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Calculation of metrological characteristics of EFC

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1. Purpose:

1.1 Master the technique of an estimation error of measurement, using NMC EFC.

1.2 Learn how to choose the mode of EFC, which provides the minimum error.

 

Key Provisions

2.1 Individual task consists of four tasks. In the first and the second problem should be using the NMC EFC, the best way to select the operating mode parameters and calculate the error. Record the measurement result on the scoreboard showing the dimension.

A third challenge is the result of measurement error estimate of the frequency ratio. It is also necessary to record the measurement result on the scoreboard. This task is necessary to pay attention to the correct choice of frequencies, which should be in the range of measurement EFC.

Fourth task will assess the result of measurement error of the frequency (period, frequency ratio), submitted to the board. This inverse problem is solved.

2.2 Normalized metrological characteristics (NMC) EFC - a metrological characteristics (MC), the regulatory and technical documentation (TD).

To NMC EFC are:

- in the mode frequency measurements:

a) measuring range

b) the calculation time T count

 

  ,  

 

where n = 10,ν,ν = 0, 1, 2, 3, 4....,

c) the number of digits,

d) threshold,

e) the relative error δqg crystal oscillator

 

- in the mode of measurement periods:

a) measuring range

b) label the period;

 

  ,  

 

where m – frequency multiplier crystal oscillator m = 10ε; ε = 0; 1; 2; 3; 4….,

c) the period of the factor n;

d) the number of digits

e) threshold

e)the relative error δqg crystal oscillator

- in the mode of measuring the ratio of frequencies:

a) the range of measurement frequencies

b) the range of measurement and period.

c) the period of the factor(n);

d) the number of digits

e) the threshold of sensitivity,

 

2.3 The basic error in the measurement mode frequency is given by:

 

  ,  

 

δqg – standard error of the value of the crystal oscillator;

δ N – error of discreteness

 

  ;  

 

where ,

 

  ;  
  ;  

 

, ;

Where ;

; ; ; .

 

Basic error in the measurement period is determined by the

 

.  
,  
; ; ;
,  

 

m – factor frequencyoscillator;

ε = 0, 1, 2, 3, 4.....

In the measurement of the frequency

 

  .  

 

Options for individual tasks are presented in Appendix B and are selected

for:

- full-time students under the ordinal name of academic papers;

- for students of correspondence courses according to the third letter in the name.

Rules for assignment:

1.Rewrite assignment as a table (Appendix B);

2.Rewrite NMC of given EFC (Appendix D);

3.Perform necessary computation of the parameters selected (specified) mode measurement

4.Result of solutions write in a table (instead of written answers questions).


Appendix A

 

Table A1. Variants of individual tasks for laboratory work №7.

