RU2041469C1 - Phase fluctuation characteristic meter - Google Patents

Abstract

FIELD: radio measurement technology. SUBSTANCE: meter has reference-frequency generator 1, frequency synthesizer 2, sampling pulse shaper 3, pulse shaper 4, pulse counter 5, register 6, retrieval and storage units 7,8, analog-to-digital converters 9,10, arc tangent computing unit 11, control unit 12, storage unit 13, arithmetic unit 14. EFFECT: enlarged functional capabilities. 2 dwg

Description

 The invention relates to radio measurement technology and can be used in satellite radio navigation systems for rangefinder, high-speed and goniometric trajectory measurements, as well as in information-measuring systems for evaluating and monitoring parameters of frequency standard signals, frequency synthesizers, etc.

 A well-known digital meter of phase fluctuation characteristics, containing a highly stable reference frequency generator, a gate pulse generator, sampling and storage units, analog-to-digital converters, an arctangent calculation unit, a control unit, a storage unit, an arithmetic unit, a controlled attenuator, a controlled phase shifter, an amplitude comparator, a phase detector, frequency divider, phase detector and low pass filter.

The operation of this meter is based on gating with short pulses the reference frequency ω _{about the} sine and cosine components of the signal under study. Using digital samples of the signals of the sine and cosine channels obtained using the sampling and storage units and analog-to-digital converters, the arctangent calculator calculates the phase value φ _{i of the} signal input to the device. The calculated phase values φ _i are recorded in the storage unit. The arithmetic unit calculates the difference of every two adjacent calculated signal phase values (φ _{i + 1} φ _i ), which are also recorded in the storage unit and represents the values of the phase incursions of the input signal for equal time intervals τ between adjacent strobe pulses
τ t _{i + 1} t _i 2 π / ω _o . The arithmetic unit also calculates the difference of adjacent values of the phase incursions, which is the phase fluctuation of the input signal δφ _i
δφ _i (φ _i φ _i-1 ) (φ _i-1 φ _i-2 ) In the absence of phase noise
φ _i ωt _i + φ _o ; φ _i φ _i-1 φ _o ; δφ _i 0.

In this meter, the frequency of a highly stable reference frequency generator is “linked” to the frequency ω of the input signal by means of a PLL. This ensures the frequency multiplicity ω and ω _о , i.e. ω m ω _o , and the measurement error due to non-linear distortion of the input signal is eliminated. PLL elements in this device are a frequency divider, a phase detector and a low-pass filter. However, the introduction of a frequency-locked loop ω _{of a} highly stable generator leads to a limitation of the device’s functionality, in particular, it excludes the possibility of measuring the frequency ω of the input signal.

 A disadvantage of the known device is the inability to provide the required accuracy for solving the radio navigation problems posed, due to the presence of additive noise in the input signal under investigation and quantization noise.

Closest to the proposed device is a meter containing a reference frequency generator, a gate pulse generator, sampling and storage units, analog-to-digital converters, an arctangent calculation unit, a control unit, a storage unit, an arithmetic unit, a controlled attenuator, a phase detector, an amplitude comparator, a phase detector [1]
Quadrature signals of equal amplitude are formed from the input signal under investigation using a controlled phase shifter, controlled attenuator, amplitude comparator and phase detector; ⁹⁰ ethyl quadrature phase shift control signal by the phase detector and kept constant in the frequency range through controlled phase shifter. The amplitude amplitudes of the quadrature signals are maintained thanks to the amplitude comparator and the controlled attenuator. Using the shaper of the strobe pulses arriving at a frequency of ω _{about the} reference signal to the control inputs of the sampling and storage blocks 7 and 8, the instantaneous voltage values of the quadrature signals are stored. Analog-code converters convert the stored voltage values of quadrature signals into digital codes, which are fed to the corresponding inputs of the arctangent calculation unit. The arc tangent calculation unit calculates the phase value φ _{i of the} input signal at the time of arrival of the i-th strobe pulse at the inputs of the sampling and storage units. The calculated phase values φ _i are recorded in the storage unit. The arithmetic unit calculates the difference of every two adjacent calculated signal phase values (φ _i φ _i-1 ). The calculated differences, the values of which are also recorded in the storage unit, represent the phase incursions of the input signal for equal time intervals between adjacent strobe pulses
τ = 2 π / ω _o . and in the absence of phase fluctuations of the input signal must have a constant value. The inability to provide the required measurement accuracy with a known device is due to both noise in the input signal under investigation and quantization noise. A relatively high measurement error leads, in turn, to an unacceptable increase in the measurement time.

