JP2021028636A - Non-synchronous fra and synchronous detector - Google Patents

Abstract

To provide a non-synchronous FRA and a synchronous detector that can obtain stable output of a measured value of an amplitude ratio and phase difference between two measured signals Vin, even if the frequency of a measured signal and a reference signal is non-synchronous.SOLUTION: A plurality of FRAs comprises a plurality of two-phase synchronous detectors. A two-phase synchronous detector includes two synchronous detectors Dt operating in two reference signals Vrs with a phase different by 90 degrees at the same frequency and an orthogonal coordinate-polar coordinate converter Trc. A synchronous detector has an input unit of a measured signal Vin, a multiplier M multiplying the measured signal and the reference signal, and an integrator I outputting a multiplication output for each time by integrating the period of reference signal by an integer multiple time larger than or equal to one. The orthogonal coordinate-polar coordinate converter has a converting unit obtaining two outputs of an absolute value and a deflection angle when an output of each synchronous detector is two components over an orthogonal coordinate. Each two-phase synchronous detector outputs difference between an absolute value ratio and a deflection angle and the FRA obtains a combination with phase difference obtained by dividing a phase of the reference signal with integer multiple of 360 degrees by an integer multiple time larger than or equal to one by multiple values. The FRA outputs the output average of a plurality of absolute values and a deflection angle difference.SELECTED DRAWING: Figure 1

Description

The present invention relates to an asynchronous FRA (Frequency Response Analyzer) and a synchronous detector that operate even if the frequencies of the reference signal and the signal to be measured are different.

Conventionally, a technique called synchronous detection (also referred to as phase detection) has been used to detect the amplitude and phase of a signal having a specific frequency from a signal mixed with noise or the like.
First, the principle of signal detection of a specific frequency will be described based on the configuration of a basic synchronous detector.
The configuration of the basic synchronous detector is shown in FIG. 13 (a). In FIG. 13A, the reference signal Vrs and the measured signal Vin are, respectively.
Vrs = 2sin (2π ・ fr ・ t) ・ ・ ・ ・ ・ ・ (1)
Vin = Va ・ sin (2π ・ fin ・ t + θin) ・ ・ ・ ・ ・ ・ (2)
Let it be a sine wave having frequencies fr and fin.
The multiplier M outputs the product of Vrs and Vin, and the output Vin · Vrs of this multiplier M is
Vin ・ Vrs
= Va ・ sin (2π ・ fin ・ t + θin) ・ 2sin (2π ・ fr ・ t)
= Va · [cos {2π · (fin-fr) · t + θin}
-Cos {2π ・ (fin + fr) ・ t + θin}] ・ ・ ・ ・ ・ (3)
Will be. That is, according to the multiplier M, the signal to be measured Vin is converted into the sum of the signals of two frequencies (fin-fr) and (fin + fr) having the information of the amplitude Va and the phase θin of the signal to be measured Vin. You can see that.

The output Vin · Vrs of the multiplier M is input to the low-pass filter (LPF). In this LPF, of the signals of the two frequencies represented by the equation (3), the component of frequency fin + fr (higher frequency) is sufficiently attenuated, and the component of frequency fin-fr (lower frequency) is sufficiently attenuated. It passes almost as it is.
The output Vs of this LPF is
Vs = Va ・ cos {2π ・ (fin-fr) ・ t + θin} ・ ・ ・ ・ ・ (4)
Will be.

In particular, if the frequency fin of the signal to be measured Vin and the frequency fr of the reference signal Vrs are the same (fin = fr),
Vs = Va ・ cosθin ・ ・ ・ ・ ・ ・ (5)
Will be. Therefore, it can be seen that a time-independent output, that is, a DC output, which has only the information of the amplitude Va and the phase θin of the signal to be measured Vin, can be obtained.
As described above, according to the synchronous detector, it is possible to extract a DC signal having amplitude and phase information of the same frequency component as the reference signal Vrs from the measured signal Vin.

In this synchronous detector, the reference signal Vrs is a sine wave as an example, but since any periodic function can be expressed by superimposing a sine wave having a basic period and a period that is a fraction of the basic period, the reference signal is a reference signal. Even if it is a periodic function such as a square wave instead of a sine wave, it is a synchronous detector that operates according to the sine wave included in the periodic signal.
If the multiplier is configured with an analog circuit, for example, it would be expensive to configure a multiplier that multiplies the signal under test by a sine wave, but it is equivalently square to the signal under test using an inverting amplifier and an analog switch. The method of multiplying waves can be realized inexpensively and easily, and is often used as a synchronous detector.

Further, as shown in FIG. 13B, a sine wave having a phase difference of π / 2 (= 90 °), that is, a cosine wave Vrc = 2cos (2πfr · t) is used for the reference signal Vrs, and the reference signal Vrc is used. When the signal to be measured Vin is multiplied by the multiplier M,
Vin ・ Vrc
= Va ・ sin (2π ・ fin ・ t + θin) ・ 2cos (2π ・ fr ・ t)
= Va · [sin {2π · (fin + fr) · t + θin}
+ Sin {2π ・ (fin-fr) ・ t + θin}] ・ ・ ・ ・ ・ (6)
Will be.
From this multiplication result, even when a cosine wave is used as the reference signal Vrs, the signal to be measured Vin is converted into two frequency components (fin-fr) and (fin + fr) as in the case of FIG. 13 (a). You can see that.

If the frequency fin of the signal to be measured Vin and the frequency fr of the reference signal Vrs are the same (fin = fr), the output Vc of the LPF is
Vc = Va ・ sinθin ・ ・ ・ ・ ・ ・ (7)
Will be. In this case as well, it can be seen that a time-independent output, that is, a DC output, which has only information on the amplitude Va and the phase θin of the signal to be measured Vin, can be obtained.

From this, if synchronous detection is performed by the reference signal Vrs whose phases differ by π / 2 (= 90 °), the amplitude Va of the measured signal Vin and the phase θin of the measured signal Vin based on the reference signal Vrs can be obtained. You can also do it.

By the way, when the frequency fr of the reference signal Vrs and the frequency fin of the signal to be measured Vin are different (fin ≠ fr), two frequency components (fin-fr) and (fin + fr) having a frequency lower than fr and a frequency higher than fr are used. AC signal appears.

Of these, a method of extracting only a signal of one of the frequencies using a bandpass filter or a lowpass filter to obtain information on the amplitude Va and the phase θin of the signal to be measured Vin is called heterodyne detection.
Heterodyne detection is widely used as a demodulation method for modulated signals in the fields of broadcasting and wireless communication represented by AM radio and FM radio.
When these are represented by a graph with frequency on the horizontal axis and amplitude on the vertical axis, (a), (b), (c), and (d) in FIGS. 13 (a) and 13 (b) are diagrams showing the principle of synchronous detection. 13 (c) and FIG. 13 (d) showing the principle of heterodyne detection are as follows.
(A): Measured signal Vin.
(A): Reference signal Vrs or Vrc.
(C): Signals of two frequency components (fin-fr) and (fin + fr).
(D): A frequency (fin-fr) signal extracted by the filter.

Regarding the low-pass filter in the synchronous detector shown in FIGS. 13 (a) and 13 (b), as a method used for the FRA (frequency characteristic analyzer) described later, as shown in FIG. 14, the period Tr (= frequency) of the reference signal Consider an integrator I that averages in time (the reciprocal of fr) or its integer n times.
The low-pass filter calculated by the integrator I is a kind of moving average filter because it is realized by digital signal processing in which an output is obtained from an input for a finite time between n and Tr.
By calculating Va and θin by the calculation of the integrator I, the outputs Vs and Vc shown in FIG. 13 can be obtained at a rate of once every time of n · Tr.
In this way, when averaging in a time n times the period Tr of the reference signal, this averaging may be expressed as n times of integration using an integer n, and in the following, the number of integrations has such a meaning. Used in.

である。
ここで、ａｔａｎ（Ｙ，Ｘ）は、Ｘ、Ｙ座標ＸＹ平面上のベクトルについて、Ｘ軸の正側となす偏角を求める４象限逆正接関数である。 Next, a method of obtaining each value of the amplitude Va and the phase θin from the two signals having the above-mentioned amplitude and phase information will be described.
First, when fin = fr, the two signals Va · cos θin and Va · sin θin are the vectors of the angle θin formed by the magnitude Va from the horizontal axis on the two-dimensional plane as shown in FIG. 15 (a). It can be geometrically interpreted as a vector component in the horizontal and vertical axes.
Considering this, as shown in FIG. 15B, the amplitude Va and the phase θin of the signal to be measured Vin can be obtained as the output V and θ by the configuration of the Cartesian coordinate-polar coordinate converter Trc.
That is,

Is.
Here, atan (Y, X) is a four-quadrant inverse trigonometric function that finds the declination of a vector on the X, Y coordinate XY plane with the positive side of the X axis.

