RU2591742C1 - Method of measuring frequency of harmonic signal and device therefor - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measurement equipment and can be used in information-measuring devices for measuring frequency of harmonic signals of precision quartz and quantum frequency standards. Analogue-to-digital conversion of measured and reference signals are carried out with time interval defined by sampling frequency of sampling signal, formed from reference signal, obtained as a result of analogue-to-digital conversion digital sampling in following one after another tetrads of sampling moments are memorised, digital samples tetrads are converted into phase values of measured and reference signals and determining sought frequency difference of reference and measured signals. Device has series-connected generator of measured signal, first analogue-to-digital converter, first random access memory and digital signal processing processor, connected to personal computer by data exchange bus. Clock input of first analogue-to-digital converter is connected to output of signal quantisation frequency synthesizer, which signal input is connected to reference signal generator output, and control input is to control output of processor of digital signal processing. Device also has second random access memory, which output is connected to processor second input of digital processing, and second analogue-to-digital converter, which signal input is connected to output of reference signal generator, clock input is connected to output of signal quantisation frequency synthesizer, and output is connected to input of second random access memory.

EFFECT: technical result consists in improvement of accuracy of measuring frequency harmonic signal while widening range of compared signals frequencies.

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Description

The claimed group of inventions relates to measuring technique and can be used in information-measuring devices for measuring the frequency of harmonic (sinusoidal) signals of precision quartz and quantum frequency standards.

The issues of estimating the time-frequency parameters of signals are extremely important for achieving the maximum permissible technical characteristics of various radio systems for accuracy and noise immunity and constantly attracts the attention of researchers, see, for example, [1] Falkovich S.E., Khomyakov E.N. / Statistical theory of measuring radio systems // M., Radio and Communications, 1981, p. 117-121; [2] Equipment for frequency and time measurements / Ed. A.P. Gorshkova // M., Sov. Radio, 1971. p. 7-15.

A number of known methods for measuring the frequency of sinusoidal signals are presented in the patents: [3] RU No. 2530445, G01R 23/00, 10/10/2014; [4] US 4,144,489, G01R 23/02, 03/13/1979; [5] RU 2503019, G01R 23/00, 12/27/2013; [6] RU 2478213, G01R 23/00, 03/27/2013, however, they are not statistically optimal from the point of view of measuring the frequency against the background of noise and fundamentally do not allow to achieve accuracy close to the boundaries determined by the Rao-Cramer inequality.

A number of known methods for measuring the frequency of sinusoidal signals are presented in the patents: [7] RU 1352390, G01R 23/00, 11/15/1987; [8] RU 2363004, G01R 23/00, 07.27.2009; [9] RU 2183839, G01R 23/00, 06/20/2002, based on the use of the Fourier transform, where the frequency estimate is taken as the argument of the maximum spectral power density of the signal mixture with noise. These methods of frequency measurement are statistically optimal from the point of view of measuring the frequency of sinusoidal signals against a background of noise. However, they require large computational costs associated with the implementation of one or more Fourier transforms, which does not allow to obtain an estimate of the frequency on a time scale close to real. In addition, when digitally implemented, these methods acquire an additional error in the estimation of the frequency due to quantization of the measured parameter with the frequency of the temporal sampling of the signal.

Known methods for measuring the frequency of sinusoidal signals presented in the patents: [10] RU 2041469, G01R 23/00, 08/09/1995; [11] RU 2363004, G01R 23/00, 04/10/2008, based on obtaining the values of the current phase of the signal as an argument of a complex number, followed by the use of phase difference statistics of the signal. These methods are also statistically optimal from the point of view of measuring the frequency of sinusoidal signals against the background of noise, reaching for the large Cramer-Rao boundary with large sample sizes.

The main disadvantage of this type of method is the inherent measurement error arising from the difference in the amplitudes of the signals in the quadrature channels, which cannot be realized perfectly identical. To reduce this error in frequency measurement, methods are used that are based on the formation of frequency estimates as a function of the ratio of digital signal samples obtained in one channel, see, for example, patents: [12] RU 2256928, G01R 23/00, 07.20.2005; [13] RU 2111496, G01R 23/00, 05.20.1998.

