RU2700334C1 - Method of measuring phase difference of harmonic signals at outputs of linear paths with low signal-to-noise ratios - Google Patents

Abstract

FIELD: measurement technology.

SUBSTANCE: invention relates to the metrology. Method for measuring phase difference comprises generating a harmonic measurement signal, in transmitting said signal through analyzed paths, in estimation of signal frequency, in determination and setting of heterodyne signal frequency, in transfer of output signals of analyzed paths to intermediate frequency, obtaining harmonic signals, in measurement of phase difference of signals of intermediate frequency, in determination of phase difference of harmonic signals at outputs of analyzed paths, in display of value of phase difference and frequency of measuring signal. At that value of intermediate conversion frequency is chosen considerably less than values of frequencies of final set of measuring signals, procedure of "optimum heterodyning of signals" is performed, determining and memorizing the value of the frequency of the measurement signal transmitted through the analyzed channels and the heterodyne frequency, sequence of harmonic signals of intermediate frequency and signals of local reference generator of procedure "quadrature phase synchronization of signals" and "quadrature measurement of phase difference of signals" is performed, as well as frequency conversion channels are calibrated. For this purpose, harmonic signal is generated, supplied to inputs of both frequency conversion channels, performing "quadrature phase-out of signals", measured phase difference of signals at outputs of frequency conversion channels is accepted as calibration correction, subtracted from previously measured phase difference and obtained unknown phase difference of output signals of analyzed paths.

EFFECT: high accuracy of measuring phase difference of output signals of analyzed paths.

4 cl, 4 dwg

Description

The alleged invention relates to the field of measurement technology and can be used to measure the phase difference of harmonic signals at the outputs of various linear physical paths with finite passband and quasi-white noise, for example, when measuring the phase-frequency characteristics of the paths of various electronic devices and systems, non-destructive testing and measuring the properties of materials , other application areas using phase measurements with heterodyning of signals at an intermediate frequency, in the condition ia, when the measuring harmonic signal arrives at the inputs of the studied paths from some source, which is one of the signals of a given finite set of measuring signals falling into the passband of the studied paths, with frequencies a priori unknown at the place of measurement, it is only known that the frequencies of the measuring signals constituting said set are multiples of the intermediate conversion frequency.

A number of methods have been developed to measure the phase difference of harmonic signals. The most common of them are: a method of converting a time interval into a voltage [1], a digital method of counting the number of pulses (discrete counting method) [2-4], a method of measuring the phase difference with frequency conversion [1, 2], correlation methods of measurement [1 , 2, 5], the Fourier transform method [2, 6-8], fitting to a sinusoidal signal using the least squares method [9].

The accuracy of measuring the phase difference using these methods depends significantly on the signal-to-noise ratio at the outputs of the studied paths. High measurement accuracy (absolute error at the level of 0.1 degrees) is provided in these methods only with signal-to-noise ratios in the studied paths of at least 50-60 dB [10, 11]. With signal-to-noise ratios of less than 30 dB, the accuracy of the phase difference measurement is already unacceptably low for most practical applications.

переданного измерительного сигнала, в определении и задании частоты ƒ_г сигнала гетеродина, в переносе с использованием этого гетеродина выходных сигналов x(t), у(t) исследуемых трактов на промежуточную частоту ƒ_пр и получением соответствующих гармонических сигналов X(t), Y(t), в измерении искомой разности фаз Δϕ_изм путем подсчета количества импульсов известной высокой частоты ƒ_ог от местного опорного генератора на периоде колебаний промежуточной частоты и временном интервале между соответствующими переходами через нулевой уровень гармонических сигналов X(t), Y(t) промежуточной частоты, в отображении измеренной разности фаз Δϕ_изм и частоты

в удобном для дальнейшего использования виде.The closest to the claimed method in terms of features and technical essence (prototype) is a combined method [12] for measuring the phase difference of harmonic signals, combining methods of measuring the phase difference with frequency conversion and discrete counting, consisting in measuring with some instrumental error at the output of one of the studied frequency paths

of the transmitted measuring signal, in determining and setting the frequency ƒ _{g of} the local oscillator signal, transferring the output signals x (t), y (t) of the studied paths to the intermediate frequency ƒ _pr and using the given local oscillator, and obtaining the corresponding harmonic signals X (t), Y ( t), in the measurement of the desired phase difference Δϕ _ism by counting the number of pulses of a known high frequency ƒ _og from the local reference oscillator during the period of oscillations of the intermediate frequency and the time interval between the corresponding transitions through the zero harmonic level signals X (t), Y (t) of the intermediate frequency, in the display of the measured phase difference Δϕ _ISM and frequency

in a form convenient for further use.

A generalized composition of the functional elements of the prototype method is shown in FIG. 1. The studied paths are devices or physical media at the output of which measuring harmonic signals are observed, the phase difference of which is to be measured. Frequency conversion paths include devices that transfer measuring harmonic signals from the outputs of the studied paths to an intermediate frequency for further measurements.

The combined method of measuring the phase difference of harmonic signals is the most common due to the fairly high accuracy of measuring the phase difference at a low intermediate frequency in a relatively wide range of operating frequencies, due to the use of heterodyning (frequency conversion) signals.

The absolute error in determining the phase difference Δϕ _ds at an intermediate frequency by the method of discrete counting under white noise conditions (prototype method) can be estimated [12] based on the following relationship:

where δƒ _og - relative frequency instability of the local reference generator; ƒ _og - frequency (Hz) of the local reference generator; ƒ _ol - the intermediate frequency (Hz) of the conversion paths; N _CR - the signal-to-noise ratio (dB) in the frequency conversion paths.