№ (stationary) 3d letter of surname (extramural student) Frequencies in kHz Period of marks Т m
  А ƒ 1 0,08·100; 0,08·101; 0,08·102; 0,08·103; 0,08·104; 0,08·105 Let’s take for 7- digit frequency counters Тm =10-4s=0,1ms   For 8- digit and higher Тm =10-6s=1 µs
ƒ 2 0,04; 0,02; 0,08; 0,1; 0,64; 0,8
  Б ƒ 1 0,12·100; 0,12·101; 0,12·102; 0,12·103; 0,12·104; 0,12·105
ƒ 2 0,02; 0,04; 0,06; 0,2; 1; 1,2
  В ƒ 1 0,16·100; 0,16·101; 0,16·102; 0,16·103; 0,16·104; 0,16·105
ƒ 2 0,04; 0,08; 0,05; 0,2; 1; 3,2
  Г ƒ 1 0,20·100; 0,20·101; 0,20·102; 0,20·103; 0,20·104; 0,20·105
ƒ 2 0,04; 0,08; 0,1; 0,5;;2; 5
  Д ƒ 1 0,24·100; 0,24·101; 0,24·102; 0,24·103; 0,24·104; 0,24·105
ƒ 2 0,06; 0,01; 0,08; 0,48; 1,2; 1,5
  Е ƒ 1 0,28·100; 0,28·101; 0,28·102; 0,28·103; 0,28·104; 0,28·105
ƒ 2 0,14; 0,05; 0,2; 0,5; 1,4; 2,8
  Ж ƒ 1 0,32·100; 0,32·101; 0,32·102; 0,32·103; 0,32·104; 0,32·105
ƒ 2 0,2; 0,16; 0,32; 0,8; 1,6; 6,4
  З ƒ 1 0,36·100; 0,36·101; 0,36·102; 0,36·103; 0,36·104; 0,36·105
ƒ 2 0,06; 0,09; 0,03; 1,5; 1,8; 6
  И ƒ 1 0,40·100; 0,40·101; 0,40·102; 0,40·103; 0,40·104; 0,40·105
ƒ 2 0,2; 0,16; 0,2; 1,25; 4; 5
  К ƒ 1 0,44·100; 0,44·101; 0,44·102; 0,44·103; 0,44·104; 0,44·105
ƒ 2 0,11; 0,2; 0,2; 1,1; 2; 5
  Л ƒ 1 0,48·100; 0,48·101; 0,48·102; 0,48·103; 0,48·104; 0,48·105
ƒ 2 0,12; 0,15; 0,2; 2; 2.4; 8
  М ƒ 1 0,52·100; 0,52·101; 0,52·102; 0,52·103; 0,52·104; 0,52·105
ƒ 2 0,26; 0,08; 0,4; 4; 5; 6,5
  Н ƒ 1 0,56·100; 0,56·101; 0,56·102; 0,56·103; 0,56·104; 0,56·105
ƒ 2 0,14; 0,2; 0,4; 2; 1,4; 5
  О ƒ 1 0,60·100; 0,60·101; 0,60·102; 0,60·103; 0,60·104; 0,60·105
ƒ 2 0,2; 0,3; 0,4; 2,5; 1,2; 6
  П ƒ 1 0,64·100; 0,64·101; 0,64·102; 0,64·103; 0,64·104; 0,64·105
ƒ 2 0,08; 0,4; 0,16; 2; 1; 8
  Р ƒ 1 0,68·100; 0,68·101; 0,68·102; 0,68·103; 0,68·104; 0,68·105
ƒ 2 0,17; 0,34; 0,68; 1,7; 8; 4
  С ƒ 1 0,72·100; 0,72·101; 0,72·102; 0,72·103; 0,72·104; 0,72·105
ƒ 2 0,08; 0,36; 0,6; 1,8; 7,2; 8
  Т ƒ 1 0,76·100; 0,76·101; 0,76·102; 0,76·103; 0,76·104; 0,76·105
ƒ 2 0,19; 0,38; 0,4; 1,9; 3,8; 5
  У ƒ 1 0,80·100; 0,80·101; 0,80·102; 0,80·103; 0,80·104; 0,80·105
ƒ 2 0,4; 0,32; 0,5; 6,4; 8; 4
  Ф ƒ 1 0,84·100; 0,84·101; 0,84·102; 0,84·103; 0,84·104; 0,84·105
ƒ 2 0,21; 0,35; 0,6; 2,4; 4,2; 4

 

 

Continuation of table And

№ (stationary) 3d letter of surname (extramural student) Frequencies in kHz Period of marks Т m
  Х ƒ 1 0,88·100; 0,88·101; 0,88·102; 0,88·103; 0,88·104; 0,88·105 Let’s take for 7- digit frequency counters Тm =10-4s=0,1ms   For 8- digit and higher Тm =10-6s=1 µs
ƒ 2 0,11; 0,4; 0,55; 1; 4; 4,4
  Ц ƒ 1 0,72·100; 0,72·101; 0,72·102; 0,72·103; 0,72·104; 0,72·105
ƒ 2 0,08; 0,36; 0,6; 1,8; 7,2; 8
  Ч ƒ 1 0,78·100; 0,78·101; 0,78·102; 0,78·103; 0,78·104; 0,78·105
ƒ 2 0,39; 0,6; 0,65; 1,95; 1,3; 8
  Ш ƒ 1 0,82·100; 0,82·101; 0,82·102; 0,82·103; 0,82·104; 0,82·105
ƒ 2 0,82; 0,41; 0,82; 4,1; 5; 4
  Щ ƒ 1 0,86·100; 0,86·101; 0,86·102; 0,86·103; 0,86·104; 0,86·105
ƒ 2 0,43; 0,2; 0,86; 2,5; 8,6; 5
  Э ƒ 1 0,90·100; 0,90·101; 0,90·102; 0,90·103; 0,90·104; 0,90·105
ƒ 2 0,3; 0,2; 0,6; 1,5; 4,5; 9
  Ю ƒ 1 0,94·100; 0,94·101; 0,94·102; 0,94·103; 0,94·104; 0,94·105
ƒ 2 0,47; 0,94; 0,47; 1; 2,5; 5
  Я ƒ 1 0,98·100; 0,98·101; 0,98·102; 0,98·103; 0,98·104; 0,98·105
ƒ 2 0,49; 0,2; 0,98; 1,96; 7; 5