In particular, the method for measuring the frequency of a harmonic signal, presented in the patent [13], includes the operations of analog-to-digital conversion of the signal, storing its values in S following one after another triad of time points, the frequency being determined in accordance with the expression:

A significant drawback of this method is its inherent large estimation error due to the discontinuity of the derivative of the arccos (A / B) function.

To demonstrate this statement, we estimate the error of the frequency estimate due to the error ΔА in the calculation of the fraction numerator in the argument of the arccos function. To do this, find the differential:

Passing to finite increments from expression (2), we find:

, что нарушает непрерывность процесса измерения.It follows from expression (3) that for close values of the numerator A and the denominator B, the error Δω can be anomalously large. In addition, this method requires a condition check

, which violates the continuity of the measurement process.

The closest in technical essence to the claimed method and device are the method and device for measuring the harmonic signal frequency, presented in [14] - Shang-Shian Chen, Chia-Shu Liao / Using DSP Technique to Average ADC Samples for Improving the Frequency Measurement Resolution // 19th European Frequency and Time Forum, Besancon, France, 2005 (pp 545-549), adopted as prototypes.

A method for measuring the frequency of a harmonic signal, adopted as a prototype, is based on a statistically optimal algorithm for estimating the phase of the signal. In this case, the components of the complex signal are formed by successive digital samples of the measured signal, which eliminates the measurement error due to the difference in the amplitudes of the quadrature components of the complex signal.

The prototype method is as follows. An analog-to-digital conversion of the measured signal is performed with a time sampling interval determined by the frequency f _{s of} the sampling signal generated from the reference signal with a frequency f ₀ in accordance with the expression f _s = 4 · f ₀ , the digital samples obtained as a result of the analog-to-digital conversion are stored in S following one after another notebooks of time instants U ₀ (k), U ₁ (k), U ₂ (k), U ₃ (k), where k = 0, 1, 2, 3 ... S, these digital samples are converted tetrad in the phase value ϕ (k) of the measured signal in accordance with the expression

after which the samples ϕ (k) of the phase are converted into the values of the desired frequency difference y (k) of the reference and measured signals in accordance with the expression

where N = T _m · f _s ,

T _m is the measurement time equal to N periods of the sampling signal.

A device for measuring the frequency of a harmonic signal, adopted as a prototype, which implements the prototype method, comprises serially connected a measured signal generator, an analog-to-digital converter, random access memory and a digital signal processing processor connected to a data exchange bus with a personal computer. The synchronization input of the analog-to-digital converter is connected to the output of the frequency synthesizer of the quantization signal, the input of which is connected to the output of the reference signal generator.

In the process of implementing the prototype method, the measured signal generator generates a harmonic (sinusoidal) signal at its output, which is fed to the signal input of an analog-to-digital converter. The synchronization input of the analog-to-digital converter receives a sampling signal (quantizing pulses).

Quantizing pulses are generated using the frequency synthesizer of the quantization signal, which performs the operation of multiplying by four the frequency f _{0 of the} reference signal from the output of the reference signal generator to the signal input of the frequency synthesizer of the quantization signal.

. Этим обеспечивается фазовый сдвиг между смежными выборками измеряемого сигнала, равный

.An analog-to-digital converter performs analog-to-digital conversion of the measured signal with a time sampling interval determined by the sampling signal, i.e.

. This ensures a phase shift between adjacent samples of the measured signal, equal to

.

Digital samples of the measured signal generated using an analog-to-digital converter with a time interval t _s are stored in random-access memory in S following one after another tetrads of time instants U ₀ (k), U ₁ (k), U ₂ (k) , U ₃ (k), where k = 0, 1, 2, 3 ... S.

The digital signal processing processor reads digital codes from the random access memory, calculates the phase ϕ (k) and the offset y (k + 1) of the frequency of the measured signal in accordance with expressions (4) and (5), respectively, and outputs the values of ϕ (k) and y (k + 1) to a personal computer for displaying the results and statistical processing of individual measurements.

The disadvantages of the prototype method and the prototype device are the relatively low accuracy and significantly limited frequency range of the compared signals due to the presence of the operation of multiplying the frequency by “four” when generating a signal of temporary sampling of the measured signal.