(3) где N_o мощность шума;
ε_с энергия сигнала, накопленная за время наблюдения, т.е.The total Δ _Σ random measurement error for this device can be written as
Δ _Σ Δ _w + Δ _k (1) where Δ _{w the} error due to noise in the input signal under investigation;
Δ _{to the} error from quantization. The variance σ ² (Δ _Σ ) of the total error is expressed
σ ² (Δ _Σ ) σ ² (Δ _w + σ ² (Δ _k ), (2) where σ ² (Δ _w ) and σ ² (Δ _k ), respectively, are the variances of the noise error and the quantization error.
σ ² (Δ _W )

(3) where N _{o is the} noise power;
ε _с signal energy accumulated during the observation time, i.e.

A²sin²ωtdt (4) В известном устройстве отсчеты измеряемого сигнала в квадратурных каналах берутся в короткие моменты стробирования, поэтому выражение (4) можно переписать
ε_c= A²

sin²ωtδ(t-t_c)dt A²sin²ωt_c (5) где σ (.) дельта-функция Дирака. Из (5) следует, что ε_с зависит от t_c. Поэтому необходимо найти среднее значение ε_с, полагая распределение фазы сигнала равномерным на интервале

=

A²

sin²ωt_cdt_c=

(6) где Т 2 π/ω. С учетом (6) выражение (3) примет вид
σ²(Δ_ш)

1/q (7) где q A²/N_o отношение сигнал-шум. Для определения σ²(Δ_к) положим, что разрядность АЦП равна n. При этом напряжения А_с и А_к сигнала в каждом из квадратурных каналов квантуется на 2ⁿ уровней. Очевидно, что значение фазы сигнала, равное φ_i arctg(A_c/A_к), квантуется на 2ⁿ⁺¹ уровней, т.е. Δ_о 2 π/2ⁿ⁺¹.ε _c =

A ² sin ² ωtdt (4) In the known device, samples of the measured signal in quadrature channels are taken at short gating times, therefore, expression (4) can be rewritten
ε _c = A ²

sin ² ωtδ (tt _c ) dt A ² sin ² ωt _c (5) where σ (.) is the Dirac delta function. It follows from (5) that ε _c depends on t _c . Therefore, it is necessary to find the average value of ε _s , assuming that the phase distribution of the signal is uniform over the interval

=

A ²

sin ² ωt _c dt _c =

(6) where T 2 π / ω. In view of (6), expression (3) takes the form
σ ² (Δ _W )

1 / q (7) where q A ² / N _{o is} the signal-to-noise ratio. To determine σ ² (Δ _k ), we assume that the ADC capacity is n. In this case, the voltage A _c and A _{k of the} signal in each of the quadrature channels is quantized into 2 ⁿ levels. Obviously, the signal phase value equal to φ _i arctan (A _c / A _k ) is quantized into 2 ^{n + 1} levels, i.e. Δ _about 2 π / 2 ^{n + 1} .

(8) Суммарную дисперсию погрешности измерения фазы, учитывая статистическую независимость составляющих, можно выразить в виде
σ²= σ²(Δ_ш)+σ²(Δ_к) 1/q +

(9) При малых отношениях сигнал/шум (например, в системах дальней радионавигации) определяющий вклад в суммарную погрешность фазовой синхронизации вносит шумовая составляющая, поэтому выражение (9) в этом случае можно приближенно записать
σ²

1/q Для достижения требуемой точности фазовой синхронизации современных навигационных систем необходимо, чтобы относительная дисперсия погрешности оценки фазы была равна
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{о}}$ _т=