Next, when fin ≠ fr, it can be considered that the phase relationship between the phase θin of the signal to be measured and the reference signals Vrs and Vrc changes with time. In that case, the measured value θ of the phase is
θ = atan (Vc, Vs) = θin + 2π (fin-fr) t ... (10)
Therefore, a time-dependent measurement result can be obtained.

Further, as shown in FIG. 16, two integral type synchronous detectors Di (two of the synchronous detectors D shown in FIG. 13 may be used) as the synchronous detector Dis and the Dic on the input side of the orthogonal coordinate-polar coordinate converter Trc. If the reference signals have the same frequency fr and the phases differ by π / 2 (= 90 °) due to the relationship between the sine wave and the cosine wave, the phase of the reference signal Vrs of the sine wave is used as the reference phase, and the measurement result is It is a two-phase synchronous detector Dxy that can obtain the amplitude and phase of the same frequency component as the frequency fr of the reference signal of the signal to be measured Vin.
The principle of measuring the amplitude of the frequency component of the reference signal Vrs and the phase of the measured signal Vin with reference to the phase of the reference signal Vrs has been described above for a certain signal Vin.

It will be described below that the amplitude ratio Go and the phase difference θd between the plurality of measured signals Vin can be measured by using a plurality of the two-phase synchronous detectors.
FIG. 17 shows a configuration in which two sets of two-phase synchronous detectors Dxy as shown in FIG. 16 are provided, and two measured signals Vin1 and Vin2 are measured by different two-phase synchronous detectors Dxy1 and Dxy2, respectively. ..
Further, the amplitude ratio Go and the phase difference θd are calculated from the amplitudes Va1 and Va2 and the phases θin1 and θin2 obtained by the two-phase synchronous detectors Dxy1 and Dxy2, and the measurement result is output.
Go = Va1 / Va2 ... (11)
θd = θin1-θin2 ... (12)

As shown in FIG. 17, the frequency is provided as a measuring device specialized for measuring the vector ratio of the same frequency components as the reference signal Vrs between the plurality of measured signals Vin input to each input unit. There is a characteristic analyzer (Frequency Response Analoger: FRA).
In addition to the configuration shown in FIG. 17, some frequency characteristic analyzers have a built-in oscillator OSC synchronized with the reference signal Vrs inside the FRA shown in FIGS. 18 and 19. Here, the OSC-FRA, which is a frequency characteristic measuring instrument with an oscillator, and the FRA, which does not include the output of the oscillator OSC, are used to distinguish between OSC-FRA and FRA.

As a measurement example of OSC-FRA, as shown in FIG. 18, an output from an oscillator OSC, which is a signal having the same frequency as the reference signal Vrs, is input to an amplifier or filter from the outside, and two output signals such as an amplifier or filter are input. When the signals to be measured are input as Vin1 and Vin2 and measured, the gain and phase characteristics of the amplifier and filter can be measured.
Further, as shown in FIG. 19, the voltage across the electrical component Z and the voltage across the shunt resistance connected in series with the electrical component Z are input as two FRA measured signals Vin1 and Vin2, and the amplitude ratio Go By measuring the phase difference θd and dividing the measurement result of the amplitude ratio by the resistance value R of the shunt resistance, the impedance of the electric component Z can be measured including the phase.
As shown in FIGS. 18 and 19, in FRA, when measuring the amplitude and phase of the signals to be measured Vin1 and Vin2, the output from the oscillator OSC, which is a signal synchronized with the frequency of the reference signal Vrs, is directly or the oscillator OSC. Is used as a signal source in the form of being output via an amplifier, and the frequency fin of the signal to be measured Vin and the frequency fr of the reference signal Vrs are generally measured in a state of matching.
The above has described the basic configurations of synchronous detection, FRA and OSC-FRA, and their operating principles without distinguishing between analog and digital. In recent years, measuring instruments in which each component such as a filter is realized by a digital circuit or a digital arithmetic means have become widespread, and FRA and OSC-FRA are no exception. Rather, if the measurement method is mainly arithmetic, for example, the input unit of the signal to be measured may be converted into a numerical value by an A / D converter, and subsequent components such as a synchronous detector may be performed by arithmetic processing. An analog circuit may be used up to the multiplier M, A / D conversion may be performed there, and the low-pass filter and subsequent parts may be processed by numerical calculation.
The output does not have to be an analog signal, and the processing mode may be displayed numerically on the screen, or a numerical value for expressing the measurement result on a personal computer may be acquired by an external control command.
Regarding such FRA (frequency characteristic analyzer), its configuration and usage mode are already known (FIG. 2 of Patent Document 1 and paragraphs 0014 to 0027 and Non-Patent Document 1).

JP-A-2015-155870

Frequency characteristic analyzer technical commentary (published in March 2008, NF Circuit Design Block Co., Ltd.)

By the way, regarding the measurement of amplitude and phase difference, if there is a deviation between the frequencies of the signal to be measured Vin and the reference signal Vrs, a measurement error occurs due to a change in magnitude and time according to the deviation, and highly accurate measurement can be performed. There was a problem that it could not be done.

In the measurement using the conventional FRA, it is used in the form of OSC-FRA, and it is assumed that the signal to be measured Vin and the reference signal Vrs are synchronized, and the signal component to be measured is converted into a DC component. , The AC component is passed through an integrator or a low-pass filter to extract only the DC component.
In such a process, how and how large the error caused by the frequency deviation between the measured signal Vin and the reference signal Vrs will be described, including a quantitative aspect.

For example, a commercial power source has frequencies of 50 Hz and 60 Hz, and may originally have a specific frequency depending on the measurement target.
It is assumed that such a signal is used as the signal to be measured, the frequency of the reference signal Vrs is set to 50 Hz or 60 Hz, and the synchronous detector shown in FIG. 13 or the two-phase synchronous detector shown in FIG. 16 is used for the measurement.
In this case, the frequency of the commercial power supply and the frequency of the reference signal Vrs of the synchronous detector do not match, and in most cases, a relative deviation occurs.

When the frequency fin of the signal to be measured Vin and the frequency fr of the reference signal Vrs are different, each output (c) of the multiplier M shown in FIGS. 13 (a) and 13 (b) is given by the equations (3) and (6). It is an AC signal having two frequency components, fin-fr and fin + fr.
As shown in FIG. 14, consider a case where this signal is passed through a low-pass filter composed of an integrator that integrates in a section of a constant multiple of the period of the reference signal Vrs.
In this case, when fin is an integral multiple other than 1 of fr (for example, when fr = 50 Hz and fin is 100 Hz or 150 Hz), the output of the low-pass filter composed of an integrator becomes 0 due to the periodicity of the sine wave.

If the frequency does not apply to the above, it will not be zero even if the signal is attenuated by passing it through a low-pass filter.
Here, in order to quantitatively handle the influence of the frequency deviation between a plurality of signal sources on the measurement result, a parameter δ indicating the degree of deviation is introduced.
If the frequency fin of the signal to be measured Vin is expressed using the reference signals Vrs and δ,
fin = (1 + δ) fr ... (13)
Will be.
For example, if δ = +0.01 at fr = 50 Hz, it means that the frequency fin of the signal to be measured Vin is 1% (= 0.01 × 100%), which is higher than the frequency fr of the reference signal Vrs.
To show this concretely,
fin = (1 + 0.01) x 50Hz = 50.5Hz ... (14)
Will be.

ただし、図１３（ａ）（ｂ）に示す同期検波器中のローパスフィルタは、図１５に示す積分器Ｉの構成である。 According to the synchronous detector shown in FIGS. 13A and 13B, if the frequency of the signal to be measured Vin is fin instead of fr, the output of the multiplier is given by the equations (3) and (6), respectively.
Replacing fin in equations (3) and (6) with (1 + δ) fr, the outputs Vs and Vc in the synchronous detector can be expressed by the following equations (15) and (16), respectively.

However, the low-pass filter in the synchronous detector shown in FIGS. 13 (a) and 13 (b) has the configuration of the integrator I shown in FIG.

Here, the function of sinc (x) appearing in the equations (15) and (16) is a function defined by the following equation (17).

Further, when the amplitude V and the phase θ when the Vs and Vc given by the equations (15) and (16) are input to the Cartesian coordinate-polar coordinate converter Trc shown in FIG. 15 (b), the amplitude V and the phase θ are calculated as follows. Can be represented.

Considering how the equations (18) and (19) behave, first, sinc (δnπ) and | sinc (δnπ) | are defined by dividing the sine wave function by its argument, FIG. 20. It is an even function that behaves as shown in.
In FIG. 20, the argument is represented in the form of a constant multiple of π. When the argument is 0, the absolute value is always smaller than 1, and when the argument is other than 0, the absolute value is always smaller than 1, and the argument is an integral multiple of π excluding 0. It is a function that becomes 0 when.
In particular, when δ = 0, Vs, Vc, and V are Vs = Va · cosθin ... (20)
Vc = Va ・ sinθin ・ ・ ・ ・ ・ ・ (21)
V = Va ... (22)
θ = atan (sin θin, cos θin) = θ in ... (23)
It can be confirmed that the result is the same as when fin = fr.
When δ ≠ 0, that is, when fin ≠ fr, as the measurement result of the in-phase components of sin and cos, respectively,
・ Amplitude Va is multiplied by a coefficient represented by a sinc function, which is determined by δ and n. ・ It can be seen that the phase is shifted by δnπ (θin → θin + δnπ).

