RU2730875C1 - Method for storage of electric oscillation frequency - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method of storing the frequency of electric oscillations with a frequency measure can be used when creating precision frequency and time standards. Method consists in measuring the initial deviation of the measure frequency from the reference frequency at a certain initial interval T₀. At the end of interval T₀, the measurement frequency is corrected by the value of the measured initial deviation, and further during a certain time interval T, the frequency of the measure signal is further divided, two-channel analogue-to-digital conversion of a measure signal in main frequency and divided frequency channels with a time sampling interval determined by the frequency of the sampling signal generated from the measure signal. Transformations of the obtained digital samples U₁(k), U₂(k) into quadrature components of complex signals of the fundamental frequency channel U_1s(k), U_1c(k) and the shared frequency channel U_2s(k), U_2c(k), where k=0, 1, 2, 3…, – current number of samples. Determining the phase ϕ₁(k) of the fundamental frequency channel signal and ϕ₂(k) of the divided frequency channel signal as complex number arguments in accordance with expressions ϕ₁(k)=tg^-1(U_1s(k)/U_1c(k)) and ϕ₂(k)=tg^-1(U_2s(k)/U_2c(k)). Phase difference is determined Δϕ₁(k)-ϕ₂(k) and calculating current value of measure frequency correction β(k)=-ƒ₀Δϕ(k)/πjk. Values are compared β(k) with threshold β_thr, where β_thr is the resolver power of the measure frequency, and correction of the measure frequency is carried out by the value – β(k_thr), where k_thr is the value of current sample number, at which |β(k)|≥β_thr.

EFFECT: technical result consists in reduction of frequency error due to frequency drift of frequency of frequency measure.

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Description

The invention relates to the field of metrology and can be used to create generators of highly stable electrical oscillations and high-precision clocks based on them - frequency and time standards.

A known method of storing the frequency of electrical oscillations as a measure of frequency (see, for example, [1] - Pikhtelev A.I. et al. / Frequency and time standards based on quantum generators discriminators // M., Sov. Radio and communication, 1978, ( p. 252-262), containing periodically repeated operations of comparing the frequencies of the measure and the standard and correcting the frequency of the measure by the value of the measured deviation Measurements of the deviation of the frequency of the measure signal from the frequency of a spatially distant standard is carried out by radio signals of exact time or by the method of transported clocks.

The disadvantage of this method [1] is a large frequency error due to the presence of a systematic drift of the frequency of quantum frequency standards in the intertesting interval associated with aging of elements, and the rate of the aging process changes over time.

There are a number of methods for storing the frequency of electrical oscillations presented in patents: [2] - RU 2178196 C1, G04F 5/00, G04G 5/00; [3] - RU 8167 U1, H01S 1/00, 16.10.1998; [4] - RU 70727 U1, H01S 1/00, 10.02.2008; containing the operation of measuring the deviation of the frequency of the measure from the frequency of the standard at the time interval T ₀ , correcting the frequency of the measure by the value of the measured deviation and additional periodic correction of the frequency of the measure during the time interval T of autonomous operation. The value and time points of the additional periodic correction are determined based on the predicted rate of the systematic drift of the measure frequency, and the predicted rate of the systematic drift of the frequency over the time interval T is assumed to be equal to the measured rate of the systematic drift of the frequency over the time interval T ₀ , while the frequency change is assumed to be linear.

The disadvantage of these methods [2] - [4] is a large frequency error due to the inaccuracy of the linear forecast model for the change in the frequency of the measure, since, firstly, the parameters of this model include the parameters of the systematic drift of the frequency of the reference signal, and, secondly, the rate of systematic drift of the measure frequency is not constant, but changes over time.

Дополнительную периодическую коррекцию частоты меры выполняют на величину β, которую уменьшают со временем на протяжении интервала времени Т в соответствии с прогнозируемым уменьшением скорости систематического дрейфа частоты меры. Начальную величину дополнительной периодической коррекции устанавливают в соответствии с неравенством

а ее знак - противоположным знаку ν₀. Прогноз поведения частоты меры основывается на измерениях ее отклонения от частоты эталона на начальном интервале времени Т₀ (достаточно большом, до нескольких месяцев), а также на исследованиях поведения частоты мер данного типа на длительных интервалах времени, много больших Т₀ (на протяжении нескольких лет).The closest in technical essence to the claimed is the method described in the patent [5] - RU 2279115 C9, G04G 3/00, G04G 7/00, G04F 5/00, 06/27/2006, and adopted as a prototype. The known method of storing the frequency of electrical oscillations by a measure of frequency contains the operations of comparing the frequency of the measure with the frequency of the standard ƒ ₀ during the initial time interval T ₀ , determining the initial deviation Δƒ _{0 of the} frequency of the measure from the frequency of the standard and the initial speed ν _{0 of the} systematic drift of the frequency of the measure relative to standard frequency, correction of the measure frequency by the value of the measured initial deviation Δƒ ₀ at the end of the time interval T ₀ and subsequent additional periodic correction of the measure frequency during the time interval T at times kΔt, where k = 1, 2, 3,

