RU2096828C1 - Method for detection of amplitude ratio of harmonic signals - Google Patents

Abstract

FIELD: instruments, in particular, calibration of measuring channels for detection of their amplitude and phase characteristics. SUBSTANCE: dividend signal x(t) is divided by divisor signal y(t) in order to achieve quotient signal f(t) = x(t) / y(t) for time t1 which corresponds to middle point of half- wave of divisor signal y(t). Quotient signal f(t1) and its derivative f'(t1) are measured and amplitude ratio K is calculated using equation

Description

 The invention relates to the field of measuring equipment, in particular to methods for determining the ratio of the amplitudes of periodic signals that vary in harmonic law, and can be used to calibrate the measuring channels when determining their amplitude and phase characteristics. The method has high requirements for accuracy, speed and ease of implementation.

 A known method for determining the ratio To the values of the amplitudes of harmonic signals [1] based on the time-pulse conversion of the sum and difference of the signals to be divided into bipolar voltage pulses and a number of transformations. This method is quite complicated and is characterized by low speed.

 A known method for determining the ratio of the quotient of the division of two common-mode sinusoidal signals [2] based on the summation of one of the input signals with a phase-shifted other input signal, the phase shift of the dividend signal being set equal to half the phase shift of the linear sum of the dividend and divider signals; the time interval corresponding to the phase shift between the total signal and the input common-mode signal numerically corresponds to the quotient of the division of the two signals, and measuring this interval allows you to determine the desired value.

 The method is quite complicated, the measurement accuracy is limited, the speed is low.

 The most common is the method of direct measurement of the amplitudes [3] in accordance with which the values of the amplitudes of the signals are directly measured, and the ratio of the amplitudes of the studied signals is determined as the module of the measured ratio. The method is quite simple and accurate, but its speed is low.

 The closest technical solution to the claimed one for a larger number of similar essential features is a method for determining the ratio of signal amplitudes [4] in accordance with which one signal is shifted in phase relative to another so that they are not in-phase or out-of-phase, allocate a time interval common to two signals on one of their half-periods, such that there is no change in the sign of the studied signals, measure the instantaneous values of these signals at a certain point in time t 1, corresponding to half the selected time interval, and the ratio of the amplitudes is determined as the modulus of the ratio of their instantaneous values.

 The method has advantages over other methods in terms of accuracy and speed, since the measurements are made at the same time, however, it has some implementation difficulties because of the need to determine the middle of the selected time interval, and the speed is limited due to the need to analyze the selected time interval.

 The aim of the invention is to increase performance while simplifying implementation.

В предлагаемом способе нет необходимости выбирать временной интервал, где не происходит изменения знаков гармонических сигналов, и определять середину этого временного интервала, что влечет некоторые технические трудности и ограничение по быстродействию.The goal in the implementation of the method for determining the ratio of the values of the amplitudes of harmonic signals based on the measurement at a certain instant of time t1 of the instantaneous values of harmonic signals is achieved by the fact that the values of the harmonic signal X (t) are divided by the values of the harmonic signal Y (t), the particular signal f ( t) = X (t) / Y (t), at time t1, which is selected in the middle of the half-wave of the divisor signal Y (t), the values of the signal-quotient f (t1) and its derivative f '(t1) are determined, and ratio K of the amplitudes of the harmonic signals X (t) and Y ( t) is determined by the formula:

In the proposed method, there is no need to choose a time interval where there is no change in the signs of harmonic signals, and to determine the middle of this time interval, which entails some technical difficulties and a speed limit.

To prove the validity of this method, the input harmonic signal-divisible X (t) of the voltage U _x (t) and the harmonic signal-divider Y _{t of the} voltage U _y (t) can be represented as separate functions considered at half-time intervals of the divider signal Y _t , not equal to zero:
U _x (t) = U _x (b _j ); U _y (t) = U _y (b _j ), (1)
where t is the current time during registration of the studied signals;
U _x (b _j ), U _y (b _j ) the corresponding signals at the considered time intervals b _j .

где А1, А2 значения амплитуд сигналов;
ω = (2π/T) значения круговой частоты сигналов;
t время;
F1, F2 начальные фазы, исследуемых сигналов.For harmonic signals without a constant component, the signals U _x (b _j ) and U _y (b _j ) on the same time intervals b _j can be represented in the following form (see figure 1):

where A1, A2 are signal amplitudes;
ω = (2π / T) values of the circular frequency of the signals;
t time;
F1, F2 are the initial phases of the studied signals.

Consider the signal-private f (t) from dividing the signal values in expressions (2) and (3):
f (t) = K [sinωt + F1)] / sin (ωt + F2)],
where f (t) is a function on the time interval b _j determined by the ratio of the two studied signals U _x (b _j ) and U _y (b _j );
K = A1 / A2 is the desired ratio of the amplitudes.