Further, the amplitude V is obtained from the equation (18).
(1) When δn is an integer other than 0, it becomes 0 (that is, the measurement sensitivity is lost).
(2) It can also be seen that it is a periodic function having a period of π (= 180 °) with respect to θin.

、そのｘ軸、ｙ軸方向の成分としてそれぞれＶｓ、Ｖｃのうち共通の係数で割ったｃｏｓθｉｎ、ｓｉｎθｉｎとする。 すなわち、

と表すと、図２１（ａ）のように、

のＸ軸からの偏角はθｉｎを表わし、θｉｎを０から２πまで変化させてみると、

はこの平面上で半径１の円を描く。 In the synchronous detector, the amplitude and phase are processed based on the following geometric interpretation.
Planar vector

, The components in the x-axis and y-axis directions are cosθin and sinθin divided by a common coefficient among Vs and Vc, respectively. That is,

Is expressed as, as shown in FIG. 21 (a).

The declination from the X-axis represents θin, and when θin is changed from 0 to 2π,

Draws a circle with a radius of 1 on this plane.

、そのＸ軸、Ｙ軸方向の成分としてそれぞれＶｓ、Ｖｃのうち共通の係数で割ったものとすると、

は

と表せる。
この

は、（θｉｎ＋δｎπ）をパラメータとして、図２１（ｂ）のような実線部の楕円を表わすベクトル方程式になっている。 Next, in the case of fin ≠ fr, a geometrical consideration is made in the same manner as above.
The vector of the plane in this case

, Assuming that the components in the X-axis and Y-axis directions are divided by the common coefficient of Vs and Vc, respectively.

Is

Can be expressed as.
this

Is a vector equation representing an ellipse in the solid line portion as shown in FIG. 21 (b) with (θin + δnπ) as a parameter.

の偏角（＝位相の測定値）ではなく、図２１（ｂ）の楕円とともに描かれている点線の補助円上の点を表わすベクトルの偏角であり、θｉｎ、ｎおよびδに応じて決まる偏角のずれφが存在する。 And in this case, (θin + δnπ) is

It is not the declination (= measured value of phase) of, but the declination of the vector representing the point on the auxiliary circle of the dotted line drawn together with the ellipse in FIG. 21 (b), and is determined according to θin, n, and δ. There is a deviation φ of the declination.

That is, when a signal having a phase of θin and having a frequency fin = (1 + δ) fr deviated by a ratio of δ from the frequency fr of the reference signal Vrs is asynchronously detected as the signal to be measured, the phase measurement value θ in the synchronous detector is θ. Is as follows.
θ = atan ((1 + δ) sin (θin + δnπ), cos (θin + δnπ))
・ ・ ・ ・ ・ ・ (26)
Here, θ is expressed using the deviation φ from θin + δnπ, that is, θ = θin + δnπ + φ ... (27)
When φ is defined as, φ represents the declination shown in FIG. 21 (b) and FIG. 22.
That is, it can be seen that φ represents the deviation of the phase measurement value due to the asynchronous fin and fr.

Then, from equations (26) and (27), φ is tan (θin + δnπ + φ) = (1 + δ) tan (θin + δnπ).
φ = atan ((1 + δ) sin (θin + δnπ), cos (θin + δnπ))
− (Θin + δnπ) ・ ・ ・ ・ ・ ・ (28)
It becomes the form.

However, if | δ | <1, the phase obtained by atan has the same quadrant as θin + δnπ, and tan (x), which is a function of sin (x) divided by cos (x), has a period π. Considering that φ is a periodic function of, when θin is considered as a variable, φ becomes a periodic function of period π, that is, φ as a function of θin is
φ (θin) = φ (θin + π) ・ ・ ・ ・ ・ ・ (29)
Meet.

という形となる。 Based on the above, consider a case where two signals Vin1 and Vin2 having the same frequency fin (= (1 + δ) fr) asynchronous with the reference signal Vrs are measured in the amplitude ratio and the phase difference in the configuration shown in FIG.
In this case, if the above considerations are applied to each of Vin1 and Vin2, the amplitude ratio Go'and the phase difference θd'are

It becomes the form.

From the above, when the frequency fin of the measured signal Vin and the frequency fr of the reference signal Vrs are asynchronous, the original amplitude ratio (Va1 / Va2) and the phase difference θd = (θin1-θin2) of the measured signal Vin itself. On the other hand, it can be seen that a measurement error occurs with the phases θin1 and θin2 of the signal to be measured Vin, the degree of frequency deviation δ, and the number of integrations n as parameters.

ただしψは、
ψ＝ａｔａｎ（（１−ｃｏｓ２θｄ），ｓｉｎ２θｄ） ・・・・・・（３４）
で定義される、被測定信号Ｖｉｎ間の位相差θｄのみで決まる定数である。
Ｇｏ’は｜δ｜＜＜１のとき（３３）のように近似でき、２つの被測定信号Ｖｉｎ間の位相差θｄ（＝θｉｎ１−θｉｎ２）に対し、以下のような振る舞いになる。
θｄが０もしくはπ（＝１８０°）、つまり同じ向きもしくは逆向きのベクトルの測定であれば、式（３３）の根号の中の１−ｃｏｓ２θｄは０となるため、式（３３）の大括弧［ ］の中身は１となり被測定信号Ｖｉｎ間の本来の振幅比Ｇｏに対して、Ｇｏ’には１次近似の範囲では誤差はあらわれない。
θｄが±π／２（＝±９０°）の時は、式（３３）の根号の中の１−ｃｏｓ２θｄは最大値である２となるため、式（３３）の大括弧［ ］の中は、参照信号Ｖｒｓを基準にした被測定信号Ｖｉｎの位相に応じて、最大約（１±δ）の範囲で値の差異が生じる。 Since it is difficult to imagine with the formula alone, the approximate formula when | δ | << 1 and the degree of error with some specific values are shown by simulation.
First, in approximating the calculation result, as an approximate expression that holds when | x | << 1 (for example, 5%, about 0.05 or less)
(1 + x) ⁿ ≒ 1 + nx ... (32)
Is given by (32) for equations (30) and (31) of Go'and θd', taking into account that the reciprocal is n = -1 and √ is n = 1/2. Use a first-order approximation.
First, consider Go'formula (30).

However, ψ is
ψ = atan ((1-cos2θd), sin2θd) ... (34)
It is a constant defined only by the phase difference θd between the signals to be measured Vin.
Go'can be approximated as in (33) when | δ | << 1, and the behavior is as follows with respect to the phase difference θd (= θin1-θin2) between the two signals to be measured Vin.
If θd is 0 or π (= 180 °), that is, if vectors are measured in the same or opposite directions, 1-cos2θd in the radical of equation (33) will be 0, so the equation (33) is large. The content of the parentheses [] is 1, and an error does not appear in Go'in the range of the first-order approximation with respect to the original amplitude ratio Go between the measured signals Vin.
When θd is ± π / 2 (= ± 90 °), 1-cos2θd in the radical of equation (33) is 2, which is the maximum value, so it is in parentheses [] in equation (33). Has a value difference in a maximum range of about (1 ± δ) depending on the phase of the signal to be measured Vin with reference to the reference signal Vrs.

ここで、

の近似を用いると、φは、

と、φをδに関して一次近似できる。 From the above, it can be seen that when Go'is considered as a function of θd, behavior that seems to be approximate as a periodic function having a period of π (= 180 °) with respect to θd is observed.
Further, the measured value θd'of the phase difference is set to θin.

here,

Using the approximation of, φ is

And φ can be first-order approximated with respect to δ.

と１次近似できる。
よって、｜δｎ｜＜＜１のとき、θｄ’は、

と一次近似でき、θｄ’もＧｏ’と同様にθｄを中心とした正弦波状の振る舞いを示すことがわかる。
θｄ’は、２つの被測定信号Ｖｉｎ間の位相差θｄにより、振幅比Ｇｏ’と同様に、θｄが０もしくはπ（＝１８０°）であれば、（１−ｃｏｓ２θｄ）が０となることから、θｄ’の測定値に誤差はあらわれない（図２１（ｂ）で幾何学的に示したように、この場合はこの近似に限らず、厳密にこうなる）。 Using this, θ'in1 and θ'in2 are, respectively.

Can be first-order approximated.
Therefore, when | δn | << 1, θd'is

It can be seen that θd'also exhibits a sinusoidal behavior centered on θd, similar to Go'.
Since θd'is the same as the amplitude ratio Go', (1-cos2θd) becomes 0 when θd is 0 or π (= 180 °) due to the phase difference θd between the two signals to be measured Vin. , Θd'does not show any error (as shown geometrically in FIG. 21B, this case is not limited to this approximation, but is exactly the same).