≈ 10¹⁵-10¹⁶ Для достижения столь малой дисперсии применяется усреднение m фазовых отсчетов. При этом дисперсия уменьшается в m раз, т.е.The density distribution of the error from quantization Δ _{k is} uniform over the interval Δ _o [8] Therefore, the variance Δ _k is expressed as
σ ² (Δ _k )

(8) The total variance of the phase measurement error, taking into account the statistical independence of the components, can be expressed as
σ ² = σ ² (Δ _w) + σ ² (Δ _k) 1 / q +

(9) For small signal-to-noise ratios (for example, in long-range radio navigation systems), the noise component makes a decisive contribution to the total phase synchronization error; therefore, expression (9) in this case can be approximately written
σ ²

1 / q To achieve the required accuracy of the phase synchronization of modern navigation systems, it is necessary that the relative variance of the phase estimation error be equal to
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{about}}$ _t =

≈ 10 ¹⁵ -10 ¹⁶ To achieve such a small dispersion, averaging of m phase samples is applied. In this case, the dispersion decreases m times, i.e.

A

1 +

·cos[(k-1)ω_ot]

cos

t+

sin[(k-1)ω_ot]

Пренебрегая амплитудной модуляцией, можно записать
U′(t) A₁cos

t+

sin[(k-1)ωt]

(10) Значение фазы сигнала будет
φ_i= ωt_i+

sin[(k-1)ωt_i] (11) Поскольку в общем случае ω≠n ω_o, где ω_о частота опорного сигнала, а m целое число, то
δφ_i= φ_i+1-φ_i≠0 в отсутствии фазовых шумов. Погрешность из-за нелинейных искажений приводит к полной неработоспособности известного устройства при анализе фазовых флуктуаций периодической последовательности импульсов из-за неоднозначности фазовых отсчетов при стробировании последовательности импульсов.σ ² _from σ ² / m˙4 π ² 1 / mq˙4 π ² . With a real signal-to-noise ratio q 4, the achievement of the required accuracy is possible if m 7˙10 ¹² . In this case, the measurement time will be
T _n 7˙10 ¹² T _about , where T _{about the} duration of the period of the reference gating signal. For T _about 10 ^-9 s, T _n 7000 s. which is unacceptably large. In addition, this device is characterized by a significant error in the analysis of phase fluctuations of oscillations with a high level of nonlinear distortion. In fact, the studied oscillation V (t), to a first approximation, neglecting phase noise, can be considered as a sinusoidal oscillation with amplitude A ₁ and frequency ω, modulated in amplitude and phase by signals with frequency (k-1) ω _o , i.e. as
U (t)

A

1 +

Cos [(k-1) ω _o t]

cos

t +

sin [(k-1) ω _o t]

Neglecting amplitude modulation, you can write
U ′ (t) A ₁ cos

t +

sin [(k-1) ωt]

(10) The phase value of the signal will be
φ _i = ωt _i +

sin [(k-1) ωt _i ] (11) Since in the general case ω ≠ n ω _o , where ω _{о is the} frequency of the reference signal and m is an integer, then
δφ _i = φ _{i + 1} -φ _i ≠ 0 in the absence of phase noise. An error due to nonlinear distortions leads to the complete inoperability of the known device in the analysis of phase fluctuations of a periodic pulse sequence due to the ambiguity of phase readings during gating of a pulse sequence.

The proposed technical solution arose as a result of solving the problem of constructing a signal phase meter that provides the necessary measurement accuracy to work on the signals of radio navigation stations (RNS), in particular satellite radio navigation systems (SRNS), for example, for phase synchronization systems (SPS). In modern SRNS, the achievement of the required accuracy is possible if the relative variance of the phase estimate is 10 ^-15 -10 ^-16 . Moreover, the signal-to-noise ratio in these systems is relatively small, for example, at the receiver input it is -160 dB, and at the meter input (2-4) dB. As shown in the application materials, achieving such accuracy with such a small signal-to-noise ratio using known technical solutions requires an unacceptably long measurement time.

 The technical result of the invention is to reduce the influence of noise error and, as a result, to increase the measurement accuracy at a fixed measurement time or to achieve a given measurement accuracy in a significantly less time.

