amplitude.

, где τ - интервал дискретизации; при этом фрагмент сигнала и соответствующую ему тройку кодов выбирают так, чтобы код S₂ не равнялся нулю.Closest to the claimed method in technical essence is the method implemented in the "Device for determining the frequency of an alternating voltage" (USSR Author's Certificate No. 1185260. Publ. 30.10.88. Bull. No. 40) and includes sampling of an analog signal, presentation of its fragment by a triple digital codes S ₁ , S ₂ , S ₃ generated at time t ₁ , t ₂ , t _3, respectively, and used to calculate the frequency of the signal f according to the formula $$f=\frac{\mathrm{one}}{2\pi \tau }\arccos \frac{S_{\mathrm{one}}+S_3}{2S_2}$$

where τ is the sampling interval; wherein the signal fragment and the corresponding three codes are chosen so that the S ₂ code is not equal to zero.

, где τ - интервал дискретизации; выбор такого фрагмента сигнала и соответствующей ему тройки кодов, при котором код S₂ не равнялся бы нулю.Signs that coincide with the features of the invention: discretization of an analog signal, presentation of its fragment by a triple of digital codes S ₁ , S ₂ , S ₃ generated at time instants t ₁ , t ₂ , t _3, respectively; using codes to calculate the frequency of the signal f according to the formula $$f=\frac{\mathrm{one}}{2\pi \tau }\arccos \frac{S_{\mathrm{one}}+S_3}{2S_2}$$

where τ is the sampling interval; the choice of such a fragment of the signal and the corresponding triple of codes, in which the code S ₂ would not be zero.

The disadvantage of this method, selected as a prototype, is the underutilization of information about the signal contained in the generated digital codes S ₁ , S ₂ , S ₃ . Meanwhile, knowing the codes S ₁ , S ₂ and S ₃ , it is possible not only to measure the frequency, but in addition to the found frequency, to measure the amplitude, phase and initial phase of a continuous or pulsed harmonic signal. In addition, the measurement of the amplitude, phase and initial phase can be performed simultaneously (in parallel) with the frequency measurement. This will speed up measurements.

The task to which the invention is directed is to accelerate measurements by simultaneously using the generated digital codes S ₁ , S ₂ , S ₃ both for measuring the frequency and for measuring the amplitude, phase and initial phase of the analyzed continuous or pulsed harmonic signal.

, $$\varphi =\arccos \left(\raisebox{1ex}{$S_2$}\!\left/ \!\raisebox{-1ex}{$U$}\right.\right)$$

и φ₀=φ-2πft₂, где фаза φ соответствует моменту времени t₂.This technical result is achieved in that the existing digital codes S ₁ , S ₂ , S ₃ simultaneously with the frequency measurement are used to calculate the amplitude U, phase φ and the initial phase of the signal φ ₀ in accordance with the expressions: $$U=2\left|S_2\right|\sqrt{\raisebox{1ex}{$(S_2^2-S_{\mathrm{one}}{S}_3$}\!\left/ \!\raisebox{-1ex}{$\left[\mathrm{four}{S}_2^2-{(S_{\mathrm{one}}+S_3)}^2\right]$}\right.}$$

, $$\varphi =\arccos \left(\raisebox{1ex}{$S_2$}\!\left/ \!\raisebox{-1ex}{$U$}\right.\right)$$

and φ ₀ = φ-2πft ₂ , where the phase φ corresponds to time t ₂ .