The disadvantage of the prototype method is the low accuracy of measuring the phase difference of the harmonic signals at the outputs of two linear paths in the conditions of small signal-to-noise ratios. For example, when using the combined method of measuring the phase difference with the parameters: ƒ _pr = 1 kHz, ƒ _og = 50 MHz, δƒ _og = 10 ^-8 (see relation (1)), the absolute measurement errors Δϕ _ds ≤0.1 deg, are achieved at values of N _pr ≥58 dB, with a decrease in the signal-to-noise ratio N _pr ≤40 dB Δϕ _ds ≥0.8 deg., and when N _pr ≤20 dB the absolute measurement errors Δϕ _ds already exceed 8 degrees.

It should be noted that in many cases encountered in practice, for example, in the paths of phase direction finders of different frequency ranges and for various purposes, the signal-to-noise ratios, as a rule, do not exceed 20 dB [10], while it is not always possible to increase these ratios by various technical or organizational reasons, then it is necessary to solve the problem of reducing the measurement errors of the phase difference of the signals in physical paths with small signal-to-noise ratios.

The technical result of the proposed method is to increase the accuracy of measuring the phase difference of the signals at the outputs of two investigated linear paths with limited frequency bands, quasi-white noise, small signal-to-noise ratios and heterodyning based on the common frequency oscillator ƒ _{g of the} signals of the studied paths to an intermediate frequency ƒ _pr in conditions when the harmonic measuring signal u _ism (t) of frequency ƒ _ism , which is one of the signals of a given finite about the set of measuring signals falling into the passband of the studied paths, with a priori unknown at the place of measurement, but multiples of the intermediate conversion frequency frequencies, due to the choice of the intermediate frequency is much less than the frequencies of the final set of measuring signals, and the passband of the frequency conversion paths is significantly greater than the intermediate frequency , the use of new procedures: “optimal heterodyning of signals”, “quadrature signal phase-out”, “quadrature measuring the phase difference signal "and the corresponding sequence of operations for processing the output signals of the test paths, and the intermediate frequency signals.

переданного измерительного сигнала, в определении и задании частоты ƒ_г сигнала гетеродина, в переносе с использованием этого гетеродина выходных сигналов x(t), y(t) исследуемых трактов на промежуточную частоту ƒ_пр и получением соответствующих гармонических сигналов X(t), Y(t), в измерении разности фаз

сигналов промежуточной частоты, в использовании

для определения величины разности фаз Δϕ_изм гармонических сигналов на выходах исследуемых трактов, в отображении величины Δϕ_изм и частоты измерительного сигнала в удобном для дальнейшего использования виде, выбирают величину промежуточной частоты значительно меньше значений частот конечного множества измерительных сигналов, а величину полосы пропускания трактов преобразования частоты существенно больше значения промежуточной частоты, реализуют в процессе измерений следующую последовательность действий: выполняют процедуру «оптимального гетеродинирования сигналов», по ее результатам определяют и запоминают значение частоты переданного через исследуемые тракты измерительного сигнала, устанавливают частоту гетеродина, при которой частоты упомянутых сигналов X(t), Y(t) соответствуют выбранному значению промежуточной частоты, выполняют для гармонических сигналов X(t), Y(t) процедуры «квадратурного синфазирования сигналов», «квадратурного измерения разности фаз сигналов» и получают величину разности фаз

, выполняют калибровку трактов преобразования частоты, для чего формируют с использованием местного опорного генератора гармонический сигнал с частотой ƒ_изм, определенной в процедуре «оптимального гетеродинирования сигналов», подают его на входы обоих трактов преобразования частоты вместо выходных сигналов x(t), y(t) исследуемых трактов, последовательно выполняют процедуры «квадратурного синфазирования сигналов» и «квадратурного измерения разности фаз сигналов», измеренную разность фаз ΔΨ_изм сигналов на выходах трактов преобразования частоты принимают в качестве калибровочной поправки, вычитают ее из ранее измеренной разности фаз

и получают искомую разность фаз

выходных измерительных сигналов исследуемых трактов, отображают ее в пригодном для последующего использования виде, дополнительно отображают значение частоты ƒ_изм измерительного сигнала исследуемых трактов, определенное в процедуре «оптимального гетеродинирования сигналов».This technical result is achieved due to the fact that in the known method for measuring the phase difference of harmonic signals at the outputs of two investigated linear paths with limited frequency bands, quasi-white noise, small signal-to-noise ratios and heterodyning of the measuring signals of the studied paths to an intermediate frequency, which consists in the formation of harmonic measuring signal selected frequency ƒ _edited, one of the signals given finite set of harmonic measurement signals frequencies that are multiples of the intermediate frequency falling within the bandwidth of the test paths in the transmission of the signal with a priori unknown at the location of the measurement frequency through the paths investigated in the assessment with some instrumental error at the output of one of the measuring frequency tracts

of the transmitted measuring signal, in determining and setting the frequency сигнала _{g of} the local oscillator signal, transferring the output signals x (t), y (t) of the studied paths to the intermediate frequency ƒ _pr and obtaining the corresponding harmonic signals X (t), Y (using this local oscillator) t), in the measurement of the phase difference

intermediate frequency signals, in use

to determine the magnitude of the phase difference Δϕ _{ism of} harmonic signals at the outputs of the studied paths, in displaying the values of Δϕ _ism and frequency of the measuring signal in a form convenient for further use, the value of the intermediate frequency is much less than the frequencies of a finite set of measuring signals, and the bandwidth of the frequency conversion paths significantly greater than the value of the intermediate frequency, implement the following sequence of actions during the measurement process: perform the procedure “op “optimal heterodyning of signals”, according to its results, the frequency value of the measuring signal transmitted through the studied paths is determined and stored, the local oscillator frequency is set at which the frequencies of the mentioned signals X (t), Y (t) correspond to the selected value of the intermediate frequency, are performed for harmonic signals X ( t), Y (t) of the procedure “quadrature phase matching of signals”, “quadrature measurement of the phase difference of the signals” and get the value of the phase difference

