SU1562862A1 - Method of determining amplitude of harmonic signal of infralow frequency - Google Patents

Abstract

The invention relates to electrical measuring technique and can be used to create measuring instruments for the rapid measurement of the amplitude and constant component of the harmonic signals of an infra-low frequency. The aim of the invention is to improve the accuracy and reduce the time of measurement of the amplitude of the harmonic signal. This goal is achieved due to the fact that the instantaneous values of the signal measured at a given interval are averaged three times, with the second and third averaging operations carried out with weights that vary according to the laws of sine and cosine. According to the obtained averaging results, the quadrature components of the signal are determined by the corresponding formulas, from which the amplitude of the harmonic signal is calculated. 1 il.

Description

The invention relates to electrical measuring equipment and can be used to create measuring devices for determining the on-line measurement of the amplitude and constant component of infrared frequency harmonic signals, as well as for studying the mechanical, dielectric and thermal properties of materials using dynamic methods and frequency characteristics of four-terminal networks using harmonic external effects of infrared frequency in a time shorter than the period, in the presence of interference.

The invention is to increase the measurement accuracy by reducing the error introduced by noise, i.e.

by increasing the noise immunity of measurements, and reducing the measurement time by reducing the measurement interval.

The essence of the method is as follows.

Let the signal under study be described by

U0 (t) Acos (Ut -V) + a (t), (1) where A, CO, t are the amplitude, the circular frequency and the initial phase of the signal, respectively; a (tO is the slowly varying additive component of the signal. Expression (1) can be represented as

17 „(t) A costot + A.sincot + a (t) 8 (2)

Where A x Acostp;

Au AsinCj; - quadrature components of the signal amplitude .5 Task setting: determine (measure) the harmonic signal parameters UQ (t) in the shortest possible time. When measuring, there are always inaccuracies or interferences | (O which Aue is considered to be additive, so that a continuous signal

15628624

- AJso sot dt Oh, from where

U

with where u

AC - A, C

t / g

 j U (t) cos

-TI2

time value t

with weight coefficient

with

Tfl

co.scot

sinQT Uf

-t / g

and (o ue (O + (t),

(3)

cos Qt functions for

From the condition - ttt-ah Ah

f g

j (t) Ayco

-Tfi

Let us also accept the condition that the composition of the signal a (t) varies little during the measurement time, so that in the measurement interval the value of a (t) can be considered constant and equal to A0.

Consider the total error, 20 - A.lsinWt dt O wearable interference

t | gh

g F 1 U (t) - Ue (t) dt

T | YT / 2

  u (t) - AxcosCOt - A.sin "t -T,

(BUT)

from where

Uc A u S: - t / g

25

ABOUT,

where U5 - | U (t) s

-T (2

- Ae dt,

time average U (t) with weight sincOt;

where T is the averaging time or the duration of the signal implementation section.

Using the conditions of minimization of the B2 resolution, from equation (4) we find the values of Ax, Au, AO. To do this, we successively perform the following transformations of equation (4).

From the condition -jr7 0 we get m | gdA

| u (t) - A cosat - Aysinot -f | i

- - 0, from where

U A0 - 0,

T | i

(five)

45

% S A0 U - AX-C. When implementing the method in digital

T T,

- If,,. 2 COT, / (as the interval of averaging T (- -, y

where u --- | costit dt --sin-r - (6) 2 2J

-t 12.

WT

the average value of the signal U (t) for time T;

C - j cosOt dt - sin- - (7)

 -T | 2.

03

The average value of the cosine function over time T.

9F of the condition-x-t-0, we have

T (2

f u (t) - Atcos "t - A.sinOJt - -tli

divided by an even number of 2N sampling intervals. Then the time and sampling interval of the signal is ut T / 2N, the total number of sampling points of instantaneous values is (2N + J) j, and calling the sampling step

CUT COUT ™: r-. 2N

55 In this case, expressions (7), (10, and (13) for coefficients C, C2, take the form

U

with e u,

AC - A, C Oh,

(eight)

t / g

 j U (t) cos (0t dt (9) -musred-TI2

the value of the signal U (t) at time T

weighting factor cosWt;

with

Tfl

co.scot dt

sinQT Uf

-t / g

-l- o

) (10) - the average value

cos Qt functions over time

From the condition - ttt-0 Tas Ah

f g

j (t) Aycoscot - -Tfi

0 - A.lsinWt dt About

from where

Uc A u S: - t / g

five

Oh, (and)

where U5 - | U (t) sinWt dt (12) us-T (2

0

the value of the signal U (t), which has been reduced to time T, with the weight coefficient sincOt;

one

T

s1

T, 2.

