Solution

To calculate the standard uncertainty of type B - HB (Ka), it is necessary to take into account influencing factors:

1) The technical characteristics of the device (the limit of the basic relative error limit of the additional error of the device, the resistive component of the input resistance of the device),

2) The scheme of measurement (the output voltage source with internal resistance, the limit of the measurement device),

3) the measurement conditions (ambient temperature, humidity, pressure, etc.).

Also, to calculate the standard uncertainty is necessary to consider the rectangular distribution function.

5. We define the standard uncertainty for each voltage
U_m = 8,10Ви U = 8,15Вseparately, with a given distribution function (см. таб.2). Since the variant z voltmeters B7-26 and B3-42 have the same accuracy class and the same limit of measurement, equal to NAV.

where а –boundaries of the basic allowable error derived from the class of instrument accuracy. As in the example z accuracy class is denoted simply by the number 4.0 - this means that the normalized limit reduced error and

prev = 4%. The above error is the ratio of the absolute error in the normal miruyuschemu value: .

As a fiducial value (), the limit of measurement used by the voltmeter.Wedefinetheabsoluteerror: , т.е. .

.

6. Next, take into account the uncertainty caused by the temperature deviation from the normal Т_норм=20˚С.

В

7. We define the measurement uncertainty introduced by the amendment (ρ;):

,

where the coefficients of sensitivity , .

The calculation for the first point in the series in italics in Table.1 U_m:

В/Ом;

В/Ом.

The calculation for the first point in the series in italics in Table 1 U:

В/Ом;

В/Ом.

Since the value of load resistance and input impedance are known about and within certain limits [Rmin; Rmax], [Rvhmin; Rvhmax], assuming all the values ​​of resistors within the marked boundaries equally, we estimate their uncertainty as:

;

.

8. We define the total standard uncertainty::

,

.

9. We define the total standard uncertainty Ncv for indirect measurements:

.

10. We define the resulting standard uncertainty:

11. Expanded uncertainty of Hp with a given probability p and the known distribution law (Appendix A) is determined as follows:

Н_р= k ∙Н_å = 0,18

where k - coefficient of coverage. In accordance with the recommendations of DSTU and the assumption of normality of the distribution of values ​​of the measured quantity take k. When Po = 0,95, k = 2,228 (Annex B).

12. The result of measurements of the amplitude of the Ca is obtained from the formula:

All the results set up the table 3

Table 3 - ExampleSolution

	= 8,07 В
	= 8,07 В
	НТ0 В = ((Токр.ср—Тнорм)/10) = 0,04В
	В
	В
	Нр= k ∙Нå = 0,18
	, , , , k ∙= 2,228,Р д = 0,95, Нр= 0,18