On the other hand, when θd is ± π / 2 (= ± 90 °), (1-cos2θd) is 2, so the maximum is about (1) depending on the phase of the signal to be measured Vin based on the reference signal Vrs. A relative error occurs in the range of ± δ).

In order to confirm these things about Go'and θd', a graph comparing the exact solutions (30) and (31) with the approximate solutions (33) and (39) is shown in FIG.
It can be seen that the appearance of the change with time of the measurement result differs depending on the phase difference θd of the signal to be measured Vin, which can be almost reproduced by the approximate expression.

From these results, if the degree of deviation δ between the reference frequency fr and the frequency fin of the signal to be measured Vin is 10% or less (0.1 or less), the approximate solution almost completely reproduces the exact solution. However, it is possible to quantitatively consider the amplitude characteristics, and it is sufficiently possible to qualitatively consider the approximate characteristics even if δ is about 30%.

In this way, if there is a relative deviation (1 + δ) between the frequency fin of the measured signal Vin and the frequency fr of the reference signal Vrs, the phase difference between the measured signal Vins is measured when measuring the amplitude ratio or phase difference. The measurement error occurs in a form that depends on and is almost proportional to the deviation δ.
Further, θin2 is the phase of the signal to be measured Vin2 when the reference signal Vrs is used as a reference.
When the frequency of the reference signal and the frequency of the signal to be measured deviate in the form of fin = (1 + δ) fr, while one measurement result is obtained in the integrator I (while the time of n · Tr elapses). In addition, the phase θin2 of the signal to be measured Vin 2 advances by δn · 2π (δn rotation) with respect to the phase of the reference signal.

That is, θin2 can be expressed in the form of changing as follows as a function θin2 (t) of the time t when considering the phase of the reference signal Vrs as a reference.
θin2 (t) = θin2 (0) + δn ・ 2π ・ t / (n ・ Tr)
= Θin2 (0) + (2π ・ δ / Tr) ・ t
= Θin2 (0) + (2π ・ δ ・ fr) ・ t ・ ・ ・ ・ (40)
Expressed in this way, the time lapse of the measurement results of the amplitude ratio Go'and the phase difference θd' represented by the equations (33) and (39) is that θin2 in the argument of cos in the equation is doubled. Also note that, regardless of the number of integrations n, at a frequency of 2δ · fr (or period Tr / (2δ)), a nearly sine wave centered on the true values Go (= Va1 / Va2) and θd (= θin1-θin2). It can be seen that the time changes in the form of.

To write this again as an expression, when the frequencies of Go'and θd' are set to fmeas,
fmeas = 2δ ・ fr ・ ・ ・ ・ ・ ・ (41)
Can be expressed in the form of a frequency proportional to the frequency of the reference signal Vrs and the deviation.

Therefore, an object of the present invention is that when the frequency fin of the signal to be measured and the frequency fr of the reference signal are deviated, the measured values of the amplitude ratio and the phase difference between the two signals to be measured periodically change with time. In view of the problem of this, even when the frequency fin of the signal to be measured and the frequency fr of the reference signal Vrs are not synchronized in the measurement by the synchronous detector or FRA, the amplitude ratio between the two signal Vins to be measured and An object of the present invention is to provide a synchronous detector and an asynchronous FRA that can obtain a stable output of measured values of phase difference.

In order to solve the above problems, according to one aspect of the asynchronous FRA of the present invention, the FRA includes a plurality of FRA, the FRA includes a plurality of two-phase synchronous detectors, and the two-phase synchronous detectors have the same frequency. It is provided with two synchronous detectors and orthogonal coordinate-polar coordinate converters, each of which operates with two reference signals having a phase difference of 90 degrees, and each of the synchronous detectors has an input unit of a signal to be measured and the measured signal. It is provided with a multiplier for multiplying the signal and the reference signal, and an integrator that integrates the output of the multiplier at an integral multiple of one or more of the period of the reference signal and outputs the output at each time. When the polar coordinate converter uses the two outputs of the two synchronous detectors as two components on the orthogonal coordinates, the polar coordinate converter is provided with a conversion unit that obtains two outputs of the absolute value and the deviation angle in the polar coordinate display. The difference between the absolute value ratio and the deviation angle is output from the absolute value and the deviation angle value obtained from the combination of the two in the two-phase synchronous detector, and the plurality of FRAs have a phase of the reference signal of 360. It is composed of a combination having a phase difference obtained by dividing the phase of the integral multiple of 1 or more by a plurality of values, and the plurality of FRA outputs the average of the plurality of absolute values and the output of the plurality of deviation angles. It is characterized by outputting an average.

In the asynchronous FRA, the plurality of values obtained by dividing the phase of one or more of the integer multiples of the reference signal having a phase of 360 degrees are the values of the terms represented by powers of 2 among the prime factors of the integer multiples. It is characterized in that it is a value obtained by multiplying 2 by a value of 2 or more to the power of an integer.

In the asynchronous FRA, the phase, which is an integral multiple of 1 or more of 360 degrees, is 360 degrees, the value of the term represented by the power of 2 is 1, and the value of 2 or more is an integer power of 4. It is characterized by doing.

In order to solve the above problems, according to one aspect of the synchronous detector of the present invention, an input unit for inputting a signal to be measured, a reference signal generating unit for generating a reference signal of a specific frequency, the signal to be measured, and the above-mentioned A multiplier that multiplies the reference signal, an integrator that takes the time average of the output signal of the multiplier with an integration time that is an integral multiple of one or more of the period of the reference signal, and the signal to be measured passes through a constant amplitude value. A trigger detection unit that detects that and generates a trigger signal is provided, the reference signal generation unit is triggered by the trigger signal and outputs the reference signal in a specified phase, and the integrator outputs the reference signal. It is characterized in that it receives the signal, starts the integration operation, and outputs the result of the time averaging after the lapse of the integration time.

The synchronous detector is further characterized by including an effective value measuring unit for measuring an effective value of the signal to be measured.

The synchronous detector is further characterized by including a determination unit that compares the output of the effective value measuring unit and the output of the integrator and outputs the comparison result.

The synchronous detector is further characterized by including a signal delay unit that delays the trigger signal by a predetermined time.

The synchronous detector is characterized by being provided with any one of a low-pass filter, a band-pass filter, and a high-pass filter through which the signal to be measured is passed.

In the synchronous detector, the first detector according to any one of claims 4 to 8 and the second detector according to any one of claims 4 to 8. And a time difference measuring unit that measures the time difference between the first detection signal obtained by the trigger detection in the first detector and the second detection signal obtained by the trigger detection in the second detector. It is characterized by having.

The synchronous detector is further characterized by including a calculation means for outputting the result of calculation using a coefficient based on the period of the reference signal to the output of the time difference measuring unit.

The synchronous detector is further characterized by including an amplitude ratio calculation unit that calculates an output-to-output ratio of each of the integrators included in the first and second detectors.

The synchronous detector is further characterized in that either or both of the first and second detectors are two-phase synchronous detectors.

The synchronous detector is further characterized by including a phase calculation unit that outputs a phase difference obtained by arithmetic processing from the output of the integrator included in the first and second detectors.

According to the synchronous detector or asynchronous FRA of the present invention, the amplitude ratio and the phase difference can be measured even if there is no synchronous relationship between the frequency fin of the signal to be measured and the frequency fr of the reference signal, and a stable measured value can be obtained. Can be done.

FIG. 1 is a diagram showing a first embodiment of the present invention. FIG. 2 is a diagram showing a simulation result according to the first embodiment of the present invention. FIG. 3 is a diagram showing another simulation result in the first embodiment of the present invention. FIG. 4 is a diagram showing a second embodiment of the present invention. FIG. 5 is a diagram showing a third embodiment of the present invention. FIG. 6 is a diagram showing a fourth embodiment of the present invention. FIG. 7 is a diagram showing a fifth embodiment of the present invention. FIG. 8 is a diagram showing a sixth embodiment of the present invention. FIG. 9 is a diagram showing a seventh embodiment of the present invention. FIG. 10 is a diagram showing an outline of a simulation according to a seventh embodiment of the present invention. FIG. 11 is a diagram showing a simulation result according to the seventh embodiment of the present invention. FIG. 12 is a diagram showing an eighth embodiment of the present invention. FIG. 13 is a diagram showing the principle of synchronous detection. FIG. 14 is a diagram showing an example in which a low-pass filter is configured by an integrator. FIG. 15 is a diagram showing the relationship between the output of the synchronous detector and the amplitude / phase. FIG. 16 is a diagram showing a configuration example of a two-phase synchronous detector. FIG. 17 is a diagram showing the principle of FRA. FIG. 18 is a diagram showing measurement of gain and frequency characteristics. FIG. 19 is a diagram showing impedance measurement. FIG. 20 is a diagram showing a sinc function. FIG. 21 is a diagram showing the trajectory of the vector of the measured signal at the time of synchronization and the time of asynchronous. FIG. 22 is a diagram showing the trajectory of the vector. FIG. 23 is a diagram showing simulations of measurement results using various δs.

Hereinafter, embodiments of the present invention will be described in detail.