, calibrate the frequency conversion paths, for which, using a local reference generator, a harmonic signal with a frequency ƒ _ISM defined in the procedure of “optimal heterodyning of signals” is generated, it is fed to the inputs of both frequency conversion paths instead of the output signals x (t), y (t ) of the studied paths, sequentially perform the procedures of “quadrature phase-matching of signals” and “quadrature measurement of the phase difference of the signals”, the measured phase difference ΔΨ _{ism of the} signals at the outputs of the conversion paths frequency values are taken as a calibration correction, subtract it from the previously measured phase difference

and get the desired phase difference

output measuring signals of the studied paths, display it in a form suitable for subsequent use, additionally display the value of the frequency ƒ _{Iz of the} measuring signal of the studied paths, defined in the procedure of “optimal signal heterodyning”.

A significant difference of the proposed method is the selection of the ratios of the values of the intermediate conversion frequency, the frequencies of a finite set of measuring harmonic signals and the passband of the frequency conversion paths, which, together with the introduction of new procedures for "optimal signal heterodyning", "quadrature signal phase-out", "quadrature measurement of signal phase difference »And the corresponding sequence of actions for processing the signals of the studied paths and intermediate signals often s allows to improve the accuracy of measuring the difference between the harmonic signal phases at the outputs of the test paths with small S / N ratio due to:

сигналов промежуточной частоты на соответствующие им синфазированные сигналы от местного опорного генератора, характеризующиеся большим отношением сигнал/шум;- replacing the signals X (t), Y (t) obtained by transferring to the intermediate frequency the output signals of the studied paths, characterized by a small signal to noise ratio, when measuring the phase difference

intermediate frequency signals to their corresponding in-phase signals from the local reference generator, characterized by a large signal to noise ratio;

- calibration of the conversion paths by feeding to their inputs instead of the output signals x (t), y (t) of the studied paths a harmonic signal formed on the basis of a local reference generator with a large signal-to-noise ratio частоты _ISM defined in the “optimal signal heterodyning” procedure , and determining the calibration correction used to obtain the desired phase difference of the output signals of the studied paths.

The set of essential features of the proposed method has a causal relationship with the achieved technical result, from which we can conclude that this technical solution is new, has an inventive step, since it clearly does not follow from the existing level of technology, and is suitable for practical use.

The alleged invention is illustrated by drawings.

In FIG. 1 presents a generalized composition of the functional elements of the prototype method. In FIG. 2 shows an example of a structural diagram of a device that implements the inventive method, where are indicated: 1 - signal switches; 2 - unit for measuring the frequency of signals; 3 - signal mixers; 4 - a block for generating harmonic signals with a microcontroller for calculations; 5 - bandpass filters; 6 - gating units; 7 - calculator; 8 - indicator; 9 - control unit. In FIG. 3 shows the curves of the absolute errors of the measurement of the phase difference depending on the signal-to-noise ratios at the outputs of the frequency conversion paths for the proposed method and the prototype method. In FIG. 4 shows the increase in the accuracy of measurements of the phase difference of the proposed method relative to the prototype method, depending on the signal-to-noise ratios at the outputs of the frequency conversion paths.

The essence of the proposed method can be represented by the following actions, procedures and operations.

The measuring harmonic signal supplied to the inputs of both studied paths has the form:

where U _ISM , ƒ _ISM , ϕ _ISM - amplitude, frequency and initial phase of the oscillations, respectively.

The measuring signals at the outputs of the studied paths are characterized by the relations:

where U ₁ , U ₂ - the amplitude of the oscillations; ϕ ₁ , ϕ ₂ - phase shifts of oscillations introduced by the studied paths; Δϕ _meas - the measured phase difference of the oscillations; ξ ₁ (t), ξ ₂ (t) are realizations of quasi-white noise of the studied paths.

The measuring signal (2) supplied to the inputs of the studied paths is a signal of a given finite set of harmonic signals falling into the passband of the studied paths, the frequencies of the signals of the set are multiples of the intermediate frequency ƒ _pr , however, the specific value of the frequency ƒ _{ism of the} input, and accordingly the output signals studied tracts, a priori unknown at the place of measurement.

The output measuring signals x (t), y (t) of the studied paths are transferred to the intermediate frequency ƒ _pr using a common local oscillator, the signal of which has the following form:

where U _g , ϕ _g is the amplitude and initial phase of the local oscillator signal; ƒ _ol - intermediate conversion frequency.

Since the frequency of the output signals x (t), y (t) of the studied paths is a priori unknown, the procedure of “optimal heterodyning of signals” is performed, which allows one to obtain exact values of the frequencies of the local oscillator signal and the output signals of the studied paths.

Performing the “optimal signal heterodyning” procedure.