The foregoing can be illustrated as follows. We write the expression of the signal, the frequency deviation of which must be measured, in the form:

where A and φ ₀ are the amplitude and the initial phase, which, without loss of generality, can be taken equal to 0, that is, φ ₀ = 0.

According to the prototype method, samples of the measured signal are formed at time instants:

where n = 0, 1, 3, ....

The measurement process involves tetrads (fours) of the samples, separated by the intervals T = N · t _s (see Fig. 1). The expression for the k-th notebook of samples, where k = 0, 1, 2, 3 ..., is written in the form:

where i is the sample number in the notebook taking the values i = 0, 1, 2, and 3 (see Fig. 1).

, где Δ_i(k) - ошибка временной дискретизации.The frequency multiplication operation introduces parasitic fluctuations in the phase of the sampling signal (jitter), the power spectral density of which is proportional to the square of the multiplication coefficient, that is, sixteen. Therefore, the sampling interval of the measured signal will be equal to

where Δ _i (k) is the time sampling error.

Therefore, expression (8) can be rewritten in the form:

можно переписать:Expression (9) taking into account

can be rewritten:

. При сличении высокоточных прецизионных сигналов справедливо f₀≥≥y и время корреляции флуктуации Δ_i(k) превышает 4t_s. С учетом сказанного можно записать:In the last expression, the first term under the sign of sin can be omitted, since N · k is a multiple of four. The third term, taking into account N · k≥≥i, can be rewritten as

. When comparing high-precision precision signals, f ₀ ≥≥y is valid and the fluctuation correlation time Δ _i (k) exceeds 4t _s . With that said, you can write:

or, denoting 2π · f ₀ · Nk · Δ (k) = φ (k):

From expression (10), we can obtain expressions for the differences:

Now, from the expression (4), we can obtain the phase value as an argument of the complex signal:

Based on the expression (11) we obtain the difference of adjacent phases:

From expression (12) we obtain the expression for the measured parameter y:

Where

error in estimating the frequency difference of the compared signals due to phase fluctuations introduced by the frequency multiplication operation.

The presence of this error limits the accuracy of the prototype method and the prototype device that implements it and makes it impossible to compare signals with the same frequency stability.

Another disadvantage of the prototype method and the prototype device is a significant limitation of the frequency range of the compared signals. Indeed, let f _max be the maximum operating frequency of the operations of analog-to-digital conversion and storing of digital samples. Then the frequency range of the compared signals is limited from above by the following relation:

The technical result to which the claimed inventions are aimed is to increase the accuracy of measuring the frequency of harmonic (sinusoidal) signals by compensating for the phase error introduced by the synthesis operation of the sampling signal while expanding the frequency range of the compared signals.

и определяют искомую разность частот y(k) опорного и измеряемого сигналов. В отличие от прототипа, дополнительно осуществляют аналого-цифровое преобразование опорного сигнала с интервалом временной дискретизации, определяемой указанной частотой f_s сигнала дискретизации, формируемой в соответствии с выражением

, где

в зависимости от диапазона частот сличаемых сигналов, запоминают полученные в результате этого аналого-цифрового преобразования цифровые выборки в S следующих одна за другой тетрадах моментов времени

, где k=0, 1, 2, … S, преобразуют эти цифровые выборки тетрад в значения фазы ϕ⁰(k) опорного сигнала в соответствии с выражением

, а искомую разность частот y(k) опорного и измеряемого сигналов определяют в соответствии с выражением

, где N=T_m·f_s; T_m - временной интервал между смежными тетрадами выборок измеряемого и опорного сигналов.The essence of the proposed method for measuring the frequency of a harmonic signal is as follows. An analog-to-digital conversion of the measured signal is carried out with a time sampling interval determined by the frequency f _{s of} the sampling signal generated from the reference signal with a frequency f ₀ , and the digital samples obtained as a result of this analog-to-digital conversion are recorded in S times one after the other tetrads of time U ₀ (k), U ₁ (k), U ₂ (k), U ₃ (k), where k = 0, 1, 2, 3 ... S, convert these digital samples of notebooks into phase values ϕ (k) of the measured signal according to the expression

and determine the desired frequency difference y (k) of the reference and measured signals. In contrast to the prototype, additionally carry out analog-to-digital conversion of the reference signal with an interval of time sampling, determined by the specified frequency f _{s of} the sampling signal generated in accordance with the expression

where

depending on the frequency range of the signals being compared, they memorize the digital samples obtained as a result of this analog-to-digital conversion in S subsequent one after another tetrads of time instants

, where k = 0, 1, 2, ... S, convert these digital samples of tetrads into phase values ϕ ⁰ (k) of the reference signal in accordance with the expression

, and the desired frequency difference y (k) of the reference and measured signals is determined in accordance with the expression

where N = T _m · f _s ; T _m - the time interval between adjacent tetrads of samples of the measured and reference signals.