 To achieve a technological result in a phase fluctuation characteristic meter, comprising a reference frequency generator, a quantizer of pulse pulses, the first and second sampling and storage units connected through the first and second analog-to-digital converters, respectively, to the first and second information inputs of the arctangent calculation unit, the output of which is connected to the second information input of the storage unit, the output of which is connected to the information input of the arithmetic unit, the first, second and third you the strokes of the control unit are connected to the control inputs of the arctangent calculation unit, the storage unit, and the arithmetic unit, the output of which is connected to the third information input of the storage unit and is the output of the meter, a pulse shaper, pulse counter and a register connected in series between the reference frequency generator and the quantizer the frequency synthesizer is turned on, while the sine and cosine outputs of the synthesizer are connected to the signal inputs respectively Actually, the first and second sampling and storage blocks, the gating inputs of which are combined with the counter reset input and the register synchronization input and are connected to the output of the pulse shaper, whose input is the input of the meter, the output of the quantizer of the pulse shaper is connected to the counting input of the counter and the input of the control unit, the register output connected to the first information input of the storage unit.

Incorporation of new blocks with corresponding connections possible to use the error dependence of the input signal phase measurement of the ratio of the input frequency ω and ω _about the reference signals. Knowing a priori the signal-to-noise ratio at the meter input, using a tunable synthesizer, one can obtain such a frequency value ω _о , generating signals from quadrature channels and then gating them with pulses formed from a mixture of the input signal and noise, it is possible to minimize the phase estimation variance, i.e. e. to increase the accuracy of measurement at a given time interval.

 Figure 1 shows the proposed meter; figure 2 is a timing diagram of the operation of the meter.

 The proposed device comprises a series-connected reference frequency generator 1, a frequency synthesizer 2, a quantizer of 3 pulses, as well as sequentially connected a pulse shaper 4, a pulse counter 5 and a register 6. The output of the pulse shaper 4 is connected to a reset input of a pulse counter 5 and a synchronization input of register 6 , as well as with the gating inputs of blocks 7 and 8 of the selection and storage, the outputs of which through analog-to-digital converters 9 and 10 are connected respectively to the first and second inputs of block 11 in Calculations of arctangent. The output of the shaper 3 of quantizing pulses is connected to the counting input of the counter 5 pulses and the input of the control unit 12, the first, second and third outputs of which are connected respectively to the control inputs of the arctangent calculating unit 11, the memory unit 13 and the arithmetic unit 14. The first, second and third memory inputs unit 13 are connected respectively with the output of the register 6, the output of the arctangent calculation unit 11 and the output of the arithmetic unit 14, the output of the latter is the output of the meter. The input of the meter is the input of the shaper 4 pulses.

 The meter works as follows.