An additional periodic correction of the measure frequency is performed by the value β, which decreases with time over the time interval T in accordance with the predicted decrease in the rate of the systematic drift of the measure frequency. The initial value of the additional periodic correction is set in accordance with the inequality

and its sign is opposite to the sign of ν ₀ . The prediction of the behavior of the frequency of a measure is based on measurements of its deviation from the reference frequency at the initial time interval T ₀ (rather large, up to several months), as well as on studies of the behavior of the frequency of measures of this type over long time intervals much larger than T ₀ (over several years ).

The disadvantages of the method [5] prototype include:

- a sufficiently large frequency error due to inaccuracy in predicting the rate of the systematic drift of the measure frequency, since the parameters of the drift model include the drift of the frequency of the reference signal and can significantly deviate from the predicted values in the time interval T of the autonomous functioning of the frequency measure, especially in severe operating conditions, for example, on board a spacecraft or underwater vehicle;

- a long process of assessing the rate of the systematic drift of the measure frequency (several months), which significantly increases the cost of the product.

The technical result to which the invention is directed is to reduce the frequency error due to the systematic drift of the frequency of the frequency measure.

The essence of the invention lies in the fact that in a method of storing the frequency of electrical oscillations by a measure of frequency, containing the operation of comparing the frequency of the measure with the frequency of the standard ƒ ₀ during the initial time interval T ₀ , determining, based on the results of these comparisons, the initial deviation Δƒ _{0 of the} frequency of the measure from the frequency of the standard, correction of the measure frequency by the value of the measured initial deviation Δƒ ₀ at the end of the time interval T ₀ and subsequent, during the time interval T, additional correction of the measure frequency by β. Additionally, on the time interval T, the following operations are included:

- dividing the frequency of the measure signal with the coefficient k _d = 2j + 1, where j = 1, 2, 3,…;

- two-channel synchronous analog-to-digital conversion of the measure signal in the channels of the fundamental frequency and the divided frequency with a time sampling interval determined by the sampling signal frequency ƒ _s , synthesized from the measure signal in accordance with the expression ƒ _s = 4ƒ ₀ / (2j + 1);

- transformation of the received digital samples U ₁ (k), U ₂ (k) into the quadrature components of the complex signals of the fundamental frequency channel U _1s (k), U _1c (k) and the channel of the divided frequency U _2s (k), U _2c (k) , where k = 0, 1, 2, 3… „is the current number of samples;

- determination of the phases ϕ ₁ (k) of the channel signal of the fundamental frequency and ϕ ₂ (k) of the channel signal of the divided frequency as arguments of complex numbers in accordance with the expressions ϕ ₁ (k) = tan ^-1 (U _1s (k) / U _1c (k )) and ϕ ₂ (k) = tan ^-1 (U _2s (k) / U _2c (k)).

- determination of the phase difference Δϕ (k) = ϕ ₁ (k) -ϕ ₂ (k);

- calculating the current value of the frequency correction

β (k) = - ƒ ₀ Δϕ (k) / πjk

- comparison of the value β (k) with the threshold β _pores , where β _pores is the resolution of the governor of the measure frequency;

- the frequency of the measure is corrected by the value -β (k _pores ), where k _nop is the value of the number of the current sample, at which | β (k) | ≥ β _pores .

The essence of the proposed method is illustrated by illustrative materials presented in Fig. 1, 2, 3 and 4, where:

in fig. 1 shows the principle of stroboscopic conversion of a frequency measure signal during time sampling;

in fig. 2 schematically shows the transformation of the spectra of discrete signals in the channels of the fundamental and divided frequencies;

in fig. 3 shows an example of a block diagram of a device that implements the proposed method, where:

1 - measure of frequency;

2 - frequency divider;

3, 4 - analog-to-digital converters;

5 - frequency synthesizer;

6 - digital signal processor;

in fig. 4, the dotted line shows the graph of the frequency of the measure against time without correction, and the solid line shows the graph of the dependence of the frequency of the measure with correction according to the proposed method, starting from the time interval T ₀ .

The proposed method works as follows. At the initial time interval T ₀ , the frequency ƒ = ƒ ₀ + Δƒ _{0 of the} frequency measure is compared with the frequency ƒ _{0 of the} standard, the value of Δƒ _{0 is} measured and the frequency of the measure is corrected by the measured value Δƒ ₀ at the end of the time interval T ₀ . In this case, at the beginning of the time interval T of autonomous operation, the model of the measure signal, which takes into account the systematic drift of the frequency, is represented as:

where: ƒ ₀ is the nominal value of the frequency of the measure, measured at the time of the beginning of its autonomous operation;

α is the frequency drift rate (Hz / sec), which is to be estimated in order to form a control parameter for the frequency control circuit of the measure.

