SU1296953A1 - Method of measuring average value of periodic signal - Google Patents

Abstract

This invention relates to an electrical measurement technique. It can be used in instruments for measuring the integral characteristics of signals, Bx. The purpose of the invention is to improve the measurement accuracy. The proposed method is as follows. Periodically, the instantaneous values of the signal are measured with a period shorter than the signal period. The measured instantaneous values are summed. The average value is determined based on the obtained sum, the number of measurements, and the interval between the last measurement of the instantaneous value and the end of the signal period. A device for implementing the proposed method comprises a disc detector 1, an adder 2, a computing unit 3, a device 4 for period allocation, one-oscillators 5, 6, element II 7, a clock frequency generator 8, counters 9, 10, elements P, 15 delays, OR elements 12, 13, block 14 run I zp f-ly, 2 ill. a & (LFfeff (. CO O5 D). JV SA:

Description

The invention relates to an electrical measurement technique and can be used in instruments for measuring the integral characteristics of signals.

The purpose of the invention is to increase the measurement accuracy by taking into account the non-multiple frequency of the samples of the instantaneous values of the signal and the frequency of the signal.

FIG. 1 shows a block diagram of an apparatus for carrying out a method for measuring an average value of periodic signals; in fig. 2 is a functional diagram of a computing unit included in the device.

The method of measuring the average value of the periodic signals consists in periodically measuring the instantaneous values of the signal with a period shorter than the period of the signal, summing the measured instantaneous values and dividing the resulting sum. In addition, the time interval between the last measurement of the instantaneous value and the end of the signal period is measured, the ratio of the measured time interval to the measurement period of the instantaneous signal values is calculated, the last measured instantaneous value of the signal is multiplied by the resulting ratio before summing the instantaneous values instantaneous values and the ratio of the measured time interval to the measurement period of the instantaneous values, reduced by one. To increase the accuracy before by summing the instantaneous values, multiply the first and the last instantaneous value by the ratio of the measured time interval to the measurement period of the instantaneous values, increased by one and divided in half.

A device that implements the proposed method contains a discretization device I, a summaker 2, a computing unit 3, a device 4 for allocating a period, the first 5 and the second 6 one-one, element And 7, the generator 8 clock frequencies, the first 9 and second 10 counters ., 11 delay elements, first 12 and second 13 OR elements, start block 14 and delay element 15. The input of the device is through the sampler 1 and the adder 2 is connected to the first input of the computing unit 3, and through the device 4 for the period selection to the input of the one-shot 5 and 6 and the first

0

the input element And 7. The output of the generator 8 clock frequency is connected to the second input of the element And 7, the output of which is connected to the counting input of the counter 9. The overflow output of the counter 9 is connected to the counting input of the counter 10, a. through the delay element 11 - with the first input of the element OR 12 and with the first input of the element OR 13. The output of the start-up unit I4 is connected to the control input of the period extraction device 4, the installation input to zero of the counter 10, the second input of the input OR 12 and the installation input to zero adder 2. The output of the OR element 12 is connected to the input of the zero setting of the counter 9. The output of the one-vibrator 5 is connected to the second input of the OR element 13, the output of which is connected to the control input of the sampler I and through the delay element 15 to the control input adder 2. Output disk The detector 1 is connected to the second input of the computing unit 3. The information outputs of the counters 9 and 10 are connected respectively to the third and fourth inputs of the computing unit 3. The output of the one-vibrator 6 is connected to the fifth input of the computing unit 3, the output of which is the device output.

Computing unit 3 contains devices 16-19 sampling and storage (VHF), adder 20, multiplier 21,

5, the inverter, 22, the scale element 23, the adder 24 and the divider 25. The first, second, third and fourth inputs of the computing unit 3 are connected respectively to the inputs of the sample and storage devices 16-19, the control inputs of which are connected to the fifth input of the computing unit 3 The output of the device 16 of the sample and storage is connected to the first input of the adder 20. The output of the device 17 of the sample and storage is connected to the first input of the multiplier 21 and through the inverter 22 to the second input of the adder 20. The output of the device 18 of the sample and storage is via scale element 23 one with a second input of multiplier 21 and a first input 18 of the adder 24. The output sample and hold device connected to the second input of the adder 24, whose output is connected to the input of divider 25. The output of multiplier 21 is coupled to a third input of the adder 20, whose output is connected to the input of the dividend de0

0

five

0

five

3129

25. The output of the divider 25 is the output of the device.

To implement the calculations, the computing unit 3 must contain a fifth storage accessory device (not shown), the information input of which must be connected to the output of the resolver 1, and the control input to the output of the one-oscillator 5,

The essence of the method for measuring the average value of periodic signals is as follows.