колебаний измерительного сигнала на выходе одного из исследуемых трактовEvaluate using existing methods of measuring the frequency (for example, the method of discrete counting) and standard measuring tools that provide, in conditions of small signal-to-noise ratios, the measurement error acceptable for the proposed method, frequency

oscillations of the measuring signal at the output of one of the studied paths

where ƒ _ISM - the true value of the oscillation frequency; δƒ _ism - relative measurement error.

определяют вспомогательные параметры:According to the known value ƒ _pr and estimate

determine auxiliary parameters:

и

обозначают операции взятия целой и дробной части числа соответственно.where are the characters

and

denote operations of taking the integer and fractional parts of the number, respectively.

Calculating a value for the optimum LO frequency ƒ _r for the frequency down conversion, where the frequency of oscillation ƒ _edited, although present in the process of measurement error δƒ _edited after transformation is exactly equal _straight ƒ:

Then determine and remember the true value of the oscillation frequency of the measuring signal at the outputs of the studied paths: ƒ _ISM = ƒ _g + ƒ _etc.

For the implementation of the procedure of "optimal heterodyning signals" requires the fulfillment of three conditions.

, где

- целое число.1. Ensuring frequency multiplicity ƒ _ISM and

where

is an integer.

2. The resolution of the change ƒ _ISM should be equal to ƒ _PR .

3. The maximum relative error in measuring the frequency of oscillations of the measuring signals at the outputs of the studied paths should not exceed the value:

From the point of view of fulfilling the first condition, the intermediate frequencies during heterodyning of the measuring signals at the outputs of the studied paths should be selected from the range: 10 ³ , 10 ⁴ , 10 ⁵ Hz.

To fulfill the second condition, with a maximum number of gradations ƒ _ISM , the value of ƒ _pr should be selected as the minimum of the presented series.

When using, for example, for measuring the frequency ƒ _{ism, the} method of discrete counting is estimated, the relative error δƒ _{ism of} instrumental determination of frequency in the studied paths can be made on the basis of the following dependence [12]:

where ƒ _og - frequency (Hz) of the local reference generator; δƒ _og - relative frequency instability of the local reference generator; T _ISM - time (s) measuring the frequency; N _ISM - signal-to-noise ratio (dB) in the studied paths.

Performed on the basis of the relation (8), calculations show that in the test ƒ _edited paths bandwidth = ⁴ ... 10 10 ¹⁰ Hz and ƒ _og = 50 MHz, δƒ _og = 10 ^-8, T = _MOD 10 condition 3, for signal / N H _edited measuring signals over -20 dB and values of the intermediate frequencies is not more than 10 ⁵ Hz is always executed, indicating a lack of practical limitations on the use of "optimal heterodyning signals" procedure in this frequency range.

The frequency ƒ _{g of} harmonic oscillations of the local oscillator signal is set in the frequency conversion paths, according to the results of the “optimal signal heterodyning” procedure, for transferring the output signals x (t), y (t) of the studied paths to the intermediate frequency ƒ _etc.

The output signals of the studied paths after frequency conversion and filtering the difference frequency oscillations are described by the following relationships:

where μ ₁ , μ ₂ - transmission coefficients of frequency converters (mixer + filter);

ξ ₃ (t), ξ ₄ (t) are the implementation of the quasi-white noise of the frequency conversion paths.

Recall that the bandwidths of the frequency conversion paths are chosen to be significantly larger than the intermediate frequency, providing a small correlation interval for quasi-white noise in the paths compared to the oscillation period of the selected intermediate frequency.

Perform the procedure of "quadrature signal phase-out."

Form on the basis of the local reference generator quadrature components Z1 (t), Z2 (t) of the harmonic signal Z (t) of intermediate frequency ƒ _pr with signal-to-noise ratios of at least 80 dB:

where U ₀ , ϕ ₀ is the amplitude and initial phase of the quadrature components of the signal Z (t).

The intermediate frequency signals X (t), Y (t), Z1 (t), Z2 (t) are subjected to synchronous sampling with the number of samples K _sf during the oscillation period and the total number of samples L _sf in the averaging sample:

- порядковый номер отсчета в усредняемой выборке.Where

- serial number of the reference in the averaged sample.

To reduce the error of further calculations of the phase difference of the signals X (t), Y (t), the following values of the sampling and averaging parameters can be recommended: K _sf ≥4, L _sf ≥10 ² ⋅K.

The weighting factors W1 and W2, which determine the projection of the signal X (t) onto the quadrature components of the signal Z (t), are calculated and stored:

The weighting factors W3 and W4, which determine the projection of the signal Y (t) onto the quadrature components of the signal Z (t), are calculated and stored:

Using the procedure allows one to find projections of the signals X (t), Y (t) with small signal-to-noise ratios on the quadrature components Z1 (t) and Z2 (t) of the harmonic signal Z (t) having large signal-to-noise ratios.

These projections are used later in the procedure “quadrature measurement of the phase difference of the signals” to obtain a pair of harmonic signals of the local reference oscillator with large signal-to-noise ratios, in phase with the signals X (t), Y (t) of the frequency conversion paths having small signal-to-noise ratios , which is reflected in the name of the procedure itself.

This allows you to move from measuring the phase difference of the intermediate frequency signals with small signal-to-noise ratios in the prototype method to similar measurements, but only signals with large signal-to-noise ratios, which improves the accuracy of measurements of the phase difference in the inventive method.