 

Note. Frequency ƒ 2 is taken only for frequency mode ratio.


Appendix B

 

Frequency comparator

 

Metrological characteristics of the frequency comparator Ч7-12:

- frequencies of input signals 1 and 5 МHz with a maximum deviation from the nominal frequency not exceeding 1 Hz;

- input voltage from 0.5 to 1.5 V;

- maximum relative difference between the values of input signals frequency is determined by:

where δ all – allowable error of frequency instability measurement of input signals, δall =10-7... 10-12;

– frequency difference of input signals;

f qg– reference signal frequency.

In this case following condition must be satisfied:

, Hz

where М – multiplication factor of input signal frequency difference.

- voltage of input signals not less than 0.65 V at the load resistance R = 75 Ohm.

 

Frequency standard

Metrological characteristics of frequency standardЧ1-53:

- relative error not more than 5·10-6 after 4 times from the date of switching;

- the relative frequency deviation of the initial signal per day - not more than

5·10-9 after 24 hours of work;

- root mean square relative deviation of the output signal period after 24 hours of work - not more than 2·10-11 for 1 sec;

- the level of initial signals – at least 1 V at the load of 50 Ohm.

 

Frequency synthesizer

Metrological characteristics of frequency synthesizer:

- frequency of the initial signal is set within the 50-49999999,99 Hz with step 0,01 Hz. Dialing of value using the trigger switch on the front panel or remotely using of DC signals;

- initial voltage on the external load 50 Ohm – 0,5 V;

- error of installation the nominal frequency – not more than ± 5·10-8;

- frequency instability the initial signal after 2 hours of self-heating – not more than 5·10-10 in 10 s; 5·10-9 in 10 min.


Appendix C

Individual task

Measurement of the frequency and period by digital frequency counter

 

Table C1 – Task variants.

Variant Frequency counter type Frequency Period Frequency ratio Count-ing time Period multiplier Time marks The result on the digital display ± δΣ
    А Ч3-35 120 kHz ? ? ? ? ? ? ? ?
? 0,7 µs ? ? ? ? ? ? ?
33 MHz/3 kHz ? ? ? ? ?
? ? ? ? 00297.444 kHz ? ? ?
    Б Ч3-57 2,2 MHz ? ? ? ? ? ? ? ?
? 400 µs ? ? ? ? ? ? ?
15 MHz/1 kHz ? ? ? ? ? ?
? ? ? 4841.227 kHz ? ? ?
    В Ч3-24 750 kHz ? ? ? ? ? ? ? ?
? 0,3 µs ? ? ? ? ? ? ?
? 42 MHz/20 kHz ? ? ? ? ? ?
? ? ? 0000.0009 kHz ? ? ?
    Г Ч3-36 10 kHz ? ? ? ? 10-5 ?
? 0,1 µs ? ? ? ? ? ? ?
? ? 47 MHz/10 kHz ? ? ? ? ? ?
? ? ? ? 1 µs 07842.09 µs ? ? ?
    Д Ч3-57 300 kHz ? ? ? ? ? ? ? ?
? 0,08 µs ? ? ? ? ? ? ?
4,5 MHz/12 kHz ? ? ? ? ? ?
? ? 00077.75kHz ? ? ?
    Е Ч3-22 630 kHz ? ? ? ? ? ? ? ?
? 0,25 µs ? ? ? ? ? ? ?
21 MHz/7 kHz ? ? ? ? ? ?
? ? ? 5555.5555 kHz ? ? ?