[First Embodiment]
FIG. 1 is a diagram showing a synchronous detector according to the first embodiment. In the first embodiment, one synchronous detector is configured for one signal.
The synchronous detector according to the first embodiment is an integral type synchronous detector with a trigger Dit in which a trigger detector T is added to the synchronous detector Di (FIG. 14) in which the low-pass filter LPF is configured by the integrator I. It is a synchronous detector Dt with a trigger that is configured and the phase of the reference signal Vrs starts from a predetermined phase, for example, 0 °, in accordance with the timing of the trigger signal.

As an example, the trigger detector T outputs the timing at which the input signal to be measured Vin passes a predetermined level set in advance as a logic signal.
The output of the trigger detector T is applied to the reference signal generator Q that generates the reference signal Vrs and the low-pass filter LPF by the integrator I.
The reference signal generation unit Q outputs a reference signal Vrs having a determined phase, for example, starting from 0 ° of a sine wave, by a trigger signal from the trigger detector T.
Further, the reference signal generation unit Q may output a plurality of outputs having arbitrary phases set in advance, such as a sine wave and a cosine wave.

Similarly, the integrator I also starts the integration operation by the trigger signal from the trigger detector T, and the phase of the reference signal Vrs at the start of integration is always the same (0 ° in the example given here).
The integrator I performs time integration of the product n · Tr of the period Tr (reciprocal of frequency fr) of the reference signal Vrs and the number of integrations n, and divides by n · Tr, which is the average value of the integration interval, and as a result, the output signal. Output Vs.

In FIG. 2, according to the configuration of the synchronous detector Dt, the frequency fr of the reference signal is 50.00 Hz, AC100 Vrms, the number of integrations n of the integrator I is 1, and the frequency deviation δ of the signal to be measured is 0.001 (0. The simulation results of 1%, fin = 50.05 Hz), 0.01 (1%, fin = 50.5 Hz), and 0.1 (10%, fin = 55 Hz) are shown.
From this result, it can be seen that the vibration of the measured value due to the frequency deviation δ caused by the above-mentioned conventional technique does not appear.
However, in the present embodiment, when | δ | (frequency deviation) becomes large, when δ = 0.1, the output Vs is measured to be about 90 Vrms with respect to 100 Vrms of the signal to be measured. It can be seen that the deviation of the measured value itself is also large.

Further, in FIG. 3, the frequency deviation is δ = -0.001 (fin = 49.95 Hz), the effective value is equal to that of the signal to be measured Vin, and the Gaussian noise whose effective value is 100 Vrms is superimposed and the number of integrations is performed. The case where n is set to 1, 10, and 100 is shown. It can be seen that increasing the number of integrations reduces the effect of noise and reduces the variation in measured values for each measurement.
When the number of integrations is 100, the measured output is about 90 Vrms. This is because nδ = −0.1 and n times δ is measured as a deviation as expressed by the equation (18).

[Second Embodiment]
FIG. 4 is a diagram showing a synchronous detector according to the second embodiment.
In the synchronous detector Dtj according to the second embodiment, the effective value measuring unit V and the determining device J are added to the first embodiment.
The effective value measuring unit V is an effective value measuring means other than the synchronous detector, and outputs the effective value of the input signal to be measured Vin. This effective value measuring unit V can be used, for example, as a means for measuring the effective value of the signal to be measured Vin, such as effective value conversion by mean value detection and thermoelectric conversion type using a thermal converter.
The determination device J inputs each output of the synchronous detector and the effective value measuring unit, and outputs a determination result as to whether or not the difference between them is within the preset determination standard.

The measurement conditions are ideal for the effective value Vrms of the signal to be measured Vin measured by a method different from the synchronous detection and the effective value Vs measured by the synchronous detector Dt with a trigger. For example, the frequency fr of the reference signal Vrs and the signal to be measured. If the frequency fins of Vin are the same (fr = fin) and the signal to be measured Vin is a single sine wave, the effective values Vrms and Vs are the same.
If the state deviates from this ideal state, for example, fin and fr deviate from each other, the measurement result also deviates from the effective value of the signal to be measured Vin, as discussed in the first embodiment. Further, if the signal to be measured Vin is a signal containing a large amount of noise components and harmonic components of frequency fins, the reliability of the measurement result is lowered.

If the effective value measuring unit V and the judgment device J are provided, for example, if the difference between the effective values Vs and Vrms is equal to or greater than the preset judgment standard, the judgment device J warns that the reliability of the measured value is low. It is output and the validity of the measurement result can be judged.
For example, when the judgment criterion is set to 10%, as shown in the simulation result in the first embodiment, the measurement result of the effective value Vs has an absolute value | δ | of the frequency deviation of about 0.1 or more. If this is the case, a warning should be issued.
The number of 10% given here is only an example of the judgment criteria, and the specific value indicating the influence of the frequency deviation δ on the effective value of the signal to be measured Vin and the measured value Vs is as shown in the equation (18). is there.
However, when the signal to be measured Vin contains noise, the measured value Vrms of the effective value measuring unit V is a value including noise and harmonic components.

[Third Embodiment]
FIG. 5 is a diagram showing a synchronous detector according to the third embodiment.
In the synchronous detector according to the third embodiment, a frequency close to the frequency fr of the reference signal Vrs is set as a pass band in the input unit of the effective value determination and trigger synchronous detector Dtj according to the second embodiment. It is a synchronous detector Dtjf to which the filter F to perform is added.
In the second embodiment, components other than the sine wave of the frequency fin included in the signal to be measured Vin are also measured by the effective value measuring unit V.
When the deviation between the frequency fin of the signal to be measured Vin and the frequency fr of the reference signal Vrs affects the measurement result is the main determination factor of the determination device J, the frequency included in the signal Vin to be measured. It is preferable that the noise and harmonic components other than the fins are removed by the filter F before being input to the effective value measuring unit V.
The filter F may be a low-pass filter, a band-pass filter, or a high-pass filter, depending on the nature of the signal to be blocked.
Further, a band elimination filter may be used for applications in which the noise source to be removed is limited, such as removal of hum due to the frequency of a commercial power source.
The filter F for passing the measured signal Vin to be input to the effective value determination and the synchronous detector Dtj with a trigger may be either an analog circuit or a digital circuit. If the filter F is a digital filter, the signal to be measured Vin may be A / D converted. If it is a digital filter, the cutoff frequency when the filter F is a low-pass filter or a high-pass filter, or the center frequency when a bandpass filter or a bandpass filter is used is linked to the frequency fr of the reference signal on the software. The configuration may be changed.
The configuration of the third embodiment may be applied to the first embodiment.

[Fourth Embodiment]
FIG. 6 is a diagram showing a synchronous detector according to the fourth embodiment.
As the synchronous detector Dtjfd according to the fourth embodiment, two sets of synchronous detectors Dtjf1 and Dtjf2 according to the third embodiment shown in FIG. 5 are prepared, and two sets of synchronous detectors Td are provided in the time difference measuring unit Td. By inputting the trigger signals Ts1 and Ts2 from the detectors Dtjf1 and Dtjf2 and measuring the time difference, it is possible to measure the time interval Tdo in which the trigger is applied to each synchronous detector Dtjf.

Further, the amplitude ratio Go can be measured by inputting the output signals Vs1 and Vs2 from the two sets of synchronous detectors Dtjf1 and Dtjf2 to the amplitude ratio calculation unit G and measuring the ratio of the output voltages. ..

In this example, the synchronous detector Dtjf according to the third embodiment is combined, but the two sets of synchronous detectors Dtjf are replaced with the synchronous detectors Dt and Dtj according to the first or second embodiment. Also, synchronous detectors Dt, Dtj, and Dtjf may be combined.

Considering that the frequency fin of the signal to be measured Vin is sufficiently close to the frequency fr of the reference signal Vrs, the period Tr of the reference signal Vrs (the inverse of the frequency fr of the reference signal Vrs) is 2π (= 360 °), and the time interval Tdo Therefore, it is possible to measure the phase between two signals to be measured Vin by converting the phase into 2π · Tdo / Tr.

If the time Tin from the trigger signal generated from the same signal to be measured Vin to the next trigger signal can be measured with higher accuracy than δ, which is the deviation between the frequencies fr and fin, it is set as 2π · Tdo / Tin. When converted to the phase difference, it is possible to measure the phase difference between the two signals to be measured Vin without being affected by the deviation δ.

Further, since the amplitudes of the two signals to be measured Vin can also be obtained, the amplitude ratio between the two signals to be measured Vin can be obtained by the amplitude calculation unit G.

[Fifth Embodiment]
FIG. 7 is a diagram showing a synchronous detector according to the fifth embodiment.
As shown in FIG. 7 (a), the synchronous detector Dttjfd shows the configuration of the phase difference measurement, the input filter, the effective value determination and the triggered synchronous detector Dtjfd according to the fourth embodiment in FIG. 7 (b). ) Is replaced with the two-phase synchronous detector Dttjf, and is composed of a synchronous detector and a phase difference calculation unit P.
Further, the two-phase synchronous detector Dttjf shown in FIG. 7B is composed of the filter F shown in FIG. 7C and the synchronous detector Dttj.
The synchronous detector Dttj shown in FIG. 7C is composed of the two-phase synchronous detector Dtt shown in FIG. 7D, the effective value measuring unit V, and the determining device J.
Further, the synchronous detector Dtt shown in FIG. 7D is composed of a two-phase synchronous detector Dxy, a signal generation unit Q, and a trigger detection unit T.