The essence of the claimed device for measuring the frequency of the harmonic signal is as follows. The device contains a series-connected generator of the measured signal, the first analog-to-digital converter, the first random access memory and a digital signal processor connected to the data bus with a personal computer, while the synchronization input of the first analog-to-digital converter is connected to the output of the frequency synthesizer of the quantization signal, the signal input of which is connected to the output of the reference signal generator. Unlike the prototype, the device contains a second random access memory, the output of which is connected to the second input of the digital processing processor, and a second analog-to-digital converter, the signal input of which is connected to the output of the reference signal generator, the synchronization input is connected to the output of the synthesizer of the quantization signal frequency, and the output is connected to the input of the second random access memory, while the control output of the digital signal processor is connected to the control input of the synthesizer simplicity quantization signal.

The essence of the claimed method and device is illustrated by the illustrative materials presented in FIG. 1 and 2, where:

in FIG. 1 shows in schematic form the position of the quantizing pulses relative to the measured harmonic signal;

in FIG. 2 is a structural diagram of a device for measuring the frequency of a harmonic signal, with the help of which the inventive method for measuring the frequency of a harmonic signal is carried out.

The inventive device for measuring the frequency of a harmonic signal that implements the inventive method for measuring the frequency of a harmonic signal contains, see FIG. 2, the measured signal generator 1, the first analog-to-digital converter 2, the first random access memory 3 and the digital signal processing processor 4 connected to the data exchange bus with a personal computer 5 in series. The synchronization input of the first analog-to-digital converter 2 is connected to the output of the synthesizer 6 of the frequency of the quantization signal, the signal input of which is connected to the output of the reference signal generator 7. The device also contains a second random access memory 8, the output of which is connected to the second input of the digital processing processor 4, and a second analog-to-digital converter 9, whose signal input is connected to the output of the reference signal generator 7, the synchronization input is connected to the output of the synthesizer 6 of the quantization signal frequency, and the output is connected to the input of the second random access memory 8, while the control output of the processor 4 digital signal processing is connected to the control input of the synthesizer 6 frequency s drove quantization.

The operation of the claimed device for measuring the frequency of a harmonic signal, illustrating the feasibility of the proposed method for measuring the frequency of a harmonic signal, is as follows.

The generator 1 of the measured signal generates a harmonic signal at its output, which is fed to the signal input of the first analog-to-digital converter 2.

The reference signal generator 7 generates at its output a harmonic signal with a frequency f ₀ , which is fed to the signal input of the second analog-to-digital converter 9, as well as to the signal input of the synthesizer 6 of the sampling signal frequency, to the control input of which a signal from the control output of the digital processor 4 signal processing.

Sampling frequency synthesizer 6 generates the sampling signal a signal representing the quantizing pulses following a frequency f _s:

в зависимости от диапазона частот сличаемых сигналов.Where

depending on the frequency range of the compared signals.

The value of the selected index j is input through a personal computer 5 into the digital signal processing processor 4, which controls the synthesis coefficient of the synthesizer 6 of the sampling signal frequency in accordance with expression (16).

From the output of the synthesizer 6, the frequency of the sampling signal, quantizing pulses are fed to the synchronization inputs of the first 2 and second 9 analog-to-digital converters, providing simultaneous formation of digital samples of the measured and reference signals with a sampling frequency f _s .

Digital samples of the measured signal generated using the first analog-to-digital converter 2 with a time interval t _s are stored in the first random access memory 3 in S of the following one after another tetrads of time instants U ₀ (k), U ₁ (k), U ₂ (k), U ₃ (k), where k = 0, 1, 2, 3 ... S.