The accuracy of the out-of-phase signals sufficient to obtain a small error in the measurement of the phase difference is achieved by choosing the intermediate frequency value significantly lower than the frequency values of a finite set of measurement signals, and the passband frequency conversion paths significantly higher than the intermediate frequency value, while the correlation processing of the intermediate frequency signals against the background of weakly correlated quasi-white noise allows you to realize the effect of coherent accumulation, good widely known in the theory of noise-immune signal processing [13].

Perform the procedure "quadrature measurement of the phase difference of the signals."

To do this, the signals Z1 (t) and Z2 (t) are synchronized again, but with a large and multiple of four counts K _rf during the oscillation period and the total number of samples in the sample is 1.25⋅K _rf :

In this case, the parameter K _rf should be selected from the condition K _rf ≥10 ³ .

отсчетов, принадлежащих сигналам местного опорного генератора, синфазным с сигналами X(t) и Y(t) соответственно, и имеющим в результате процедуры «квадратурного синфазирования сигналов» большие отношения сигнал/шум:Two arrays are formed and stored.

samples belonging to the signals of the local reference generator, in phase with the signals X (t) and Y (t), respectively, and resulting in the procedure of "quadrature phase matching of the signals" large signal-to-noise ratios:

where the weighting coefficients W1, W2, W3, W4 are determined in the "quadrature signal phase-out" procedure.

путем их представления своими знаками по правилу:Arrays are normalized

by presenting them in their own signs according to the rule:

The correlation coefficients β and γ are calculated:

сигналов местного опорного генератора, синфазированных с сигналами X(t), Y(t), используя одну из предпочтительных формул:Calculate the phase difference

signals of the local reference oscillator in phase with the signals X (t), Y (t), using one of the preferred formulas:

In order to eliminate the influence of the non-identical phase-frequency characteristics of the frequency conversion paths on the accuracy of measuring the phase difference, they are calibrated, for this:

- fed to the inputs of both paths of the frequency conversion instead of the output signals of the studied paths, a calibration harmonic signal generated on the basis of the local reference generator with a frequency ƒ _ISM defined in the procedure of "optimal signal heterodyning";

- operate for signals resulting from heterodyne calibration signal to an intermediate frequency, procedures "sinfazirovaniya quadrature signal" and "quadrature signal phase difference measurement", resulting in a calibration correction value ΔΨ _edited.

синфазированных сигналов местного опорного генератора и получают искомую разность фаз Δϕ_изм выходных гармонических сигналов исследуемых трактов:Subtract calibration ΔΨ correction _edited previously calculated phase difference

common-mode signals of the local reference generator and get the desired phase difference Δϕ _{ism of the} output harmonic signals of the studied paths:

The obtained value of the phase difference of the output harmonic signals of the studied paths Δϕ _{ism is} displayed in a form suitable for subsequent use, and the true value of the frequency ƒ _{Iz of the} measuring signal of the studied paths determined in the procedure of "optimal signal heterodyning" is additionally displayed.

Thus, a possible technical implementation (Fig. 2) of the proposed method when applying to the inputs of the studied paths of the measuring signal of a priori unknown frequency ƒ _ISM suggests the following sequence of actions.

1. Carry out by employing the frequency measurement unit 2, the unit 4 forming the harmonic signals and control unit 9, the procedure "optimum heterodyne signals" a determination of the true values of the frequency ƒ _edited measurement signal and the frequency ƒ _r of the local oscillator for the frequency conversion.

2. Applied to the heterodyne inputs of the mixers 3, using the harmonic signal generating unit 4 and the control unit 9, the harmonic local oscillator signal with a frequency calculated in the procedure of “optimal signal heterodyning”.

3. On the basis of mixers 3, band-pass filters 5, harmonic signal generating unit 4 and control unit 9, the frequency of the output signals x (t), y (t) of the studied paths is converted to obtain the corresponding intermediate signals X (t), Y (t) frequencies ƒ _pr

4. Using the block 4, the formation of harmonic signals, blocks 6 gating, calculator 7 and block 9 control over the measuring signals X (t), Y (t) of the intermediate frequency procedure "quadrature signal phase-shifting" and calculate the weight coefficients W1, W2, W3 W4 to generate the corresponding common-mode signals of the local reference oscillator with a large signal-to-noise ratio.

сигналов местного опорного генератора, синфазированных с сигналами X(t), Y(t) трактов преобразования частоты.5. Carry out using the block 4 of the formation of harmonic signals, blocks 6 gating, calculator 7 and block 9 of the control procedure "quadrature measurement of the phase difference of the signals" and get the value of the phase difference

signals of the local reference oscillator in phase with the signals X (t), Y (t) of the frequency conversion paths.

6. Submit a command from the control unit 9 through the switches 1 of the signals to the signal inputs of the mixers 3 of the frequency conversion paths harmonic calibration signal generated in the block 4 of the formation of harmonic signals with a frequency ƒ _ISM defined in the procedure of "optimal signal heterodyning".

7. On the basis of mixers 3, bandpass filters 5, unit 4 for generating harmonic signals, and unit 9 for controlling, heterodyning of the harmonic calibration signal to produce intermediate frequency signals is performed.

8. Using the block 4 of the formation of harmonic signals, blocks 6 of the gating, calculator 7 and block 9 of the control over the calibration signals of the intermediate frequency, the procedure of "quadrature phase matching of the signals" and calculate the weight coefficients W1, W2, W3, W4 to generate the corresponding common-mode signals of the local reference generator.