In the synchronous detector according to the fifth embodiment (FIG. 7A), the two-phase synchronous detector Dtt is provided, so that each input filter, effective value determination, and triggered two-phase synchronous detector are provided. With Dttjf1 and Dttjf2, it is possible to measure the phase with the phase of the reference signal Vrs as the reference phase.
Therefore, in contrast to the fourth embodiment, in the fifth embodiment (FIG. 7A), a phase difference calculation unit P for calculating the phase difference θd between the two using the phases θ1 and θ2 is provided. There is. The phase difference calculation unit P outputs the calculation result of the phase difference θd (= θ1-θ2).

By the operation of the trigger detector T, the measurement of the measured signal Vin, which is always in a constant phase relationship with respect to the phase of the reference signal Vrs, is performed.
For example, when a trigger is applied by each synchronous detector based on the rising portion of 0V of the measured signals Vin1 and Vin2, the phase of the measured signal is also two-phase synchronized with respect to 0 of the reference signal. The measurement is equivalent to the measurement performed by the detector.

In the present embodiment, since the synchronous detector has a two-phase configuration, even if the phases of the signal to be measured and the reference signal are arbitrary, in the fifth embodiment, up to the fourth embodiment. Unlike the configuration, the measured values of the amplitude and phase of the signal to be measured Vin are obtained.
Therefore, it is not necessary to start the operations of the reference signals Vrs, Vrc, the integrators Is, and Ic at the same time when the trigger detectors T1 and T2 detect the trigger.

と表せ、特に、θｉｎ１＝０のときは、
θ１≒δｎπ ・・・・・・（４３）
となる。 In the fifth embodiment, the synchronous detector is operated with a delay of giving a constant phase difference between the measured signal Vin and the reference signal Vrs, and the phase value corresponding to the delay is corrected by calculation. You may.
Here, assuming that the frequency fr of the reference signal and the frequency fin of the signal to be measured are close to each other, using a first-order approximation when | δ | << 1 can be regarded, the measurement result of the phase θ1 shown in FIG. 7A is obtained.

In particular, when θin1 = 0,
θ1 ≒ δnπ ・ ・ ・ ・ ・ ・ (43)
Will be.

That is, when the measured signal is measured from 0 ° with a two-phase synchronous detector, the measurement result is δnπ (δnπ is an angle in radians. To convert this to the radian method (°), use this value. Multiply 180 ° / π≈57.3 °, or multiply δn by 180 °).

From this, as shown in FIG. 7A, the measurement results of the phases θ1 and θ2 serve as a guide for determining the reliability of the measurement.
Therefore, for example, the following usage can be considered in this synchronous detector.
(1) The value of the frequency deviation δ is estimated by calculation from the measured value of this phase, and the reference frequency fr is increased or decreased so that the phase approaches 0.
(2) When the phase, which is the measurement result, deviates from the preset judgment standard, it warns that the reliability of the amplitude and phase measurement result is low.
For example, if the determination criterion is determined to be within ± 5 °, an alarm is issued when δnπ in the equation (43) is out of the range of ± 5 ° ≈ ± 0.087 rad.
However, in the first to fifth embodiments, it is necessary to obtain a trigger signal from the signal to be measured Vin.

[Sixth Embodiment]
FIG. 8 is a diagram showing the FRA according to the sixth embodiment.
The FRA according to the sixth embodiment is effective for processing the measured signal Vin, for which it is difficult to obtain a trigger that matches the period of the measured signal Vin. In this FRA, vibration is performed by a low-pass filter LPF-OV that removes amplitude ratio vibration and a low-pass filter LPF-OP that removes phase difference vibration from each of the amplitude ratio and phase difference, which are the output signals of FRA shown in FIG. The component is removed, and the amplitude ratio Go and the phase difference θd are output.
The amplitude ratio Go and the phase difference θd are expressed by the equations (33) and (39) due to the deviation δ between the frequency fin of the signal to be measured Vin and the frequency fr of the reference signal Vrs.
Further, as the amplitude ratio Go and the phase difference θd, as expressed in the equation (40), the amplitude of the measurement output of the amplitude ratio Go and the amplitude of the measurement output of the phase difference θd change at the frequency fmeas = 2δ · fr. ..
That is, the amplitude of the measurement output is proportional to the deviation δ and the reference signal fr. Therefore, if a low-pass filter LPF having a characteristic that the output amplitude is inversely proportional to a frequency higher than the cutoff frequency or a characteristic that approaches this characteristic is used and the cutoff frequency of this LPF is set to the reference signal fr or less, the deviation δ The change in the measured output can be canceled.
Further, if a low-pass filter of a second order or higher is used, as the deviation δ becomes larger, it can be attenuated from the amplitude change of the measurement output, the degree of attenuation can be strengthened, and more stable measurement becomes possible.
In this way, if a low-pass filter having a cutoff frequency corresponding to the reference signal fr is provided in the output stage, the measurement output can be stabilized.

However, in this embodiment, in order to reduce the vibration width of the measured value due to the deviation δ, that is, the vibration width of the measured value given as the sine wave amplitude shown in the equations (33) and (39), a low-pass filter is used. Cutoff frequency needs to be lower.
Considering the measurement in the order that the frequency is about the frequency of the commercial power supply (50 Hz to 60 Hz) and the frequency deviation is 1% or less, the cutoff frequency is preferably about 1 Hz or less.

The response time of the low-pass filter will be considered below.
When the cutoff frequency of the first-order low-pass filter is 1 Hz, the time constant Tc of the transient response is about 0.16 s (≈1 s / (2π)).
Assuming that the measured signal Vin2 is set to a constant level input and the measured signal Vin1 is suddenly changed from 0 to the same amplitude as the measured signal Vin2, the time constant Tc is approximately until 95% of the steady state output is reached. It takes three times as long (1-exp (-3) ≈ 0.95), in this case about 0.5 seconds.
As described above, the time from the sudden change of the measured signal Vin to the stabilization of the measurement result is about 25 times the period of the measured signal Vin in the case of the first-order low-pass filter.

In this sixth embodiment, when the frequency fins of the signals to be measured Vin1 and Vin2 are not fixed, it is necessary to change the cutoff frequency of the low-pass filter according to the frequency fr of the reference signal Vrs, that is, the frequency to be measured.
Therefore, it is difficult to secure the measurement accuracy in a wide measurement frequency band with an analog low-pass filter.
In the digital filter, it is relatively easy to change the cutoff frequency by using the measurement frequency as a parameter.
The characteristics of the low-pass filter need not be a primary system, and if a low-pass filter having a steep frequency characteristic is used, it takes time according to the transient response characteristics of the low-pass filter until the measurement result becomes stable.

[7th Embodiment]
FIG. 9 is a diagram showing the FRA according to the seventh embodiment.
The FRA according to the seventh embodiment includes four sets of FRA1, FRA2, FRA3, and FRA4 in which the phase of the reference signal Vrs starts from the same value for each Tr / 4 obtained by dividing the period Tr of the reference signal into four equal parts. It is an asynchronous FRA that takes the average of four measured values of amplitude ratio and phase difference obtained from each FRA1, FRA2, FRA3, and FRA4, and outputs the values as measured values of amplitude ratio and phase difference.

In this example, the number of integrations n is 1.
In this case, the integration interval of each FRA is
・ FRA 1: 0 to Tr
・ FRA2: Tr / 4-5 Tr / 4
・ FRA3: 2Tr / 4-6Tr / 4
・ FRA4: 3Tr / 4-7Tr / 4
This measurement is repeated in each of FRA 1 to 4 for each period Tr of the reference signal.

FIG. 10 shows the respective integration intervals of FRA 1 to 4 and the state in which the measured value outputs of the four FRA are sequentially updated every Tr / 4 cycle.
In FIG. 10, for simplification, one signal to be measured and the reference signal of each FRA are shown only in Vrs, but there is another signal to be measured, and the reference signal Vrs of each FRA is Vrs and π / 2 ( = 90 °) Some Vrcs are out of phase.

In FIG. 11, the measured signals 1 and 2 having a frequency fin = (1 + δ) fr (3 ways of δ = 0.001, 0.01 and 0.1) and a phase difference π / 2 are measured with the configuration shown in FIG. It is a simulation result when.
Since the vibrations appearing in the measurement results in one measurement are almost canceled by averaging, it can be seen that the stability of the measurement results of the amplitude ratio and the phase difference is greatly improved by this averaging process.