, где k=0, 1, 2, … S.Digital samples of the reference signal generated using the second analog-to-digital converter 9 with the same time interval t _s are stored in the second random access memory 8 in S subsequent to one another time notebooks of time

where k = 0, 1, 2, ... S.

Moreover, the synthesis of the sampling frequency in accordance with expression (16) ensures the orthogonality of adjacent digital samples of the measured and reference signals stored in the first random access memory 3 and the second random access memory 8, respectively.

From the outputs of random access memory devices 3 and 8, digital samples of the measured and reference signals are received at the corresponding inputs of the digital signal processing processor 4.

, вычисляет фазы ϕ(k), ϕ⁰(k) и отклонение частоты y(k) измеряемого сигнала в соответствии с выражениями:The digital signal processing processor 4 reads digital codes of samples of the measured and reference signals from the first random access memory 3 and the second random access memory 8, respectively, and splits them into notebooks U ₀ (k), U ₁ (k), U ₂ (k), U ₃ (k) and

calculates the phases ϕ (k), ϕ ⁰ (k) and the deviation of the frequency y (k) of the measured signal in accordance with the expressions:

where N = T _m · f _s ,

T _m - the time interval between adjacent tetrads of samples of the measured and reference signals.

The calculated phase values φ (k), φ ⁰ (k) and the frequency deviation y (k) of the measured signal are issued in a personal computer 5 for displaying the results and statistical processing of individual measurements.

At the same time, in contrast to the prototype, the accuracy of measuring the frequency of the harmonic signal is improved by compensating for the phase error introduced by the synthesis operation of the sampling signal, and it also provides an extension of the frequency range of the compared signals.

опорного сигналов:To illustrate the achievement of the indicated technical result, we write the expressions for the kth tetrads of samples U ₀ (k), U ₁ (k), U ₂ (k), U ₃ (k) of the measured and

reference signals:

where i is the sample number in the notebook, taking values i = 0, 1, 2, and 3 (Fig. 1);

Δ _i (k) is the time sampling error;

y is the frequency deviation to be measured.

According to the proposed method, we have:

.Where

.

), то есть формирование квадратурных выборок комплексного сигнала последовательно во времени, что, в отличие от формирования параллельных квадратурных каналов, позволяет исключить ошибку из-за неидентичности амплитуд квадратурных сигналов.Such a choice of the time sampling interval ensures the orthogonality of adjacent samples (the phase shift between adjacent samples is equal to

), that is, the formation of quadrature samples of the complex signal sequentially in time, which, in contrast to the formation of parallel quadrature channels, eliminates the error due to the non-identical amplitudes of the quadrature signals.

In fact, substituting expression (19) into expressions (17) and (18), we obtain:

In expressions (20) and (21), as in the case of the prototype, the terms under the sign of sin, equal to the integer 2π, are omitted, and it is taken into account that f ₀ ≥≥y, N · k≥≥i.

, но, поскольку при формировании фазовых выборок используются отношения разностей этих величин, сдвинутых по фазе на π, а интервал времени T_m кратен целому числу периодов измеряемого сигнала (Фиг. 1), знак не имеет значения. Таким образом, окончательно имеем:We denote 2π · f ₀ · Nk · Δ _i (k) = φ _i (k) ≈φ (k) and note that the first terms under the signs sin π · i · j in expressions (20) and (21) can be omitted . In fact, in the even product i * j - π · i · j is equal to the integer 2π, and the odd i * j changes the sign of U _i (k) or

but, since when forming phase samples, the relations of the differences of these quantities are used, shifted in phase by π, and the time interval T _m is a multiple of an integer number of periods of the measured signal (Fig. 1), the sign does not matter. Thus, we finally have:

In accordance with the proposed method, the phases of the measured and reference signals are sampled accordingly:

Find the adjacent phase differences of the measured signal in the form:

where we get the expression of the measured frequency difference

A comparison of expressions (26) and (13) shows that the analog-to-digital conversion and storing of the samples of the reference signal at coinciding times with the analog-to-digital conversion and storing of the samples of the measured signal makes it possible to compensate for the measurement error due to fluctuations in the phase of the sampling signal synthesis operation, then there is to increase the measurement accuracy and reduce the requirements for a sampling frequency synthesizer.

Achieving the effect of expanding the frequency range of the compared signals will be considered as an example.