9. performed using block 4 forming the harmonic signals, the gating block 6, the calculator 7 and the procedure control unit 9 'of the quadrature signal phase difference measurement "and the phase difference value obtained ΔΨ _edited local reference signal generator to calibration signal sinfazirovannyh frequency conversion paths which taken as a calibration correction.

сигналов местного опорного генератора, синфазированных с измерительными сигналами X(t), Y(t) трактов преобразования частоты.10. Calculate in the calculator 7 the desired phase difference Δϕ _{ism of the} measuring signal at the outputs of the studied paths, subtracting the calibration correction ΔΨ _ism from the previously calculated phase difference

local reference oscillator signals in phase with the measuring signals X (t), Y (t) of the frequency conversion paths.

11. Use the indicator 8 to display, in a suitable form for subsequent use, the values of the phase difference Δϕ _ISM and frequency ƒ _{ISM of the} measuring signal of the studied paths.

With the technical implementation of the proposed method, a modern element base and digital signal processing technologies can be used.

The switches 1 of the signals necessary for the calibration of the frequency conversion paths can be performed, for example, in the form of sealed relays ARA210A03 with frequencies of switched signals up to 1 GHz [14].

Block 2 measuring the frequency of the signals at the output of one of the studied paths can be implemented, for example, on the basis of a programmable frequency meter NM8123 with a range of measured frequencies 0.001 Hz - 3 GHz [15].

As mixers of 3 signals of the frequency conversion paths, for example, AD834 analog four-quadrant multipliers with a frequency range of 0-500 MHz can be used [16].

Block 4 for generating harmonic signals with a microcontroller for calculations, generating local oscillator signals, measuring signals of the studied paths, signals of quadrature components of the intermediate frequency and sampling signals of the gating blocks, can be performed, for example, on the basis of a frequency generator-synthesizer НМ8134-3 with a frequency range of 1 Hz - 1.2 GHz [17], coupled with a microcontroller of the AtmelAVR family of RISC architecture.

Band-pass filters 5 of the frequency conversion paths, for filtering fluctuations of the differential frequency and suppressing by-products of the conversion of mixers 3, can be implemented, for example, in the form of fourth-order filters based on the MAX274 / 275 microcircuit [18].

Gating units 6 for sampling intermediate frequency signals can be made in the form of analog-to-digital converters, for example, 14-bit low-noise ADCs of the LTC1742 series with a conversion frequency of up to 65 MHz [19].

As a calculator 7, for example, a microcontroller of the megaAVR family, equipped with a large volume of program and data memory [20], can be used.

As indicator 8, any digital display or other electronic device can be used that provides an appropriate display of measurement results.

As the control unit 9, a personal computer or laptop with the necessary set of communication interfaces and matching devices can be used.

The considered technical implementation of the proposed method can be used in the frequency range from 50 kHz to 500 MHz with the limits of the change in signal-to-noise ratios from 0 to 60 dB. Calculations show that the maximum absolute error of measurements of the phase difference at the indicated boundaries of the frequency ranges and levels of harmonic signals will be in the range from 0.012 to 0.2 degrees.

Presented in the claimed method, the procedures and operations were modeled in the mathematical environment of Mathcad 15 and received a quantitative assessment.

To compare the effectiveness of the prototype method and the proposed method in FIG. 3 shows the dependences of the absolute errors of measuring the phase difference of the signals of the prototype method (calculations based on expression (1)) and the maximum absolute errors of measuring the phase difference of the signals of the proposed method on the signal-to-noise ratios in the frequency conversion paths obtained with the following calculation parameters:

- ƒ _pr = 1 kHz, δƒ _og = 10 ^-8 , ƒ _og = 50 MHz - provide maximum efficiency (minimum measurement error) of the prototype method;

- the parameters of sampling and averaging during the out-of-phase signals in the claimed method K _sf = 4, L _sf = 4⋅10 ³ ;

- discretization parameter when measuring the phase difference of the signals in the inventive method K _rf = 10 ⁴ ;

- the signal-to-noise ratio for quadrature signals Z1 (t) and Z2 (t) in the present method is 80 dB;

- quasi-white noise of the frequency conversion paths in the averaging sample in the present method are samples of random processes with zero mean and a given dispersion corresponding to a frequency band approximately 50 times higher than the intermediate conversion frequency.

Improving the accuracy of measuring the phase difference of the signals in the inventive method compared with the prototype method is characterized by the graph in FIG. 4 derived from the dependencies shown in FIG. 3.

From the graph it follows that for a range of signal-to-noise ratios of 0-60 dB in the frequency conversion paths, the accuracy of measuring the phase difference of the signals in the present method with respect to the prototype method increases from 7 to 450 times depending on the magnitude of the signal-to-noise ratio, and measurements increases significantly with a decrease in this ratio.

The proposed technical solution allows to achieve the desired effect - improving the accuracy of measuring the phase difference of harmonic signals in the region of small signal to noise ratios due to the combination that has not been applied so far: choosing the necessary ratio of the frequencies of the measuring signals of the studied paths and the intermediate frequency when heterodyning, a wide bandwidth of the conversion paths frequencies significantly exceeding the value of the intermediate frequency, the use of new procedures: “optimal signal heterodyning “”, “quadrature signal phase-out”, “quadrature measurement of the phase difference of the signals” and the corresponding sequence of operations for processing the output signals of the studied paths and intermediate frequency signals.