, где τ - интервал дискретизации; при этом фрагмент сигнала и соответствующую ему тройку кодов выбирают так, чтобы код S₂ не равнялся нулю, одновременно с измерением частоты, те же коды используют для вычисления амплитуды U, фазы φ и начальной фазы сигнала φ₀ в соответствии с выражениями:To achieve a technical result in a method for jointly measuring the frequency, amplitude, phase and initial phase of a harmonic signal, including sampling an analog signal, presenting its fragment with a triple of digital codes S ₁ , S ₂ , S ₃ generated at time t ₁ , t ₂ , t _3, respectively, and used to calculate the frequency of the signal f according to the formula $$f=\frac{\mathrm{one}}{2\pi \tau }\arccos \frac{S_{\mathrm{one}}+S_3}{2S_2}$$

where τ is the sampling interval; while the signal fragment and the corresponding three codes are selected so that the S ₂ code is not equal to zero, simultaneously with the frequency measurement, the same codes are used to calculate the amplitude U, phase φ and the initial phase of the signal φ ₀ in accordance with the expressions:

, $$\varphi =\arccos \left(\raisebox{1ex}{$S_2$}\!\left/ \!\raisebox{-1ex}{$U$}\right.\right)$$

и φ₀=φ-2πft₂, где фаза φ соответствует моменту времени t₂. $$U=2\left|S_2\right|\sqrt{\raisebox{1ex}{$(S_2^2-S_{\mathrm{one}}{S}_3)$}\!\left/ \!\raisebox{-1ex}{$\left[\mathrm{four}{S}_2^2-{(S_{\mathrm{one}}+S_3)}^2\right]$}\right.}$$

, $$\varphi =\arccos \left(\raisebox{1ex}{$S_2$}\!\left/ \!\raisebox{-1ex}{$U$}\right.\right)$$

and φ ₀ = φ-2πft ₂ , where the phase φ corresponds to time t ₂ .

Comparison of the proposed method with the prototype shows that it contains new features, i.e. meets the criterion of novelty. From a comparison with analogues it follows that the claimed method meets the criterion of "significant differences", as in the analogues are not found new claimed features.

To prove the existence of a causal relationship between the claimed features and the achieved technical result, we consider the essence of the proposed method for jointly measuring the frequency, amplitude, phase and initial phase of a harmonic signal and compare it with the prototype method and analog methods.

Harmonic signal

$$S(t)=U\cos (2\pi ft+\varphi )(\mathrm{one})$$

It is considered completely known if the amplitude U, the frequency f, and the initial phase φ of the signal are known. This signal is considered completely known because, knowing U, f and φ, it is possible to calculate (and this is a direct task) the value of the signal at any time t.

On the other hand, there is a one-to-one correspondence between the signal S (t) and its parameters U, f, and φ. Therefore, if the signal S (t) is known (for example, given by a sequence of discrete samples obtained with a time interval τ), then the parameters U, f, and φ can be determined. To determine them (inverse problem) it is enough to compose and solve three equations of the form with respect to U, f and φ:

$$S(t_j)=U\cos (2\pi f{t}_j+\varphi )(2)$$

with three unknowns. Show it.

Denote:

$$t_j=\tau j;S(t_j)=S_j;2\pi f{t}_j=2\pi f\tau j=\alpha j;gde\alpha =2\pi f\tau .(3)$$

Given these notations, equation (2) takes the form:

$$S_j=U\cos (\alpha j+\varphi )(\mathrm{four})$$

We make 3 equations of the form (4) for -1≤j≤1:

$$S_{-\mathrm{one}}=U\cos (-\alpha +\varphi )(5)$$

$$S_0=U\cos \varphi (6)$$

$$S_{\mathrm{one}}=U\cos (\alpha +\varphi )(7)$$

where S _-1 , S ₀ , S ₁ - signal samples.

We reveal equations (5) and (7):

$$S_{-\mathrm{one}}=U\cos (-\alpha )\cos \varphi -U\sin (-\alpha )\sin \varphi ,(8)$$

$$S_{\mathrm{one}}=U\cos \alpha \cos \varphi -U\sin \alpha \sin \varphi .(9)$$

Given the parity of the function cos (x) and the oddness of the function sin (x), we add equations (8) and (9):

$$S_{-\mathrm{one}}+S_{\mathrm{one}}=2U\cos \alpha \cos \varphi (10)$$

Substituting into this equation instead of Ucosφ the value S ₀ from equation (6) and solving the obtained equation with respect to cosα, we obtain:

$$\cos \alpha =(S_{-\mathrm{one}}+S_{\mathrm{one}})/(2S_0).(\mathrm{eleven})$$

The angle α and frequency f are now determined by the formulas:

$$\alpha =\arccos ((S_{-\mathrm{one}}+S_{\mathrm{one}})/(2S_0)),(12)$$

$$f=\alpha /(2\pi \tau )=\frac{\mathrm{one}}{2\pi \tau }\arccos \frac{S_{-\mathrm{one}}+S_{\mathrm{one}}}{2S_0}(13)$$