 


Variant Frequency counter type Frequency Period Frequency ratio Count-ing time Period multiplier Time marks The result on the digital display ± δΣ
    Ж Ч3-35 ? 0,01 ms ? ? 10-3 kHz ? ?
? 0,04 µs ? ? ? ? ? ? ?
17 MHz/2 kHz ? ? ? ? ? ?
? ? ? 103 ? 00300.0000 ms ? ? ?
    З Ч3-22 575 kHz ? ? ? ? ? ? ? ?
? 0,35 µs ? ? ? ? ? ? ?
906 kHz/3 kHz ? ? ? ? ? ?
? ? ? 0000.0220 kHz ? ? ?
    И Ч3-57 966 kHz ? ? ? ? ? ? ? ?
? 2 µs ? ? ? ? ? ? ?
19 MHz/25 kHz ? ? ? ? ? ?
? ? ? 0006757. kHz ? ? ?
    К Ч3-35 2,5 MHz ? ? ? ? ? ? ? ?
? 0,33 µs ? ? ? ? ? ? ?
2,9 MHz/1,5 kHz ? ? ? ? ? ?
? ? ? ? 0,1 ms 0049.0000 ms ? ? ?
    Л Ч3-24 ? 0,03 µs ? ? ? ? ? ? ?
? 7 µs ? ? ? ? ? ? ?
10,5 MHz/2,5 kHz ? ? ? ? ? ?
? ? ? 37886.420 kHz ? ? ?
    М Ч3-22 31 MHz ? ? ? ? ? ? ? ?
? 34 µs ? ? ? ? ? ? ?
20,2 MHz/6 kHz ? ? ? ? ? ?
? ? ? ? ? 089124.38 µs ? ? ?
    Н Ч3-24 9,4 MHz ? ? ? ? ? ? ? ?
? 8 µs ? ? ? ? ? ? ?
3,8 MHz/3 kHz ? ? ? ? ? ?
? ? ? 0003333.3 kHz ? ? ?



 

Variant Frequency counter type Frequency Period Frequency ratio Count-ing time Period multiplier Time marks The result on the digital display ± δΣ
    О Ч3-57 12 MHz ? ? ? ? ? ? ? ?
? 0,02 µs ? ? ? ? ? ? ?
1,2 MHz/0,3 kHz ? ? ? ? ? ?
? ? ? 06245.74 kHz ? ? ?
    П Ч3-36 15,3 MHz ? ? ? ? ? ? ? ?
? 27 µs ? ? ? ? ? ? ?
27 MHz/5 kHz ? ? ? ? ? ?
? ? ? 102 ? 010.0000 ms ? ? ?
    Р Ч3-22 1001 kHz ? ? ? ? 10-6 ?
85 kHz ? ? ? ? ? ? ? ?
5,9 MHz/5 kHz ? ? ? ? ? ?
? ? ? 01378.000 kHz ? ? ?
    С Ч3-24 3,85 MHz ? ? ? ? ? ? ? ?
360 kHz ? ? ? ? ? ? ? ?
18,4 MHz/2 kHz ? ? ? ? ? ?
? ? ? 000.04250 kHz ? ? ?
    Т Ч3-57 14,6 MHz ? ? ? ? ? ? ? ?
? 35 µs ? ? ? ? ? ? ?
35 MHz/1,2 MHz ? ? ? ? ? ?
? ? ? 00000.22 kHz ? ? ?
    У Ч3-35 17,3 MHz ? ? ? ? ? ? ? ?
? 22 µs ? ? ? ? ? ? ?
4,4 MHz/2,2 MHz ? ? ? ? ? ?
? ? ? 9999.9999 kHz ? ? ?
    Ф Ч3-24 940 kHz ? ? ? ? ? ?
2,9 MHz ? ? ? ? ? ? ? ?
7,75 MHz/2 MHz ? ? ? ? ? ?
? ? ? 01000.000 kHz ? ? ?