Для произвольного значений разности фаз F₀ между сигналами X(t) и Y(t) примем значение начального фазового сдвига F2=0 пpи F1>F2, тогда выражение (6) можно преобразовать и записать в следующем виде:
f(t) = K[cosF0+sinF0/tgωt)] (7)
Рассмотрим выражение (7) в момент времени t1 на середине полуволны сигнала-делителя, когда значение wt1 соответствует моменту времени равному четверти периода исследуемых колебаний T/4, где T/4 = π/2. В этом случае второе слагаемое в правой части обращается в ноль, следовательно:
f(t1)=KcosF₀(8)
Продифференцируем выражение (8) и получим:
f'(t1)=K(-sinF₀) (9)
После несложных преобразований из выражений (8) и (9) получим соответственно:
[f(t1)]²=K²cos₂F₀ (10)
[f'(t1)]²=K²(-sinF₀)² (11)
Из (9) и (10) получим:
[f(t1)]²+(f'(t1)]² K²[cos²F₀+(-sinF₀)²] (12)
Выражение в квадратных скобках правой части выражения (12) равняется единице, поэтому из (12) можно получить выражение для определения отношения K значений амплитуд гармонических сигналов:

Таким образом, получили математическое выражение для определения отношения K значений амплитуд гармонических сигналов.The function of the signal-private f (t) from (4) after some transformations can be represented in the following form:

For arbitrary values of the phase difference F ₀ between the signals X (t) and Y (t), we take the value of the initial phase shift F2 = 0 for F1> F2, then expression (6) can be transformed and written in the following form:
f (t) = K [cosF0 + sinF0 / tgωt)] (7)
We consider expression (7) at time t1 in the middle of the half-wave of the divider signal, when wt1 corresponds to a time equal to a quarter of the period of the studied oscillations T / 4, where T / 4 = π / 2. In this case, the second term on the right-hand side vanishes, therefore:
f (t1) = KcosF ₀ (8)
Differentiate expression (8) and get:
f '(t1) = K (-sinF ₀ ) (9)
After simple transformations from expressions (8) and (9) we obtain, respectively:
[f (t1)] ² = K ² cos ₂ F ₀ (10)
[f '(t1)] ² = K ² (-sinF ₀ ) ² (11)
From (9) and (10) we get:
[f (t1)] ² + (f '(t1)] ² K ² [cos ² F ₀ + (- sinF ₀ ) ² ] (12)
The expression in square brackets on the right-hand side of expression (12) is equal to unity; therefore, from (12), we can obtain an expression for determining the ratio K of the amplitudes of harmonic signals:

Thus, we obtained a mathematical expression for determining the ratio K of the amplitudes of the harmonic signals.

 Figure 2 presents a device for implementing the method.

 The device contains a block 1 division and indicator 2 on the CRT. The blocks in the device are connected as follows. The first input of the device is connected to the first input of the division unit 1. The second input of the device is connected to the first input of the indicator 2 on the CRT and to the second input of the division unit 1, the output of which is connected to the second input of the indicator 2 on the CRT.

The device operates as follows. The voltage U _x (t) of the divisible signal is supplied to the first input of the device and to the first input of the division unit 1, the second input of which receives the voltage U _y (t) of the divider signal from the second input of the device. At the output of the division unit 1, a voltage U ₁ (t) corresponding to the function f (t) of the private signal is received, which is fed to the second input of the CRT indicator 2, the first input of which receives the voltage U _y (t) of the divider signal.

Заявляемый способ приемлем в широком диапазоне частот и имеет преимущества по быстродействию, что важно при изменениях в широком частотном диапазоне. В предлагаемом способе нет необходимости выбирать временной интервал, где не происходит изменения знаков гармонических сигналов, и определять середину этого временного интервала, что влечет некоторые технические трудности и ограничение по быстродействию. Здесь момент времени t1 для измерений легко определяют на середине полуволны сигнала-делителя.In accordance with the claims, at time t1 corresponding to the middle half-wave of the divider signal U _y (t), the value of the derivative of the function f '(t1) is determined by the slope of the voltage function U ₁ (t) of the signal-private, and the ratio

The inventive method is acceptable in a wide range of frequencies and has advantages in terms of speed, which is important for changes in a wide frequency range. In the proposed method, there is no need to choose a time interval where there is no change in the signs of harmonic signals, and to determine the middle of this time interval, which entails some technical difficulties and a speed limit. Here, the time t1 for measurements is easily determined in the middle of the half-wave of the divider signal.

Information Sources Used
1. USSR author's certificate N 474817, G 06 G 7/16, 1976.

 2. USSR author's certificate N 582515, G 06 G 7/16, 1977.

 3. илиilinskas R-P.P. Relationship meters. M. Sov. Radio 1975, pp. 37-46.

 4. RF patent, N 1825190, G 06 G 7/16, BI 24, 1993.

Claims (1)

The method for determining the ratio of the values of the amplitudes of harmonic signals, which consists in the fact that the values of the first harmonic signal X (t) are divided by the values of the second harmonic signal Y (t), receive the signal-private f (t), determine its value at a certain point in time t ₁ characterized in that the time t _{1 is} selected in the middle of the time interval when the second signal does not change its sign, at the time t ₁ , the values of the derivative f '(t ₁ ) of the frequency signal are determined, and the ratio K of the amplitudes of the harmonic signals X ( t) and Y (t) determined by the formula

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