U and φ can be found from equations (5), (6), (7) and (9) by the substitution method. Find the amplitude U. For this, from equation (6) we obtain cosφ:

$$\cos \varphi =S_0/U(\mathrm{fourteen})$$

and substitute it in (9). Bearing in mind that sin ² x = 1-cos ² x, we square equation (9) and, after transformations, we obtain:

$$U=\raisebox{1ex}{$\sqrt{S_0^2+S_{\mathrm{one}}^2-2S_0{S}_{\mathrm{one}}\cos \alpha }$}\!\left/ \!\raisebox{-1ex}{$\sin \alpha (\mathrm{fifteen})$}\right.$$

or taking into account (11) and the formula sin ² x = 1-cos ² x:

$$U=2\left|S_0\right|\sqrt{\raisebox{1ex}{$(S_0^2+S_{-\mathrm{one}}{S}_{\mathrm{one}})$}\!\left/ \!\raisebox{-1ex}{$\left[\mathrm{four}{S}_0^2-{(S_{-\mathrm{one}}+S_{\mathrm{one}})}^2\right]$}\right.}(16)$$

Now we find the initial phase φ from equation (14):

$$\varphi =\arccos \left(\raisebox{1ex}{$S_0$}\!\left/ \!\raisebox{-1ex}{$U$}\right.\right)(17)$$

The phase calculated by the formula (17) corresponds to the moment of obtaining the reference S ₀ . Knowing the position of the reference S ₀ on the time axis, we can calculate the phase incursion of the signal relative to the zero point in time. With its help, we can recalculate φ to the zero point in time, i.e. calculate the initial phase of the signal φ ₀ .

Considering that the essence of the above will not change from the replacement of indices, we replace in formulas (13), (16) and (17): S _-1 by S ₁ ; S ₀ at S ₂ and S ₁ at S ₃ and get the formula given in the claims of the present invention. In addition, we take into account that the phase incursion mentioned in the previous paragraph can be represented by the expression 2πft ₂ in the context of the claims.

The implementation of the proposed method will allow for three samples S ₁ , S ₂ , S ₃ signal without additional costs, transformations and actions to simultaneously calculate both the frequency and other parameters of a continuous or pulsed harmonic signal (amplitude, phase and initial phase). The simultaneous performance of these measurements will reduce the total measurement time, i.e. speed up measurements.

Claims (1)

A method for jointly measuring the frequency, amplitude, phase and initial phase of a harmonic signal, including sampling an analog signal, representing its fragment by a triple of digital codes S ₁ , S ₂ , S ₃ generated at time instants t ₁ , t ₂ , t ₃ and used to calculate signal frequency f according to the formula $$f=\frac{\mathrm{one}}{2\pi \tau }\arccos \frac{S_{\mathrm{one}}+S_3}{2S_2}$$ where τ is the sampling interval; in this case, the signal fragment and the corresponding three codes are selected so that the S ₂ code is not equal to zero, characterized in that at the same time as measuring the frequency, the same codes are used to calculate the amplitude U, phase φ and initial phase of signal φ ₀ in accordance with the expressions:
$$U=2\left|S_2\right|\sqrt{\frac{\left(S_2^2-S_{\mathrm{one}}{S}_3\right)}{\left[\mathrm{four}{S}_2^2-{\left(S_{\mathrm{one}}+S_3\right)}^2\right]}},$$

$$\varphi =\arccos \left(\frac{S_2}{U}\right)$$

and φ ₀ = φ-2πft ₂ ,
where the phase φ corresponds to time t ₂ .