Starting from the beginning of the signal period, its instantaneous values of V. are measured. With a period of T. The last instantaneous value is measured at a time interval & T T after the measurement of the preposition

last instantaneous value of v. The interval lt is measured. At the same time, the area bounded by the change curve

h-1

signal in time is equal to zz v t +

1: About

+, and the period T of the signal is expressed as follows:

T (tg-1) T „+ & T„. The average value of the periodic signal is

GUiT. ,

V

: (n-j)

(&,

i 1 & T

(I)

where di --- is the ratio measured

about

time interval to the measurement period of the instantaneous values of the signal.

More precisely, the average value of the signal is determined from the expression

and -1- / g V 4- ii V + cp „, +. (2- V; + 2

12

 -9- v)

To analyze the error of the method, it is possible to consider the averaging of a sinusoidal signal equal to

Ug, (t) (2irft),

where V and f are the amplitude and frequency of the measured voltage.

For convenience of further analysis, expressions (I) and (2) are respectively presented as follows:

V.,. -: j; - Z V. + (-}) Vj (4)

V - f G V + V

 n-l + dLfTT

.-: lvj (5)

The measurements (sampling) of the instantaneous values of the measured signal are made, starting from the moment of time, at intervals of time T 1 / f, where f is the frequency of the samples. The average value of the sinusoidal voltage (3) over a period is zero. Therefore, by substituting (3) into expressions (4) and (5), we obtain the values of the absolute measurement uncertainties, the ratio of which to V gives the corresponding reduced errors

Vn b n: sinl2Jt (i-l) f / f.

+ (d-1) sinUi "(n-l) f-

(6)

S - - 5 n-H-ol

(li: (i-l) §- + L J

+ - sin 2G. (p-1) (7)

The sum of sines in expressions (6) and (7) can be represented in the following way:

i :: sin 2B (i-i) f-

 iisL (nii) l f sinlD u k)

(I)

sin (71 | -)

k

35

n - 1 + d ..

(eight)

40

Using the obtained expressions, we simplify expressions (6) and (7)

sin ("r §-) sin (dL-1) 71 f-

45

- (

- I-sin (f

+ (l-cJL) sin (2ild. §-)

 about j

 Г sin 0.5т1-) sin (d.-l) 1t 7-1 fc f ..

(9)

D

sin ("| -)

- n

(3)

 out- 50

+ -2 sin (23Td | -)

(ten)

The sampling frequency is chosen higher than the frequency of the measured signal,

so that the inequality holds - 1. In this case, expressions (9)

about

And (10) can be simplified. as a result we get

S, -. I (l-ci) Tr (f-) S (P)

 ABOUT

b, yL-0 f- (| -)

(12)

Maximum values of errors

occur at c (–1 / 2 for the expression 2 NIN (11) and for dL for the expression

(12)

S I-c G (7)

JMOKC

4 h „

S A f-v

Va.C, 12 4j

(13)

(14)

When measuring the cosine voltage U (t) (2Ift), the wire is a similar calculation, we obtain, respectively, the error values

From “2.7 (| -) (15)

f 8 K1, E (| -)

SMttKC f

(sixteen)

When measuring a sinusoidal voltage with an arbitrary phase V C, (t) V ,, sin (27 rft + 4) error

equals

cos H + & sin y

IMOlM

s s.

max1 moha

De. & i "u ...

Tey calculated by the formulas (i4), (15), (16) and (17), respectively.

(17) - the value of the error 12969536

The proposed method can be used to measure not only the mean value of periodic signals, but also other integral characteristics of periodic signals. At the same time, in expressions (1) and (2), instead of the instantaneous values of the measured signal, one should substitute their absolute value when measuring the average direct voltage, the square of the instantaneous values when measuring the effective voltage and the production of instantaneous values of current and voltage when measuring active power.

A device that implements the proposed method works as follows.