Одновременно импульсы исследуемого сигнала с выхода формирователя 4 импульсов поступают на вход синхронизации регистра 6, в котором фиксируется код l_i с выхода счетчика 5 импульсов. Счетчик 5 импульсов осуществляет подсчет квантующих импульсов опорной частоты (фиг.2,д), сформированных из сигнала U₃ перестраиваемого синтезатора частоты формирователем 3 квантующих импульсов. По окончании i-го импульса исследуемого сигнала, поступающего также на вход сброса счетчика 5, последний обнуляется и начинает счет с нулевого значения. Поэтому число l_i равно целому числу импульсов опорного сигнала частоты ω_о, сформированных в интервале времени Т_i между i-ым и (i-1)-ым импульсами исследуемого сигнала. Значения φ_i и l_i заносятся в запоминающий блок 13. Арифметический блок 14 вычисляет разность каждых двух смежных вычисленных значений фазы Φ₁ φ_i φ_i-1 исследуемого сигнала. Формирователь 4 импульсов и формирователь 3 квантующих импульсов, а также счетчик 5 и регистр 6 могут быть выполнены любым известным образом [8] в качестве блоков 7 и 8 выборки и хранения могут быть использованы микросхемы ключей, например 564 КП1, с запоминающим конденсатором на выходе [6] Могут быть использованы микросхемы АЦП, содержащие устройства выборки и хранения, например 1107ПВ1, 1107ПВ2 и т.п. [7] Арифметический 14 и запоминающий 13 блоки могут быть реализованы, например, на микросхемах 580ВМ80 и 537РУ10. Блок 12 управления представляет собой распределитель импульсов, созданный на основе, например, сдвигового регистра, счетчика или делителя, реализованных на микросхемах серии 533, 530 и т.п. Синтезатор частоты представляет собой перестраиваемый синтезатор и может быть выполнен, например, как показано в [9] Значение фазы φ_i опорного сигнала в момент времени t_iстробиpования равно
φ_i ω_ot_i.In accordance with the a priori known signal-to-noise ratio at the meter input, from the signal of a highly stable reference frequency generator 1, a sine U ₁ Asin ω _o t and cosine U ₂ Acos ω _o t sine signals are generated using a frequency synthesizer 2 (Fig. 2 c, d ) The signals U ₁ and U ₂ are fed to the signal inputs of the blocks 7 and 8 of the sample and storage, respectively. The strobe inputs of these blocks receive a periodic sequence of pulses (Fig.2, b) with a frequency ω, formed in the shaper 4 pulses at the moments of transition of the voltage of the input signal U _I (Fig.2, a) through the zero level with a positive derivative. In blocks 7 and 8 of the sampling and storage, which are, for example, a capacitor, which is disconnected from the charge and discharge circuits with the help of keys, the instantaneous values of the voltage of the reference frequency U ₁ ⁱ and U ₂ ^{i of the} quadrature channels are stored. Analog-to-digital converters 9 and 10 convert the stored voltage values of the quadrature signals of the reference frequency into digital codes, which are supplied to the corresponding inputs of the arctangent calculation unit 11. The arc tangent calculation unit 11 calculates the phase value φ _{i of} the reference frequency signal at the time of arrival of the i-th pulse of the signal under study at the gating inputs of sampling and storage units 7 and 8 in accordance with the following algorithm:
φ _i = arctg

At the same time, the pulses of the signal under study from the output of the pulse shaper 4 are fed to the synchronization input of the register 6, in which the code l _i is fixed from the output of the 5 pulse counter. The counter 5 pulses calculates the quantizing pulses of the reference frequency (figure 2, e), formed from the signal U ₃ tunable frequency synthesizer generator 3 quantizing pulses. At the end of the i-th pulse of the signal under study, which also arrives at the reset input of counter 5, the latter is reset and starts counting from zero. Therefore, the number l _i is equal to the integer number of pulses of the reference signal of frequency ω _о formed in the time interval T _i between the i-th and (i-1) -th pulses of the signal under study. The values of φ _i and l _i are entered in the storage unit 13. The arithmetic unit 14 calculates the difference of each two adjacent calculated phase values Φ ₁ φ _i φ _{i-1 of} the signal under study. Shaper 4 pulses and shaper 3 quantizing pulses, as well as counter 5 and register 6 can be performed in any known manner [8] as blocks 7 and 8 of the sampling and storage can be used chip chips, for example 564 KP1, with a storage capacitor at the output [ 6] ADC circuits containing sampling and storage devices, for example 1107PV1, 1107PV2, etc., can be used. [7] Arithmetic 14 and memory 13 blocks can be implemented, for example, on chips 580VM80 and 537RU10. The control unit 12 is a pulse distributor based on, for example, a shift register, counter or divider implemented on 533, 530 series microcircuits, etc. The frequency synthesizer is a tunable synthesizer and can be performed, for example, as shown in [9]. The phase value φ _{i of the} reference signal at the sampling time t _i is equal to
φ _i ω _o t _i .