Here, it will be described that the measurement output of the amplitude ratio and the phase difference is improved by dividing the period of the reference signal Vrs into four equal parts and averaging them.
When one period of a sine wave is divided into two equal parts starting from an arbitrary phase, the sum of the values of the two sine waves becomes 0.
This is π (= 180 °) when the bisector of one cycle is expressed in phase.
sin (x + θ) + sin (x + θ + π)
= Sin (x + θ) -sin (x + θ)
= 0 ... (44)
Therefore, it can be easily proved.

The reason why the measurement output of the amplitude ratio and the phase difference in FRA vibrates at the frequency of fmeas represented by the equation (41) is that the phase of the signal to be measured Vin is based on the phase of the reference signal Vrs. This is because the time changes in the form given in 40).
This means that, for example, if two FRAs, FRA1 and FRA2, which have different phases π / 2 (= 90 °) of the reference signal Vrs, are prepared and the same signal to be measured Vin is measured, the measurement output of the FRA1 can be measured. In the measurement output of FRA2, the phase of θin2 in the amplitude ratio and phase difference expressed by the equations (30) (31) or (33) (39) is π / 2 (= 90 °). The output when shifted will be obtained.

That is, the time change occurring at the frequency of 2δfr can be intentionally created by preparing a plurality of reference signals having a time difference within one cycle of the reference signal Vrs.
The time for one integration cycle corresponds to a change of 2π (= 360 °) in θin2.

Then, the amplitude ratio and the phase difference represented by the equations (33) and (39) appear as sine waves for two cycles due to the change of 2π of θin2.
Since the change of 2π (= 360 °) of θin2 corresponds to two cycles, the phase of the reference signal Vrs is shifted by π / 2 (= 90 °), and the integration start time is also shifted by that amount by the FRA. If measured, the measurement output of the amplitude ratio and phase difference represented by the equations (33) and (39), which were measured by shifting the relative θin2 by π / 2, takes θin2 of the equations (33) and (39) as an argument. The output is shifted by half a cycle of the sine wave.
As described above, it can be seen that the sinusoidal portions of the outputs of FRA1 and FRA2 perform outputs having a deviation of half a cycle.

Then, as given by the equation (44), the sum of the sine waves deviated by half a cycle is always 0, so that the FRA1 and FRA2 of the amplitude ratio and the phase difference represented by the equations (33) and (39) are always 0. The sum of the sinusoidal portions of the output is 0, and the sinusoidal change can be canceled.
However, since the frequency fr of the reference signal Vrs and the frequency fin of the signal to be measured have a deviation δ, strictly speaking, the frequencies are different, so that the phase of the reference signal Vrs is shifted by π / 2 (= 90 °). It is different to shift the phase of θin2 by π / 2 (= 90 °).

となる。
ただし、ニアリイコール（≒）とした過程で、｜δ｜＜＜１として１次近似を用いた。
余弦波（ｃｏｓ）は絶対値の最大値が１の関数であるので、式（３３）（３９）で表わされた振幅比および位相差のＦＲＡ１とＦＲＡ２それぞれが持つ出力の正弦波部分の振幅は、和を取ることにより、０とはならないまでも元の振幅を１として、最大でもδ程度に小さくできる、ということになる。 Therefore, the sinusoidal portions of the outputs of FRA1 and FRA2 are not exactly deviated by half a cycle, but are strictly deviated by δ from the half period.
In this case, the value corresponding to equation (44) is

Will be.
However, in the process of making it near equal (≈), a first-order approximation was used with | δ | << 1.
Since the cosine wave (cos) is a function of the maximum absolute value of 1, the amplitude ratio and the amplitude of the phase difference between FRA1 and FRA2 are the amplitudes of the sine wave portions of the outputs of each of the FRA1 and FRA2. Means that by taking the sum, the original amplitude can be set to 1 even if it does not become 0, and can be reduced to about δ at the maximum.

By the way, the amplitude of the sinusoidal portion of the output of each of FRA1 and FRA2 is originally given by Eqs. (33) and (39) with respect to the deviation δ between the frequency fr of the reference signal and the frequency fin of the signal to be measured. As shown above, since the maximum value is approximately δ, it can be seen that the sum of the outputs of FRA1 and FRA2 corresponding to the equation (44) is the square of δ.
Since one cycle of the reference signal corresponds to two cycles in the sine wave with θin2 as an argument given in the equations (33) and (39), the results shown in FIG. 11 show FRA3, in addition to FRA1 and FRA2. This is the result of dividing one cycle of the reference signal into four equal parts as the FRA4, using four FRAs, and averaging the four sets of reference signals having different phases by π / 2 (= 90 °).
Checking the simulation results in FIG. 11,
(A) δ = 0.001, and the amplitude after averaging the amplitude ratio is about 0.000001.
(B) δ = 0.01, and the amplitude after averaging the amplitude ratio is about 0.0001.
(C) δ = 0.1, and the amplitude after averaging the amplitude ratio is about 0.01.
As for the phase, it can be seen that the result expressed by the equation (45) is supported by using δrad≈57.3 ° · δ.
Also, as can be seen from the fact that the moving average of 4 points is taken in this case, even if there is a sudden change or momentary noise mixed in the input signal, if the average of 4 points is taken, it will be due to noise etc. Sudden changes in output can be mitigated.

[Eighth Embodiment]
FIG. 12 is a diagram showing an asynchronous FRA according to the eighth embodiment.
The asynchronous FRA according to the eighth embodiment is based on the equation (44) in which the sum of the sine waves having a half-period phase shift is 0, and the asynchronous FRA according to the seventh embodiment is more generalized. It was done.

ここで、ｍ２がｋの約数でないことから、ｋ／ｍ２は整数ではないので、

である。
（ちなみにｋ／ｍ２が整数であれば、この和はｅｘｐ（ｊθ）のｍ２倍となる、つまり初期位相θにおけるｃｏｓもしくはｓｉｎを単純にｍ２個足した値となるだけである。）
よって、式（４６）の大括弧［ ］内は、初項１、公比が式（４７）で与えられる１ではない値、項数がｍ２の等比数列の和になるので、

となることがわかる。 By the way, sin is the value obtained by dividing 2π representing one cycle by an integer m1 of 2 or more, and the sum of m1 sins whose phase is shifted by 2π / m1 is also 0 as in the equation (44).
For example, it is easy to see that the sum of three sine waves of the same amplitude that are out of phase by 2π / 3 (= 120 °) is zero.
Further generalized, the sum of m2 sins phase-shifted by k · 2π / m2, which is the value obtained by dividing the k period of sin by an integer m2 that is not a divisor of k, where k is an integer of 1 or more. It becomes 0 as in the equation (44).
This can be shown as follows.

Here, since m2 is not a divisor of k, k / m2 is not an integer.

Is.
(By the way, if k / m2 is an integer, this sum is m2 times exp (jθ), that is, it is simply the value obtained by adding m2 of cos or sin in the initial phase θ.)
Therefore, the numbers in parentheses [] in equation (46) are the sum of the geometric progression with the first term 1, the common ratio not 1 given in equation (47), and the number of terms m2.

It turns out that

であるから、この関係と式（４８）の結果を実部および虚部のそれぞれで比較すれば、ｋを１以上の整数として、ｓｉｎのｋ周期をｋの約数でない整数ｍ２で割った値である、ｋ・２π／ｍ２ずつ位相をずらしたｍ２個のｓｉｎの和も式（４４）と同様に０となることがわかる。
幾何学的には、複素平面上の０を中心とする円周上に、重ならない形で等間隔にｍ２個
配置した点における複素数の値を足し合せれば０になり、等間隔がたまたま２πの整数倍にあたり、ｍ２個の点が同じ複素数を表わす場合は、その複素数のｍ２倍、ということである。
積分回数の１回が参照信号１周期であるＴｒの時間に相当し、位相に換算すると、式（３３）（３９）で表わされた振幅比および位相差は、θｉｎ２の２πの変化によって２周期分の正弦波に相当する。 by the way,

Therefore, when this relationship and the result of equation (48) are compared for each of the real part and the imaginary part, the value obtained by dividing the k period of sin by an integer m2 which is not a divisor of k, where k is an integer of 1 or more. It can be seen that the sum of m2 sins whose phases are shifted by k · 2π / m2 is also 0 as in the equation (44).
Geometrically, if you add the complex numbers at the points where m2 are arranged at equal intervals in a non-overlapping form on the circumference centered on 0 on the complex plane, it becomes 0, and the equal intervals happen to be 2π. When m2 points represent the same complex number, which is an integral multiple of the above, it means that it is m2 times the complex number.
One integration count corresponds to the time of Tr, which is one cycle of the reference signal, and when converted to phase, the amplitude ratio and phase difference expressed by equations (33) and (39) are 2 due to the change of 2π of θin2. It corresponds to a sine wave for a period.

From this, the number of integrations n times corresponds to the phase for 2n cycles when converted to the phase of the period of the measured values of the amplitude ratio and the phase difference.
Based on this idea, the number of integrations n times corresponds to 2n when converted to k.
Therefore, a positive integer that is not a divisor of 2n may be selected as m2 such that 2n is substituted into the equation (46) to become 0, and as a generalized form of the seventh embodiment, The expression is as follows.

