MAGNETORESISTIVE TRANSFORMER ON THIN FILMS

The statistical processing of the results for a three-time measurement of active power by a magnetoresistive converter is given. In the statistical processing of the threefold result of measuring the active power by a magnetoresistive converter, two problems were solved. First, some approximate value of the measured value (estimation) is determined, which best corresponds to the obtained results. Secondly, the probable deviation of the measurement results from the estimation of the measured value is determined.


I. INTRODUCTION
One of the most important energy characteristics, which is measured in electronics is power.The most promising means of measuring the active power mode "in situ" is a magnetoresistive measuring transformer on the basis of the anomalous Hall effect and anisotropic magnetoresistance in thin ferromagnetic films [1].Such measuring transformer, as compared with semiconductors, are 2 orders of magnitude higher sensitivity, a small measurement error of 3 orders of magnitude smaller values thermoelectromotive forces and the absence of rectifying contacts, which are the basis for selecting of the magnetoresistive measuring transformer for further investigation [2] - [5].

II. PROBLEM STATEMENT
A three-fold measurement of the active power was carried out by a magnetoresistive converter, the results are given in Table I.
We perform the verification of the adequacy of the electric model of the measuring transducer using the criteria of Student and Fisher [3].
The hypothesis about the adequacy of the mathematical model is not rejected if the residual variance 2 res S of the output value m X 0 ˆ, calculated on the model, in relation to the experimental p X 0 ˆ does not exceed the statistically error of the experiment, which is determined by the dispersion of the reproducibility 2 0 .S The residual variance is defined as: asymmetry and sharpness.The results of calculating the characteristics of the position of point estimates are classified in Table III.
From Table III it is seen that the largest variance of the result of the experiment (mean square deviation) is the 3rd measurement group.From the estimation of the asymmetry, we can conclude that the distribution density curve of the 1st group with negative asymmetry lies to the left of the symmetric probability distribution, whose asymmetry is equal to zero, and the 2nd and 3rd groups with positive asymmetry -to the right.Excesses in probability distribution laws will be close to zero if their probability density curve will have a ringing form.Curves with a more acute peak have a positive excess (2nd measurement group), and with a more stable one there is a negative excess (1st and 3rd measurement groups).
Since the excess E is in the range -1 < E < 1, that is, the distribution is close to normal (E = 0), then for the estimation of the distribution we take the arithmetic mean.
Define the boundaries of the random error of the measurement results given in Table I for the probability of probability P d = 0.9973 and the level of significance of the coherence criteria α = 0.05.
To determine the limits of random error based on the results of triple observations, perform the following operations: 1) We will exclude from the results of observation gross errors.
2) Calculate the arithmetic mean of the corrected observational results or estimate the mathematical expectation that is taken for the measurement result.
3) Calculate the mean square deviation of the measurement result and its estimation.
4) Let's check the hypothesis that the results of observations belong to the chosen distribution law.
5) Calculate the confidence limits of the random error of the measurement results.
By the type of histograms and cumulative curves, Fig. 1, as well as obtained point results of asymmetry and excesses, Table .III, we accept the hypothesis that the measurement results are distributed according to normal law.

III. DETERMINATION OF GROSS ERRORS AND MISSES ACCORDING TO WRIGHT'S CRITERION
The measurement result k i (k max or k min ) does not belong to the normal distribution with the given probability P, if where t p is the confidence coefficient, Table 2.1 [7].
That is, if k i goes beyond the interval ( ) and substituting (1) instead М K and σ K to their estimation k and ˆK  , taking into account that for a normal distribution law t p = 3.0 (for the probability Р = 0.9973), intervals at the border are defined (Table IV).
Outside the intervals, there is no measurement result as seen in Table IV.That is, there are no blunders and gross errors.

IV. DETERMINATION OF GROSS ERRORS AND MISSES ACCORDING TO SMIRNOV'S CRITERION
By the Smirnov criterion, the measurement result k i does not belong to a given distribution with a given probability P, if where β is a random variable that depends on P and the number of observations n.
For the number of observations n = 19 and the level of significance α = 0.05, P = 1-α = 0.95, the value of β according to Table B.1 [7] is 2.75.
From Table IV shows that all the results of the measurement k i belong to the normal distribution.

V. PEARSON'S TEST
For previously obtained values of middle of intervals histogram k resj (j = 1, …, L), value proba-bility density theoretical distribution are obtained using the formula [7] 2 mid 2 ( ) Frequency hits measurement results m jd are obtained, which are subject to a theoretical distribution: For each interval j value are calculated ) The total value of the coefficient for each measurement group is determined: In Table B.3 [7] for the probability P = 0.95 and the number of degrees of freedom k = 5 -3 = 2 the value are obtained 2 0  = 5.99.
 , we assume that the hypothesis about the normal distribution of experimental data is reliable.

VI. CHECK BY KOLMOGOROV'S CRITERION
In the Table V contains the previously obtained values of the cumulative curve at the boundaries of the interval k j .
For previously obtained estimates of mathematical expectation ˆK  and mean square deviation integral formula for normal distribution function value F jd (Table 2.4 [7]) at the points k j are defined is the value of the Laplace function.

Calculated value of the coefficient (Table V).
  B.4 [7], for a given probability P=0.95, the value of the coefficient d should be in the range of 0.7304 to 0.8768, i.e. all measurement results (Table V) satisfy the first part of the component criteria.
To check the "tails" of the empirical distribution in the second part of the criterion, the confidence intervals are defined by the formula ˆ.
For a normal distribution t p = 3.0 (Table 2.2 [7]), and the boundaries of the confidence interval will be equal to: No measurement result exceeds the specified limits, so the second part of the criterion is satisfied.Thus, the results of measurements belong to the normal distribution law.

VIII. DETERMINATION OF BOUNDARIES OF RANDOM ERROR OF MEASUREMENT RESULTS
The boundaries of the random error of the measurement results will be determined as: From [8] for the probability Р d = 0.9973 and normal distribution t p = 3.0 are obtained.
Boundaries of random error of measurement results (arithmetic mean), Table VI

IX. CONCLUSIONS
In the statistical processing of the threefold result of measuring the active power by a magnetoresistive converter, two problems were solved.First, some approximate value of the measured value (estimation) is determined, which best corresponds to the obtained results.Secondly, the probable deviations of the measurement results from the measured value are determined.

S
, it is necessary to have several values of the output parameter measured under the same conditions.Experimental values k p X 0 are obtained in three parallel studies, and the value of the output value, calculated from the model

TABLE I .
: RESULTS OF MEASUREMENT OF ACTIVE POWER BY A MAGNETORESISTIVE TRANSFORMER ON THIN FILMS ___________________________________________________________________________________________________________© National Aviation University, 2017 http://ecs.in.ua