The “optimal signal heterodyning” procedure ensures equality of the intermediate frequency of the local reference oscillator and the frequency of the measuring signals of the studied paths after heterodyning, and the choice of a low intermediate frequency and a wide passband of the frequency conversion paths helps to obtain such correlation characteristics of the mixture of the converted measuring signal and quasi-white noise in each conversion path frequencies that allow the effect of coherent accumulation of corr the measured samples of the intermediate frequency signal in the sample of weakly correlated samples of quasi-white noise during their correlation processing.

In the “quadrature signal phase-matching” procedure, oscillation in each pair of signals is achieved: a local reference oscillator and a first frequency conversion path, a local reference oscillator and a second frequency conversion path, while the signals of the local reference oscillator in each pair have a large signal to noise ratio, which allows you to go from measuring the phase difference of the oscillations of the frequency conversion paths with small signal / noise ratios to measuring the phase difference of the oscillations of the local reference generator, I have their constantly high signal / noise ratio.

The procedure of “quadrature measurement of the phase difference of the signals” allows, due to the selection of a low intermediate frequency and a large number of samples on its period during sampling, to obtain high accuracy of measuring the phase difference of the oscillations of the signals of the local reference oscillator with a large signal-to-noise ratio, which, up to the phase-shift error, is equal to the desired the phase difference of the oscillations of the output signals of the studied paths.

Such a set of distinctive features distinguishes the claimed method from the prototype method and other known methods, from the point of view of the possibility of significantly improving the accuracy of measuring the phase difference of harmonic signals in the field of small signal to noise ratios.

List of sources used

1. Chmykh M.K. Digital phase metering. M .: Radio and communications, 1993.

2. Webster J.G. (Ed.) Electrical measurement, signal processing, and displays. Boca Raton: CRC Press, 2004.

3. Metrology and radio measurements / Ed. IN AND. Nefedova. M .: Higher school, 2006.

4. Mahmud S.M. Error analysis of digital phase measurement of distorted waves // IEEE Trans. on Instrumentation and Measurement, 1989.38, N 1. C. 6-9.

5. Liang Y.R., Duan H.Z., Yeh H.C., Luo J. Fundamental limits on the digital phase measurement method based on cross-correlation analysis // Rev. Sci. Instrum, 2012. 83, N 9. C. 95-110.

6. Mahmud S.M. High precision phase measurement using reduced sine and cosine tables // IEEE Trans. on Instrumentation and Measurement, 1990.39, N 1.C. 56-60.

7. Mahmud S.M. High precision phase measurement using adaptive sampling // IEEE Trans. on Instrumentation and Measurement, 1989. 38, N 5. C. 954-960.

8. Gonorovsky I.S. Radio circuits and signals. M.: Bustard, 2006.

9. Sedlacek M., Krumpholc M. Digital measurement of phase difference a comparative study DSP algorithms // Metrology and Measurement Systems, 2005. XII, N 4. C. 427-449.

10. Saidov A.S., Tachilaev A.P. and others. Design of phase automatic direction finders. M .: Radio and communications, 1997.

11. Damdinova D.B., Poletaev A.S., Chensky A.G. Comparison of accuracy of methods for calculating the phase difference of quasi-harmonic signals. Vestnik SibGUTI, 2016. No. 2. S. 87-97.

12. Measurement of time intervals and phase shift [Electronic resource] // URL: http://reftop.ru/prakticheskaya-rabota-po-izmereniyu-intervalov-vremeni-i-fazov.html?page=41 (accessed: 01.11 .2018).

13. Tikhonov V.I., Kharisov V.N. Statistical analysis and synthesis of radio engineering devices and systems. M .: Radio and communications, 1991.

14. Sealed relays with switching frequencies up to 1 GHz [Electronic resource] // URL: http://www.fulcrum.ru/LineCard/Relays/PDF/RA.pdf (accessed: 01.11.2018).

15. Programmable frequency meter NM8123 [Electronic resource] // URL: http://mobile.rohde-schwarz.com.ua/products/test_and_measurement/hameg/HM8123/Brief (accessed: 01.11.2018).

16. Four-quadrant multiplier AD834 [Electronic resource] // URL: http://www.analog.com/en/products/analog-functions/analog-multipliers-dividers/ad834.html (accessed: 01.11.2018).

17. Frequency synthesizer NM8134-3 [Electronic resource] // URL: https://www.eskomp.ru/UFiles/bukl/GENERATOR_HMF8.pdf (accessed: 01.11.2018).

18. Technique and principles of circuitry for implementing filters on operational amplifiers [Electronic resource] // URL: http://studbooks.net/783435/tehnika/printsipy_shemotehnicheskoy_realizatsii_filtrov_na_operats ionnom_usilitele (accessed: 01.11.2018).

19. Reference on the ADC / DAC [Electronic resource] // URL: http://azp.ucoz.ru/index/ltc1742_14_razrjadnyj_maloshumjashhij_acp_s_chastotoj_preobrazovanija_65_mgc/0-75 (accessed: 01.11.2018).