--- siruot dt -r- (1 -Tfl

sinQT

of

functions over time T. At C 0, we have

) (13) - the average value of 1

35

.

Reta system of equations (5), (8) and (P), we find

A (Uc - U-C)

A (c 5-zyj

A - h

% S A0 U - AX-C. When implementing the method in digital

T T,

(14)

(15) (16)

averaging interval T (- -, y

divided by an even number of 2N sampling intervals. Then the time interval for sampling the signal is ut T / 2N, the total number of sampling points of instantaneous values is (2N + J) j, and calling the sampling interval is

CUT COUT ™: r-. 2N

In this case, expressions (7), (10) and (13) for the coefficients C, C2, take the form

c; g HCOSK K - N

 2N + 1

sin --j-- (2N + l) sin- | -; (17)

1 4- V, 1 G. .sin (2N + l) fli.n. p, Ko6 7l1 + 7 ™ lMTfn | J (18)

2 Y (2N + l) sinot J: 1. iv, 1 G. sin (2N + l) oC T 2NTT 31P K 2G (9)

tl

and expressions (6), (9) and (12), according to which the values of U, Uc and U5 are determined, take the form

and -ojr + T u (Kbt);

ZN + J K-.N

one

about" . , Xu (Kut) cosKot; (21)

/ N + j to-n

 -oGGTT- U (Kut) sinK, x :. (22) / N + J

With N 1, we have sin at ' oi, (2N + + and return to the analog variant.

The drawing shows a device that implements a method for determining 30 amplitudes of a harmonic signal.

The device contains an analog-to-cis converter (ASH1) 1, control unit 2, interface unit 3, computing unit 4, display unit 5

information. Control unit 2 serves to set the sampling tk Kit (K -N, ..., O, N) of the input signal U (t) and their numbers (2N + 1), as well as to synchronize the operation of all the nodes of the device.

The device works as follows.

The measured voltage U (t) goes to the A / D converter 1, which converts its instantaneous values at sampling times tk to proportional codes U (tK) U (Kit). The sampling times tk are set in control block 2, and at these times the trigger signals are applied to the trigger input AUF 1. The sampling times t C are determined by the averaging time T and the number of sampling points (2N + 1), which are strictly defined, but can be rearranged. The Uc codes are entered into the random access memory (RAM) of the computing unit through the interface unit 3.

recognition - 15

20)

20

(21)

(22)

neither

25

+ ovost 30

Lro- 2 is35

um and goa ex Q

4. The computational unit 4 also introduced the value of the circular (or cyclic) frequency CO j, for example, from a generator of stimulating effects when removing the frequency characteristics of quadruple circuits. According to this frequency value in computing unit 4, the coefficients C. C, S are calculated using formulas (17) - (19), respectively, and their values are also recorded in the RAM of the computing unit 4. As a result, all 4 (2N + 1) codes entered into the computing unit 4 UK, with a signal from control unit 2, is transferred to the computation mode first of the numerical values of U, Uc, IV according to Formulas (20). (22) respectively, then the quadrature components Av. Ai,

" , but

and a constant component of A0 according to Formulas (14) - (16), respectively, and finally, the amplitudes of the measured harmonic signal according to the well-known Formula

+ AV

(23)

If necessary, the initial phase of the measured harmonic signal can also be additionally determined with respect to the center of the measurement-1 tel interval t 0 by the formula

Q arctg.

(24)

Codes of measured amplitude values A (or its quadrature components AX Ats, which is convenient in determining the frequency characteristics of quadrupoles), the constant component A0 and, if necessary, the initial Lazy (j) from the computing unit 4 are entered into the display unit 5 - tion.

Claims (1)

Invention Formula The method for determining the amplitude of the harmonic signal of the infra-low frequency is that the instantaneous values of the harmonic signal are measured, by which the sought amplitude A of the harmonic signal is calculated, characterized in that, in order to increase the accuracy and decrease the measurement time, the measured instantaneous values of the signal are not selected in accordance with a given accuracy, the time interval T is three times independently averaged, the second and third averaging being carried out with weighting coefficients varying according to -retarded by the sine and cosine of the received values determined quadrature suck At 9 by formulas amplitudes A, Au, and constant A. .Uc - UC .Us , A A - - |, -; and ft) d p - g a0 and 1x where U is the average value of the signal over time T; U.S., U.C. are the averaged over time T values of the signal with weighting coefficients varying according to the sine and cosine laws, respectively; WITH - the circular frequency of the signal amplitude of the harmonic signal determined by formula X At + A R (g) L adzap cvststsch. 3 five