δΦ_i (φ_i φ_i-1) (φ_i-1- φ_i-2) 0 Найдем погрешность оценки фазы φ_i в заявляемом устройстве. Эта погрешность обусловлена аддитивными шумами U_ш(t) во входном исследуемом сигнале и шумом квантования. Аддитивный шум U_ш(t) приводит к смещению Δ t_ш момента перехода через нулевой уровень входного сигнала
t

t_i+Δt_ш=

+ Δt_ш

+ Δt

+ ω_oΔt_ш= φ_i+ω_oΔt_ш Значение для Δ t_ш можно найти из уравнения
Asin ωΔ t_ш U_ш(t)
sin ωΔ t_ш U_ш(t)/А При малых отношениях U_ш(t)/А
ωΔ t_ш ≈ U_ш(t)/А
Δ t_ш ≈ U_ш(t)/Аω Следовательно,
Δφ_ш ≈ ω_оU_ш(t)/А ω. Дисперсия "шумовой" погрешности выразится
σ²(Δφ_ш) ω_о ² N_o/A² ω² K²/q, где N_o мощность аддитивного шума;
К² ω_о ²/ω²;
q A²/N_o отношение сигнал/шум. Выразим далее погрешность от квантования. В предлагаемом измерителе импульсы исследуемого сигнала осуществляют стробирование напряжения опорного сигнала в двух квадратурных каналах с последующим преобразованием простробированных напряжений в цифровой двоичной код в аналого-цифровых преобразователях 8 и 9. Следовательно, момент t_iперехода исследуемого сигнала через нулевой уровень определяется с дискретом Δ, равным
Δ_о Т_o/2ⁿ⁺¹ (12) где n разрядность аналого-цифровых преобразователей. Отсюда следует, что измеренное значение фазы φ_изм исследуемого сигнала будет
φ_изм ω (t_i + Δ_i), где Δ_i погрешность определения момента времени t_i из-за дискpетизации. Погрешность измерения фазы выразится
Δφ_к φ_изм φ ω(t_i + Δ_i) ωt_i ωΔ_i. Соответственно для дисперсии имеем
σ²(Δφ_к) ω²σ²(Δ_i) Считая плотность распределения величины Δ_i равномерной на интервале Т_ои используя выражение (12), получим
σ²(Δφ_к) ω²Δ $\genfrac{}{}{0ex}{}{\text{2}}{\text{o}}$ /12 ω²T $\genfrac{}{}{0ex}{}{\text{2}}{\text{o}}$ /12·2ⁿ⁺¹=

При статистической независимости случайных погрешностей Δφ_ш и Δφ_кдисперсию суммарной погрешности можно выразить в виде
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{Σ}}$ σ²(Δφ_ш)+σ²(Δφ_к) K²/q+

(13) Выражение (13) показывает, что дисперсия σ_Σ ² зависит от К

.Поэтому найдем значение К_о, минимизирующее дисперсию σ_Σ ². Продифференцировав (13) по К и приравнивая производную нулю, получим
K_o=

В этом случае значение дисперсии ошибки будет

=

(14) Сравним (14) и (9)

+

(15) Выражение (15) показывает, что, выбрав соответствующим образом разрядность n аналого-цифрового преобразователя, можно получить существенный выигрыш в точности измерения. Например, при q 4, выбирая n 19, получим

100 Следовательно, заявляемое устройство, будучи примененным в системе фазовой синхронизации СРНС, позволит достичь требуемую точность оценки фазы (относительная дисперсия погрешности измерения фазы 10^-5-10^-16). При этом время измерения всего 70 с, что в сто раз меньше по сравнению с известным измерителем.Since the moments of time t _i at which phase phase φ _i samples are taken are determined by the transition points of the input signal under investigation U _in Asin (ω _t + φ _o ) through the zero level with a positive derivative, then
ω t _i + φ _o 2 π _i and therefore
t _i (2 π _{i -} φ _o ) / ω. Therefore, in the absence of phase noise
φ _i ω _o (2 π _i φ _o ) / ω
Φ _i = φ _i -φ _i-1 = 2π

δΦ _i (φ _i φ _i-1) (φ _i-1 - φ _i-2 ) 0 Find the error in the estimation of the phase φ _i in the claimed device. This error is due to additive noise U _W (t) in the input signal under investigation and quantization noise. Additive noise U _W (t) leads to a shift Δ t _{W the} moment of transition through the zero level of the input signal
t