Variant Frequency counter type Frequency Period Frequency ratio Count-ing time Period multiplier Time marks The result on the digital display ± δΣ
    Х Ч3-35 2,22 MHz ? ? ? ? ? ? ? ?
21 µs ? ? ? ? ? ? ?
7,7 MHz/7 kHz ? ? ? ? ? ?
? ? ? 02664.3740 kHz ? ? ?
    Ц Ч3-24 49 MHz ? ? ? ? ? ? ? ?
17 µs ? ? ? ? ? ? ?
8,2 MHz/250 kHz ? ? ? ? ? ?
? ? ? ? 008750.00 kHz ? ? ?
    Ч Ч3-57 6,25 MHz ? ? ? ? ? ? ? ?
750 kHz ? ? ? ? ? ? ? ?
6,25 MHz/750 kHz ? ? ? ? ? ?
? ? ? ? 0750.0000 ms ? ? ?
    Ш Ч3-22 5 MHz ? ? ? ? 10-4 ?
? 12 µs ? ? ? ? ? ? ?
5,5 MHz/0,1 MHz ? ? ? ? ? ?
? ? ? 0000.2840 kHz ? ? ?
    Щ Ч3-24 12,6 MHz ? ? ? ? ? ? ? ?
? 10 µs ? ? ? ? ? ? ?
10,8 MHz/0,7 MHz ? ? ? ? ? ?
? ? ? 00001.000 kHz ? ? ?
    Ь Ч3-57 10,25 MHz ? ? ? ? ? ? ? ?
27 kHz ? ? ? ? ? ? ? ?
2,8 MHz/40 kHz ? ? ? ? ? ?
? ? ? ? 1 ms 000088.0 ms ? ? ?
    Э Ч3-35 ? 0,9 µs ? ? ? ? ? ? ?
? 9 µs ? ? ? ? ? ? ?
14,7 MHz/0,1 MHz ? ? ? ? ? ?
? ? ? 00442.2110 kHz ? ? ?


 

Variant Frequency counter type Frequency Period Frequency ratio Count-ing time Period multiplier Time marks The result on the digital display ± δΣ
    Ю Ч3-24 16,2 MHz ? ? ? ? ? ? ? ?
66 kHz ? ? ? ? ? ? ? ?
36 MHz/4 MHz ? ? ? ? ? ?
? ? 00024.400 µs ? ? ?
    Я Ч3-35 19,8 MHz ? ? ? ? ? ? ? ?
? 6 µs ? ? ? ? ? ? ?
20 MHz/20 kHz ? ? ? ? ? ?
? ? ? 004455.663 kHz ? ? ?
  Ч3-22 ? 7,5 µs ? ? ? ? ? ? ?
? 0,6 µs ? ? ? ? ? ? ?
25 MHz/0,4 MHz ? ? ? ? ? ?
? ? ? 00000.100 kHz ? ? ?

Example of W task solution

 

Table C2 – Terms of variant W.

Variant Frequency counter type Frequency Period Frequency ratio Count-ing time Period multiplier Time marks The result on the digital display ±δΣ
W Ч3-57 5 MHz 10 kHz – ? ? ? – ? – – 2,1 MHz/3 kHz – ? ? ? ? ? ? ? – ? ? – – ? ? ? 100.000 kHz ? ? ? ? ? ? ? ? ? ? ? ?

 

1. Determination of technical specifications of Ч3-57 from table D1.

 

Table C3 – Technical specifications of Ч3-57.

Frequency counter type Range of frequency measurement Range of period measurement Counting time Period multiplier Time marks
ЧЗ-57 0,1 Hz...100 MHz 1 µs...10 s 1...104 1...104 0,1 µs...1 ms

Task №1

- determine the signal period

 

   

 

- choose the frequency counter operation mode. Since Тs is not included in range of measurement period, then select the mode of measuring the frequency.

- determine the counting time by the formula:

 

, that is 103 ms< Т count<104 ms;

 

- taking into account, that the counting time can take only those values (100; 101; 102; 103; 104) ms, let’s choose Тcount= 10 3 ms=1 s.

- absolute error of discreteness is determined by the formula:

 

   

 

- relative error of discreteness:

 

   

 

- write the result on the display 5000.000 kHz. (Decimal point on the digital display is shifted to the left for the number of digits, which corresponds to the T count degree).

 

Task №2

- determine the signal period

 

  ,  

 

- taking into account, that the frequency and period of the signal are included in the measurement range, it is recommended to choose such mode of frequency counter, where measurement error will be minimal.