A short pulse arrives from the start-up unit 14, which zeroes the counter 10, and the OR 12 element counts the 25-meter 9, starts the device 4 time periods and zeroes the adder 2. The period time device 4 generates a high level for a time equal to the period and the maximum minimum gain of exactly 30 of the signal being followed. Positive

the front of the signal from the output device 4

measurement is achieved by calculating the desired average value using the formula (2). When calculating by the formula (2) to 2

the error will be less than - (f / f) times for sinusoidal voltage

and 1.3 () times for cosine voltage. In practice, the sampling rate is set at least ten times the maximum frequency of the measured signal, therefore, the proposed method provides an increase in the measurement accuracy of the sine wave

40

a period selection opens element AND 7 and starts up; the one-shot 5, which, through the element OR 13, triggers the sampler I, which produces the first sampling of the instantaneous value of the measured signal. Through the open element And 7 at the counting input of the counter 9 from the generator 8 clock frequency begin to receive high frequency pulses. After each overflow of the counter 9, it is reset to zero through the delay element 11 and the OR element 12 (the delay time

more than 300 times the sampling time

and cosine signal more than 100 times.

When measuring the average value of arbitrary waveforms, the proposed method also provides an increase in measurement accuracy. The only exceptions are square-wave signals, for which the only way to increase the measurement accuracy is to increase the f / f ratio, i.e. for a given frequency range of the measured signal, an increase in the frequency of samples.

50

the sampler 1), adding the unit to the contents of the counter O and running the sampler 1 through the OR element element 15 55 delay and sufficient to complete the transition process in the sampler 1, are summed up in the adder 2. At the end of the period of the measured signal, the element And 7 is closed and the

five

0

a period selection opens element AND 7 and starts up; the one-shot 5, which, through the element OR 13, triggers the sampler I, which produces the first sampling of the instantaneous value of the measured signal. Through the open element And 7 at the counting input of the counter 9 from the generator 8 clock frequency begin to receive high frequency pulses. After each overflow of the counter 9, it is reset to zero through the delay element 11 and the OR element 12 (the delay time

more sampling time is selected in

sampler 1), adding unit to the contents of counter O and launching sampler 1 through the element OR 13. As a result, counter 10 accumulates a number equal to the number of samples, and sampler I samples the instantaneous values of the measured signal that, after a delay, The delay element 15 that is sufficient for the completion of the transition process in the sampler 1 is summed up in the adder 2. At the end of the measured signal period, the element 7 closes and the one-shot 6 is started, the output signal cerned sufficient for completion Sheni transient in the circuit elements supplied to the computing unit 3 performs the recording and the corresponding signals sampling devices 15-19 and storage. In this case, the device 16 for sampling and storage stores a signal equal to IlV. Device

eleven

in 17 sample and store remembers i

the last selected instantaneous value of the measured signal V. Sampling and storage device 18 stores the contents of counter 9, which is the digital equivalent of the additional time interval between the last sample and the end of the measured signal period. Sample and hold device 19 stores the contents of counter 10, one less than the number of samples. The signal from the output device 16 of the sample and storage is fed to the first input of the adder 20, the second input of which receives a signal equal to V. The scale element 23 converts the signal from the output of the water economy department 18 to a signal i equal to the ratio of the additional time interval to the period of samples. The signal A is fed to the second input of the multiplier 21, the first input of which receives the signal V. As a result of the multiplication, the third input of the adder 20 receives the signal diV and

The n-t output produces an EG - + signal.

After summing the signals d and f -1

on the adder 24 and dividing the corresponding signals in the divider 25, a signal is generated, described by the expression (O.

The proposed method for measuring the average value of periodic signals (as compared to the known ones) allows to take into account the effect of the non-multiple frequency of the instantaneous signal values.

signal frequency, which provides improved measurement accuracy.

Claims (2)

1. A method of measuring the average value of periodic signals, including periodic measurements of instantaneous values of a signal with a period shorter than the period of a signal, summing up measured instantaneous values and dividing the resulting amount, characterized in that, in order to improve accuracy, the time interval between the last instantaneous measurement is also measured the values and the end of the signal period are determined. the average value of the signal U by the ratio 35 five 0 0 five and h-1 Submarine ( "P-1 + dL 1 I where and. - one of the measured instantaneous values. AT; and „- the last measured instantaneous value. AT; n is the number of measurements of instantaneous values; ct is the ratio of the duration of the measured time interval to the measurement period of the instantaneous values. 2. The method according to claim 1, characterized in that, in order to improve accuracy, the first and last terms of the sum are determined by the ratios V, -i „,; v --Ч U .. where V and V are the first and last terms of the sum, respectively; 0 - the first instantly measured e 3 reading. / in 5 cfJuff.Z W / X