4nπ / m2 with the period Tr of the reference signal as 2π in m2 FRAs that are phase-shifted by 4nπ / m2, which is the value obtained by dividing the number of FRA integrations by n times and an integer m2 that is not a fraction of 2n. The vibration of the amplitude ratio and the phase difference can be obtained by measuring the measurements with the time shifted by the time corresponding to the phase of FRA1 to FRA (m2) and taking the average of all the amplitude ratios and phase differences. , The ratio can be reduced to about δ with respect to the measurement with FRA alone.
However, this is true when | nδ | << 1.
In this case, considering the time for n cycles as one measurement interval is the integration in n cycles. In obtaining the measurement result of one FRA, the noise component can be suppressed to 1 / √n when the number of integrations is one, so that the noise can be reduced and the accuracy can be improved.

[9th Embodiment]
The asynchronous FRA according to the ninth embodiment is an asynchronous FRA in which the overlapping measured signal Vin and the reference signal Vrs are efficiently integrated and the amount of calculation is reduced in the eighth embodiment.
In the asynchronous FRA according to the seventh embodiment, the time Tr corresponding to one integration is divided into four categories, but when the Tr time is measured by the FRA alone, the amplitude ratio and the phase difference are equivalent to two vibration cycles. It's time.
In the consideration of the seventh embodiment, not the average of the four measurement outputs at the beginning thereof, but the two FRA1 and FRA2 in which the phase of the reference signal Vrs is π / 2 (= 90 °) are considered, and the amplitude is considered. It was shown that the ratio and phase difference vibrations can be suppressed to almost 0 by taking the average of the two.

There are cases where vibration can be suppressed without taking the average using all the data divided into sections in this way.
Typical cases are listed below.
For example, in the seventh embodiment, not all four measurement outputs are used, but only two adjacent measurement outputs are averaged.
Since one integration number corresponds to the sum of complex numbers arranged at equal intervals on a circle centered on 0 on the complex plane for two rotations, the amplitude ratio and the amplitude ratio and the measurement output for one rotation can be used. The effect of suppressing the vibration of the phase difference can be obtained in almost the same manner.
Further, as shown by the equation (48) that the sum becomes 0, the result of integration of the reference signal Vrs and the measured signal Vin for at least one point of the data of m2 points is the remaining (m2 −. 1) It can be generated by using the integrated data for points.

Further, as is clear from the comparison between Vrs of FRA1 and FRA3 or FRA2 and FRA4 shown in the equation (44) and FIG. 10, since the reference signal Vrs has only a negative sign, it is for each section of Tr / 4. The result of the integration operation is only the difference between FRA1 and FRA3, or FRA2 and FRA4 with or without a negative sign, so just perform the integration operation on one of them and multiply the operation result by -1 to perform the operation processing. It is possible to finish.
Similarly, in the case of power division of 2 or more, if only half of the integral data for each section divided by that value is calculated, the integral calculation is unnecessary for the remaining half of the FRA, and the enormous multiplication process for the number of data points is simplified. Can be converted.
In the case of not a power of 2, if m2 is a number with a divisor, the remaining data can be generated from the measurement processing data of the (divisor-1) FRA, so the integration operation for the divisor can be performed. It is possible to reduce it.

Further, when m2 has a divisor is regarded as a division by the divisor (for example, m2 = 6), the divisor is 1, 2, 3, which is a possible number for averaging processing3. If only the data corresponding to FRA when considered as division is used (for example, the measurement data of FRA1, FRA3, FRA5 alongside FRA1 to 6), the measurement output with suppressed vibration of amplitude ratio and phase difference. Can be obtained. Such arithmetic processing can be simplified according to the degree of noise suppression by averaging.

According to the present invention, it is a synchronous detector or asynchronous FRA that operates asynchronously and can be used for measuring the amplitude ratio and phase difference between signals, and is synchronized between the frequency of the signal under test and the frequency of the reference signal. Even if there is no relationship, the amplitude ratio and phase difference can be measured, and stable measurement results can be obtained.

Dt Synchronous detector, Synchronous detector with trigger Dit Integral detector with trigger T Trigger detector Q Reference signal generator M Multiplier I Integrator J Judge V Effective value measuring unit F filter Dtj Effective value judgment and with trigger Synchronous detector Dtjf Input filter, effective value determination and trigger synchronous detector Dtjfd Phase difference measurement, input filter, effective value determination and trigger synchronous detector Dtjf1, Dtjf2 input filter, effective value determination and trigger synchronous detector Dttjf1, Dttjf2 Input filter, effective value determination and triggered two-phase synchronous detector Td time difference measuring unit G amplitude ratio calculation unit P phase difference calculation unit Dttj effective value determination and triggered two-phase synchronous detector FRA frequency characteristic analyzer OSC reference signal Synchronized built-in detector Frequency characteristic detector with built-in oscillator synchronized with OSC-FRA reference signal LPF-FRA Frequency characteristic analyzer with output low-pass filter LPF-OV, LPF-OP low-pass filter

Claims (13)

Equipped with multiple FRA
The FRA comprises a plurality of two-phase synchronous detectors.
The two-phase synchronous detector comprises two synchronous detectors and a Cartesian-polar coordinate converter, each operating on two reference signals having the same frequency but different phases by 90 degrees.
Each of the synchronous detectors
The input part of the signal to be measured and
A multiplier that multiplies the signal under test and the reference signal,
An integrator that integrates the output of the multiplier at an integral multiple of one or more of the period of the reference signal and outputs it at each time is provided.
When the Cartesian coordinate-Polar coordinate converter has two outputs of the two synchronous detectors as two components on Cartesian coordinates, it is provided with a conversion unit that obtains two outputs of an absolute value and an argument in polar coordinate display. ,
The difference between the ratio of the absolute value and the declination is output from the absolute value and the declination value obtained from the combination of the two in the plurality of two-phase synchronous detectors.
The plurality of FRAs are composed of a combination having a phase difference obtained by dividing the phase of the reference signal by one or more integer multiples of 360 degrees by a plurality of values.
An asynchronous FRA, characterized in that the plurality of FRAs output the output average of the plurality of absolute values and the output average of the plurality of declination differences. The plurality of values obtained by dividing the phase of one or more of the integer multiples of the reference signal having a phase of 360 degrees are the values of the terms represented by powers of 2 among the prime factors of the integer multiples. The asynchronous FRA according to claim 1, wherein the value is obtained by multiplying the above integer power value. The phase, which is an integral multiple of 1 or more of 360 degrees, is set to 360 degrees.
Let 1 be the value of the term represented by the power of 2 above.
The asynchronous FRA of claim 2, wherein the value of 2 or more to the power of an integer is 4. Input section for inputting the signal to be measured and
A reference signal generator that generates a reference signal of a specific frequency,
A multiplier that multiplies the signal under test and the reference signal,
An integrator that takes the time average of the output signal of the multiplier with an integration time that is an integral multiple of 1 or more of the period of the reference signal.
A trigger detection unit that detects that the signal to be measured passes a constant amplitude value and generates a trigger signal.
The reference signal generating unit is triggered by the trigger signal to output the reference signal in a specified phase.
A synchronous detector characterized in that the integrator receives the reference signal, starts the integration operation, and outputs the result of the time average after the lapse of the integration time. Further, an effective value measuring unit that measures the effective value of the signal to be measured,
The synchronous detector according to claim 4, wherein the detector is provided. Further, a determination unit that compares the output of the effective value measuring unit with the output of the integrator and outputs the comparison result,
The synchronous detector according to claim 5, further comprising the above. Further, a signal delay unit that delays the trigger signal by a predetermined time,
The synchronous detector according to any one of claims 4 to 6, wherein the synchronous detector is provided. The synchronous detector according to any one of claims 4 to 7, further comprising any of a low-pass filter, a band-pass filter, and a high-pass filter through which the signal to be measured is passed. A first synchronous detector using the synchronous detector according to any one of claims 4 to 8.
A second synchronous detector using the synchronous detector according to any one of claims 4 to 8.
A time difference measuring unit that measures the time difference between the first detection signal obtained by the trigger detection in the first synchronous detector and the second detection signal obtained by the trigger detection in the second synchronous detector.
A synchronous detector characterized by being equipped with. Further, a calculation means for outputting the result of calculation using a coefficient based on the period of the reference signal to the output of the time difference measurement unit, and
The synchronous detector according to claim 9, further comprising: Further, an amplitude ratio calculation unit for calculating the output-to-output ratio of each of the integrators included in the first and second synchronous detectors,
The synchronous detector according to claim 9 or 10, wherein the synchronous detector is provided. The synchronous detector according to any one of claims 9 to 11, further characterized in that either or both of the first and second synchronous detectors are two-phase synchronous detectors. .. Further, a phase calculation unit that outputs a phase difference obtained by arithmetic processing from the output of the integrator included in the first and second synchronous detectors, and
The synchronous detector according to any one of claims 9 to 12, wherein the synchronous detector comprises.

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