.Let the maximum operating frequency of hardware that implements the prototype method and the inventive method is equal to 20 MHz. When comparing signals with a nominal frequency of 5 MHz, as is done in the example implementation of the prototype method, the frequency of the sampling signal f _s = 20 MHz. Exactly the same frequency of the sampling signal can be selected for the proposed method with

.

Suppose you want to measure the frequency difference with a nominal value of 100 MHz. For the prototype method f _s = 400 MHz ≥≥ 20 MHz, which makes the prototype inoperative for given implements hardware. The inventive method remains operable for measuring frequencies with such a nominal value, since, having taken j = 2, we obtain f _s = 16 MHz ≤ 20 MHz.

The above shows that the claimed group of inventions is feasible and ensures the achievement of the technical result, which consists in increasing the accuracy of measuring the frequency of the harmonic signal while expanding the frequency range of the compared signals.

Information sources

1. Falkovich S.E., Khomyakov E.N. / Statistical theory of measuring radio systems // M., Radio and communications, 1981.

2. Equipment for frequency and time measurements / Ed. A.P. Gorshkova // M., Sov. Radio, 1971.

3. RU 2530445, G01R 23/00, publ. 10/10/2014.

4. US 4144489, G01R 23/02 publ. 03/13/1979.

5. RU 2503019, G01R 23/00, publ. 12/27/2013.

6. RU 2478213, G01R 23/00, publ. 03/27/2013.

7. RU 1352390, G01R 23/00, publ. 11/15/1987.

8. RU 2363004, G01R 23/00, publ. 07/27/2009.

9. RU 2183839, G01R 23/00, publ. 06/20/2002.

10. RU 2041469, G01R 23/00, 09/09/1995.

11. RU 2363004, G01R 23/00, publ. 04/10/2008.

12. RU 2256928, G01R 23/00, publ. 07/20/2005.

13. RU 2111496, G01R 23/00, publ. 05/20/1998.

14. Shang-Shian Chen, Chia-Shu Liao / Using DSP Technique to Average ADC Samples for Improving the Frequency Measurement Resolution // 19th European Frequency and Time Forum, Besancon, France, 2005 (p. 545-549).

Claims (2)

1. A method for measuring the frequency of a harmonic signal, in which an analog-to-digital conversion of the measured signal is performed with a time sampling interval determined by the frequency f _{s of} the sampling signal generated from the reference signal with a frequency f ₀ , the digital samples obtained as a result of this analog-to-digital conversion are stored in S following one after another notebooks of time instants U ₀ (k), U ₁ (k), U ₂ (k), U ₃ (k), where k = 0, 1, 2, 3 ... S, these digital samples are converted tetrad in phase values $$\phi \left(k\right)$$

measured signal in accordance with the expression

and determine the desired frequency difference y (k) of the reference and measured signals, characterized in that they additionally perform analog-to-digital conversion of the reference signal with a time sampling interval determined by the indicated frequency f _{s of} the sampling signal generated in accordance with the expression

where

depending on the frequency range of the signals being compared, they memorize the digital samples obtained as a result of this analog-to-digital conversion in S subsequent one after another tetrads of time instants

where k = 0, 1, 2, ... S, convert these digital samples of tetrads into phase values $${\phi }^0\left(k\right)$$

reference signal in accordance with the expression

, and the desired frequency difference y (k) of the reference and measured signals is determined in accordance with the expression

where N = T _m · f _s ; T _m - the time interval between adjacent samples tetrads measured and reference signals. 2. A device for measuring the frequency of a harmonic signal, comprising a series-connected generator of the measured signal, a first analog-to-digital converter, a first random access memory and a digital signal processing processor connected by a data bus with a personal computer, while the synchronization input of the first analog-to-digital converter connected to the output of the synthesizer of the frequency of the quantization signal, the signal input of which is connected to the output of the reference signal generator, characterized in that the device comprises a second random access memory device, the output of which is connected to the second input of the digital processing processor, and a second analog-to-digital converter, the signal input of which is connected to the output of the reference signal generator, the synchronization input is connected to the output of the frequency synthesizer of the quantization signal, and the output connected to the input of the second random access memory, while the control output of the digital signal processor is connected to the control input of the frequency synthesizer quantization signal.

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