In addition to the signal (1) of the channel of the fundamental frequency, the signal of the channel of the divided frequency is formed using the frequency division operation, namely:

синхронно подвергаются квантованию по уровню с интервалом временной дискретизации t_s, длительность которого задается синхроимпульсами сигнала квантования u_s(t), формируемому из сигнала (1) с помощью операции синтеза частоты (см. [6] - Рыжков А.В., Попов В.Н. / Синтезаторы частот в технике радиосвязи. // М.: Радио и связь, 1991. (с. 67-74):The signals u (t) and

are synchronously subjected to level quantization with a time sampling interval t _s , the duration of which is set by the sync pulses of the quantization signal u _s (t), formed from signal (1) using the frequency synthesis operation (see [6] - Ryzhkov AV, Popov V .N. / Frequency synthesizers in radio communication technology. // M .: Radio and communication, 1991. (p. 67-74):

Let the pulses of the quantization signal be formed at the moments when the signal (3) passes through the zero level with a positive derivative. Then the moments t _{k of} digital samples of signals (1) and (2) can be determined from the equation:

where k = 0, 1, 2, 3, .. current number of samples.

Therefore, to determine t _k, you can use the quadratic equation:

the solution of which, taking into account t _k ≥0, gives:

Since, even for a sufficiently large number of k, the quantity

then the radical in (5) can be expanded in a series (see [7] - Dwight GB / Tables of integrals and other mathematical formulas. // M, 1973, (p. 8):

Taking into account (6), it suffices to restrict ourselves to the linear approximation in (7). Therefore, we finally get

Expression (8) shows that, in the first approximation, the change in the duration of the quantization interval due to the linear frequency drift can be neglected.

The formulas for digital samples in the channels of the fundamental frequency signal and the divided frequency signal can be written if discrete moments of time t _k from (8) are substituted in (1) and (2) instead of continuous time t:

Without loss of generality, you can choose j = 2, 4, 6,… - an even integer. In this case, expression (9) can be rewritten as:

For odd j, the sin function in (11) will be with a minus sign.

Comparison of (10) and (11) shows that digital samples of signals with the same relative center frequency ω ₀ = 2πƒ ₀ / f ₀ = π / 2 are formed in both channels (see [8] - Fundamentals of digital signal processing. Course of lectures / A.I.Solonina et al. // Publishing 2nd revision and revision, St. Petersburg, BHV-Petersburg, 2005, pp. 195-199). The difference is that in the channel of the fundamental sampling frequency is the result of the stroboscopic effect, and in the channel of the divided frequency signal - the result of direct quantization of the signal with the central frequency ƒ ₀ / (2j + 1) (see [8] - Fig. 3a, Fig. 3b, Fig.3c). In this case, the second terms under the signs of trigonometric functions in (10) and (11) are due to the presence of a drift of the signal frequency with a velocity α.

на значения

с последующей цифровой низкочастотной фильтрацией, то есть:Next, the formation of the quadrature components of the complex signals is carried out. The channel is the fundamental frequency _{- U s (k), U} c (k), and the channel frequency divided -U ₀ (k), U ₀ (k). Such formation is performed, for example, by multiplying the samples u (k),

on values

followed by digital low-pass filtering, that is:

Determination of the signal phases of the fundamental frequency channel ϕ ₁ (k) and the divided frequency signal channel ϕ ₂ (k) as arguments of complex numbers is carried out in accordance with the expressions:

Next, the phase difference Δϕ (k) of the signals of the main channel and the channel of the divided frequency is calculated, that is:

From (12) we obtain an estimate of the rate of the systematic frequency drift:

В этом случае в формуле (13) Δϕ(k)=ϕ(k)-ϕ₂(0).It should be noted that, in order to reduce the bulkiness of the calculations, when deriving (13), it was assumed that Δϕ (0) = 0, which is permissible, since the signals in the channels and the quantizing signal are synchronized. In reality, with the practical implementation of the method, the option is possible

In this case, in formula (13) Δϕ (k) = ϕ (k) -ϕ ₂ (0).

Next, the current value β (k) of the correction of the frequency measure is estimated, which, taking into account (8) and (13), is expressed as:

At each k-th step, the value β (k) is compared with the threshold β _pores , where β _pores is the resolution of the measure frequency governor.

осуществляют коррекцию частоты меры на величину -(β(k_пор), где k_пор - значение номера текущих выборок, при котором

После операции коррекции счетчик выборок обнуляется, то есть k=0, и начинается новый интервал Т оценки α.If the condition is met

the frequency of the measure is corrected by the value - (β (k _pores ), where k _pores is the value of the number of the current samples, at which

After the correction operation, the sample counter is reset to zero, that is, k = 0, and a new estimation interval T begins.