20. Evstifeev A.V. Mega AVR Microcontrollers: User Guide. M .: Publishing house "Dodeca - XXI", 2007.

Claims (23)

1. The method of measuring the phase difference of the harmonic signals at the outputs of two studied linear physical paths with limited frequency bands, quasi-white noise, small signal-to-noise ratios and heterodyning the output signals of the studied paths to an intermediate frequency, which consists in generating a harmonic measuring signal of the selected frequency ƒ _ISM , which is one of the signals of a given finite set of harmonic measuring signals with frequencies that are multiples of the intermediate frequency falling into the strip transmission of the studied paths, in the transmission of this signal with a priori unknown frequency at the place of measurement through the studied paths, in the estimate with some instrumental error at the output of one of the frequency measuring paths

of the transmitted measuring signal, in determining and setting the frequency сигнала _{g of} the local oscillator signal, transferring the output signals x (t), y (t) of the studied paths to the intermediate frequency ƒ _pr and obtaining the corresponding harmonic signals X (t), Y (using this local oscillator) t), in the measurement of the phase difference

intermediate frequency signals, in use

to determine the magnitude of the phase difference Δϕ _{ism of} harmonic signals at the outputs of the studied paths, in the display of the value Δϕ _ism and frequency of the measuring signal in a form convenient for further use, characterized in that the value of the intermediate conversion frequency ƒ _{pr is} significantly less than the frequencies of a finite set of measuring signals and bandwidths of the frequency conversion paths, implement the following sequence of actions during the measurement process: perform the procedure “optimal heterode nirovaniya signals ", resulting in determining and storing the frequency ƒ _edited transmitted through the investigated paths of the measurement signal and the frequency of the local oscillator ƒ _r at which said signals frequency X (t), Y (t ) after heterodyning exactly corresponds to the selected intermediate frequency ƒ _etc., establish a local oscillator frequency equal to ƒ _r successively carried over harmonic signals X (t), Y (t ) and the intermediate frequency signals Z1 (t), Z2 (t ) of the local reference oscillator procedure "sinfazirovaniya quadrature signals" and "quasi- -temperature measuring signal phase difference "to yield a phase difference value

the signals of the local reference oscillator in phase with the signals X (t), Y (t), calibrate the frequency conversion paths, for which a harmonic signal with a frequency ƒ _ISM defined in the procedure of “optimal signal heterodyning” is generated on the basis of the local reference oscillator, instead of the output signals x (t), y (t) of the studied paths to the inputs of both frequency conversion paths, the procedures of “quadrature signal phase-out” and “quadrature measurement of the signal phase difference” are sequentially measured hydrochloric phase difference ΔΨ _edited signal paths for frequency conversion outputs is taken as a gauge correction, subtracting it from the previously measured phase difference

and get the desired phase difference

the output signals of the studied paths, together with the obtained phase difference value Δϕ _{ism, the} output signals of the studied paths display the frequency ƒ _{ism of the} measurement signal transmitted through the studied paths, determined in the procedure of “optimal signal heterodyning”. 2. A method for measuring the phase difference of harmonic signals according to claim 1, characterized in that the procedure of “optimal heterodyning of signals” includes the following actions and operations: they evaluate the frequency with an instrumental error at the output of one of the studied paths

transmitted measuring signal, according to the known value of the intermediate frequency ƒ _CR and measured

define auxiliary parameters

where the symbols [⋅] and {⋅} denote the operations of taking the integer and fractional part of the number, respectively, calculate and set the value of the optimal local oscillator frequency ƒ _g to convert the frequency down, at which the oscillation frequency ƒ _ISM after conversion will be exactly equal to ƒ _pr

then calculate and remember the true value of the frequency of oscillations of the measuring signal at the outputs of the studied paths, which is equal to ƒ _ISM = ƒ _g + ƒ, _etc. 3. A method for measuring the phase difference of harmonic signals according to claim 1, characterized in that the “quadrature phase-matching of signals” procedure includes the following actions and operations: form, using a local reference generator, harmonic signal Z (t) with a frequency ( _pr quadrature signals components Z1 (t) and Z2 (t), which, together with the measuring signals X (t), Y (t), obtained after heterodyning with the local oscillator frequency calculated in the “optimal heterodyning of signals” procedure, are subjected to synchronous sampling the number of samples K _sf (K _sf ≥4) on the oscillation period and the total number of samples L _sf (L _sf ≥100⋅K _sf ) in the sample X (t) → X (n), Y (t) → Y (n), Z1 (t) → Z1 (n), Z2 (t) → Z2 (n), n∈ [1 ... L _sf ], where n is the serial number of the sample in the sample, the weighting factors W1, W2 of the projections of the signal X (t) and the weighting factors W3, W4 of the projections of the signal Y (t) on the quadrature components of the signal Z (t) are calculated and stored according to the formulas

4. A method for measuring the phase difference of harmonic signals according to claim 1, characterized in that the procedure for "quadrature measuring the phase difference of the signals" includes the following actions and operations: form, as in the procedure of "quadrature signal phase-out", the signals of the quadrature components Z1 ( t) and Z2 (t) with a frequency ƒ _pr , carry out their repeated synchronous sampling Z1 (t) → Z11 (n), Z2 (t) → Z22 (n), n∈ [1 ... 1.25⋅K _rf ], with a large and multiple of four number of samples K _rf (K _rf ≥1000) during the oscillation period and the total number of samples in the sample equal to 1.25⋅K _rf , two arrays of samples R1 (n) and R2 (n) are formed and stored R1 (n) = W1⋅Z11 (n) + W2⋅Z22 (n), R2 (n) = W3⋅Z11 (n) + W4⋅Z22 (n), n∈ [1 ... 1.25⋅K _rf ], where W1, W2, W3, W4 are the weighting coefficients calculated in the “quadrature phase matching phase” procedure, normalize the samples samples R1 (n) and R2 (n) by representing them with their own signs by rule

calculate the correlation coefficients β and γ

determine the phase difference

local reference oscillator signals in phase with the measuring signals X (t), Y (t) obtained after heterodyning with the local oscillator frequency calculated in the procedure of "optimal heterodyning signals" using one of the preferred formulas

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