t _i + Δt _w =

+ Δt _w

+ Δt

+ ω _o Δt _w = φ _i + ω _o Δt _w The value for Δ t _w can be found from the equation
Asin ωΔ t _w U _w (t)
sin ωΔ t _w U _w (t) / A At small ratios U _w (t) / A
ωΔ t _w ≈ U _ш (t) / А
Δ t _w ≈ U _ш (t) / Аω Therefore,
Δφ _w ≈ ω _о U _ш (t) / А ω. Dispersion of "noise" error will be expressed
σ ² (Δφ _W ) ω _о ² N _o / A ² ω ² K ² / q, where N _{o is the} power of additive noise;
K ² ω _about ² / ω ² ;
q A ² / N _o signal to noise ratio. We further express the quantization error. In the proposed meter, the pulses of the signal under study perform the gating of the voltage of the reference signal in two quadrature channels with the subsequent conversion of the gated voltages into a digital binary code in analog-to-digital converters 8 and 9. Therefore, the moment t _{i of the} transition of the signal under study through the zero level is determined with a discrete Δ equal to
Δ _о Т _o / 2 ^{n + 1} (12) where n is the bit depth of analog-to-digital converters. It follows that the measured value of the phase φ _{ism of the} investigated signal will be
φ _ISM ω (t _i + Δ _i ), where Δ _{i is the} error in determining the time t _i due to discretization. Phase measurement error will be expressed
Δφ _to φ _ism φ ω (t _i + Δ _i ) ωt _i ωΔ _i . Accordingly, for variance we have
σ ² (Δφ _k ) ω ² σ ² (Δ _i ) Assuming that the distribution density of Δ _{i is} uniform over the interval T _о and using expression (12), we obtain
σ ² (Δφ _k ) ω ² Δ $\genfrac{}{}{0ex}{}{\text{2}}{\text{o}}$ / 12 ω ² T $\genfrac{}{}{0ex}{}{\text{2}}{\text{o}}$ / 12 · 2 ^{n + 1} =

With statistical independence of random errors Δφ _W and Δφ _{to the} variance of the total error can be expressed as
σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{Σ}}$ σ ² (Δφ _w ) + σ ² (Δφ _k ) K ² / q +

(13) Expression (13) shows that the variance σ _Σ ² depends on K

. Therefore, we find the value of K _o minimizing the variance σ _Σ ² . Differentiating (13) with respect to K and equating the derivative to zero, we obtain
K _o =

In this case, the error variance value will be

=

(14) Compare (14) and (9)

+

(15) Expression (15) shows that by choosing the appropriate bit depth n of an analog-to-digital converter, a significant gain in the accuracy of measurement can be obtained. For example, for q 4, choosing n 19, we obtain

100 Therefore, the inventive device, being used in the phase synchronization system of the SRNS, will achieve the required accuracy of the phase estimation (the relative variance of the error in the measurement of the phase 10 ^-5 -10 ^-16 ). At the same time, the measurement time is only 70 s, which is a hundred times less compared to the known meter.

 In addition to radio navigation systems, the proposed device can be successfully used in equipment for monitoring the frequency (phase) of stable frequency signal sources, for example, quantum frequency standards. In this case, the use of the proposed device allows to achieve high resolution without the use of special frequency comparators, which due to their narrow band distort the spectral structure of the input signal, introducing an additional measurement error.

Claims (1)

 PHASE FLUCTUATION CHARACTERISTIC METER, comprising a reference frequency generator, a quantizing pulse generator, first and second sampling and storage units, connected through the first and second analog-to-digital converters, respectively, to the first and second information inputs of the arctangent calculation unit, the output of which is connected to the second information input of the storage unit, the output of which is connected to the information input of the arithmetic unit, the first, second and third outputs of the control unit are connected to the control and inputs, respectively, of the arctangent calculation unit, a storage and arithmetic unit, the output of which is connected to the third information input of the storage unit and is a meter output, characterized in that a pulse shaper and a pulse counter and a register are connected in series between the reference frequency generator and the quantizer the frequency synthesizer is turned on, while the sine and cosine outputs of the synthesizer are connected to the signal inputs of the first and second sampling and storage blocks, the gating inputs of which are combined with the counter reset input and the register synchronization input and connected to the output of the pulse shaper, the input of which is the input of the meter, the output of the quantizer of the pulse shaper is connected to the counting input of the counter and the input of the control unit, the register output with the first information input of the storage unit.

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