Thus, according to the claimed method of storing the frequency of electrical oscillations, the speed of the measure frequency drift is estimated in real time, which makes it possible to increase the storage accuracy in comparison with the known method, which uses the previously obtained parameters of the measure frequency drift model, which have limited accuracy and vary during the autonomous process. work measures.

In addition, the application of the proposed method does not require a long, up to several months, procedure for assessing the model of the systematic drift of the frequency of the measure, which can significantly reduce the time for creating the frequency measure and, therefore, reduce its cost. Indeed, to measure the initial deviation Δƒ _{0 of the} frequency of the measure from the frequency of the standard during T _{0, it is} sufficient to restrict oneself to the time interval 1000 sec≤T ₀ <3600 sec.

The order of magnitude of the interval T can be determined using the example of a quantum frequency standard on a rubidium gas cell (KSCh-RGC), the systematic frequency drift of which is α = 5⋅1 ^-12 1 / month in relative units (9⋅10 ^-12 Hz / sec at nominal frequency measure 5,000,000 Hz). Resolution of the digital control frequency synthesizer KSCh-RGYa / β _pore = 5⋅10 ^-8 Hz. For these initial data, we get:

T = β _pores / α = 1.8⋅10 ⁵ sec. = 5 hours.

Considered shows that the claimed method of forming pulses is feasible and ensures the achievement of the technical result, which consists in reducing the frequency error due to the systematic drift of the frequency of the frequency measure.

Sources of information

1. Pikhtelev A.I. et al. / Frequency and time standards based on quantum generators of discriminators // M., Sov. radio and communication, 1978, (p. 252-262).

2. RU 2178196, G04F 5/00, G04G 5/00, publ. 10.01.2002.

3. RU 8167 U1, H01S 1/00, publ. 16.10.1998.

4. RU 70727 U1, H01S 1/00, publ. 10.02.2008.

5. RU 2279115 C9, G04G 3/00, G04G 7/00, G04 F 5/00, publ. June 27, 2006.

6. Ryzhkov A.V., Popov V.N. / Frequency synthesizers in radio communication technology. // M: Radio and communication, 1991, (p. 67-74).

7. Dwight G.B. / Tables of integrals and other mathematical formulas. // M., 1973, (p. 8)

8. Basics of digital signal processing. Course of lectures / A.I. Solonina and others // Ed. 2nd rev. and revised., St. Petersburg, BHV-Petersburg, 2005, (p. 195-199, Fig.3a, Fig.3b, Fig.3c).

Claims (1)

A method of storing the frequency of electrical oscillations by a frequency measure, containing the operations of comparing the frequency of the measure with the frequency of the standard ƒ ₀ during the initial time interval T ₀ , determining, based on the results of these comparisons, the initial deviation Δƒ _{0 of the} frequency of the measure from the frequency of the standard, correcting the frequency of the measure by the value of the measured initial deviation Δƒ ₀ at the end of the time interval T ₀ and the subsequent additional correction of the measure frequency by the value β during the time interval T, characterized in that, in addition, on the time interval T, the measure signal is subjected to frequency division operations with the coefficient k _d = 2j + 1, where j = 1, 2, 3, ..., two-channel synchronous analog-to-digital conversion in the channels of the fundamental frequency and the divided frequency with a time sampling interval determined by the frequency ƒ _{s of} the sampling signal, synthesized from the measure signal in accordance with the expression ƒ _s = 4ƒ ₀ / (2j +1), transforming the obtained digital samples U ₁ (k), U ₂ (k) into the quadrature components of the lex signals of the channel of the fundamental frequency U _ls (k), U _lc (k) and the channel of divided frequency U _2s (k), U _2c (k), where k = 0, 1, 2, 3 ..., is the current number of samples , determining the phases ϕ ₁ (k) of the channel signal of the fundamental frequency and ϕ ₂ (k) of the channel signal of the divided frequency as arguments of complex numbers in accordance with the expressions ϕ ₁ (k) = tan ^-1 (U _1s (k) / U _1c (k )) and ϕ ₂ (k) = tan ^-1 (U _2s (k) / U _2c (k)), determining the phase difference Δϕ (k) = ϕ ₁ (k) -ϕ ₂ (k), calculating the current correction value the frequency of the measure β (k) = - ƒ ₀ Δϕ (k) / πjk, comparing the value β (k) with the threshold β _pores , where β _pores is the resolution of the governor of the frequency of the measure, and the frequency of the measure is corrected by the value -β (k _pores ), where k _pores is the value of the number of the current sample at which | β (k) | ≥ β _pores .

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