- calculate the relative error of discreteness in the mode of frequency measurements:

 

   

 

where Тcount is calculated as in the task 1,and equals 104 ms=10 s

- calculate the relative error of discreteness in the mode of period measuring:

- choose the period of time marks, (as the rule, minimal value), that's Т m=0,1 µs=10-7s.

- give an assessment of the value of multiplier n signal period, with the restriction on the counting unit (), N - number of marks, calculated by the counter, q - number of counter digits.

Period multiplier can assume such values n =100; 101; 102; 103; 104.

 

   

 

Since 103<n<104, then the value of period multiplier equals 103.

- determine the number of marks

 

   

 

- calculate the relative error of discreteness in the mode of period measuring:

 

   

 

that is, less than in the mode of frequency measurements, and therefore choose the mode of measurement period.

- for the selected mode define the absolute error ∆ N, time counting Тcount, and the measurement result of the display.

 

   
   

 

Display result is 100.0000 µs.

Task №3

It is measured the frequency ratio 2, 1 MHz/3 kHz.

- calculate the value of period multiplier in the condition of from the equation n · Т B= N · Т А

 

   

 

where ; q =7; then  

 

, and take n =104;  

 

- determine Т count:

 

   

 

- define the absolute error of discreteness:  

 

- calculate the relative error: , where  
.  

 

Record the result on the display: 700.0000.

 

Task №4

This problem is the reverse of the previous one. It is given the measurement result on the display 100.000 kHz. Obviously, the frequency counter operates in frequency measurement mode. From the example of previous tasks, we know, that Tcount. = 103 ms = 1 s;

 

- absolute error ;  
- relative error ;  

 

- signal frequency f s=100kHz; period of the signal Т s=10-5с. The results of solving tasks are shown in Table C4

 

Table C4- Results of solving the task W.

Variant Frequency counter type Frequency Period Frequency ratio Coun-ting time Period multiplier Time marks The result on the digital display
W Ч3-57 5 MHz 10 kHz – 100 kHz 2ּ10-5s 0,1ms – 10-5s – – 2,1 MHz/3 kHz – 1s 0,1s 3,33 s 1s – 103 104 – 10-7с – – 5000.000 kHz 100.0000 µs 700.0000 0100.000 kHz 1Hz 10-10s 10-4 1Hz 2ּ10-5 10-6 0,143 ּ10-6 10-5


 

 

Appendix D

 

Table D1 – The main technical characteristics of frequency counter.

Frequency counter type Range of frequency measurement Range of period measurement Counting time, ms Period multiplier Time marks The error of quartz generator Number of digits
ЧЗ-22 10 Hz...12 MHz 10 µs...100 с 1...104 1...104 0,1 µs...1 ms 10-7  
ЧЗ-24 10 Hz...50 MHz 1 µs...100 с 1...104 1...104 0,1 µs...1 ms 10-8  
ЧЗ-36 10 Hz...50 MHz 10 µs...100 с 1...104 1...104 0,1 µs...1 ms 10-8  
ЧЗ-57 0,1 Hz...100 MHz 1 µs...104 с 1...104 1...104 0,1 µs...1 ms 10-7  
ЧЗ-35 10 Hz...50 MHz 20 µs...100 с 1...104 1...104 0,1 µs...1 ms 10-8  

Literature

 

1. «Вимірювання в системах зв’язку.» Книга 1. Загальні радіовимірювання./ Коломієць Л.В., Козаченко М.Т. та ін. - Одеса, ВМВ, 2009.

2. «Метрологія, стандартизація та вимірювання в техніці зв’язку» / Хромой Б.П., Кандінов А.В. та ін. - М.: Радіо та зв'язок связь, 1986.

3. „Метрологія у галузі зв’язку ”, книга І. Метрологія, стандартизація, менеджмент якості та оцінка відповідності / Л. В. Коломієць М. Т. Козаченко - підручник. О. Вид-во “Стандарт”. 2006.

4. ДСТУ 2681-94 Державна система забезпечення єдності вимірювань. Метрологія. Терміни та визначення.

5. ДСТУ 1.0-93 Державна система стандартизації України. Основні поняття.

 


 

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