1. MAE 3340 INSTRUMENTATION SYSTEMS 1 Laboratory 6: Wheastone Bridge and Measurement Uncertainty Lab Objectives: -- Understand Wheatstone Bridge Properties --Power Dissipation in Resistor --Reading the Resistor Labeling Code --Balancing a Resistance Bridge --Using a resistance bridge to measure and unknown resistance --Understand how to Calculate statistics levels for a random population Chapter 7, pp. 241-249, B.M.L. Chapter 3, pp. 34-63, B.M.L.

2. MAE 3340 INSTRUMENTATION SYSTEMS 2 You will build this bridge … Known Precision 100  resistors Variable Decade Resistor Unknown Resistor You will Balance this bridge … Using R 3 To determine R 4

3. MAE 3340 INSTRUMENTATION SYSTEMS 3 Excitation Voltage … The Precision 100  resistors (+1%) Have a 1/4 watt capability … but to be safe … we want To limit power dissipated To 1/40 watt … need to calculate V ex So that power dissipated in R 1, R 2 ~ 1/40 watt V ex

4. MAE 3340 INSTRUMENTATION SYSTEMS 4 Resistance Bridge Summary (see Appendix).. Infinite Meter Impedance

5. MAE 3340 INSTRUMENTATION SYSTEMS 5 Power Supply

6. MAE 3340 INSTRUMENTATION SYSTEMS 6 Decade Resistor Box There are 3 decade resistors that measure higher resistances, and 2 that measure lower resistances. They will be marked “High Resistance” or “Low Resistance”. These can create a resistance anywhere between 0.01 and 900 ohms in 0.01-ohm increments (Low Resistance), or 1 to 99,000 Ohms in 1-Ohm increments (High Resistance).

7. MAE 3340 INSTRUMENTATION SYSTEMS 7 Wheatstone Bridge on Breadboard

8. MAE 3340 INSTRUMENTATION SYSTEMS 8 Your Circuit 100  RxRx 100  Power supply Meter Decade resistance Unknown resistance You will adjust decade resistance until Meter reads zero voltage (balance)

9. MAE 3340 INSTRUMENTATION SYSTEMS 9 Balancing Technique Solve for unknown resistance Adjust R 3 until I M = 0 V ex Good way to sense An unknown resistance R 3 variable resistance … decade box

10. MAE 3340 INSTRUMENTATION SYSTEMS 10 Resistance Table 20 resistors selected at random … You will fill out this table

11. MAE 3340 INSTRUMENTATION SYSTEMS 11 Lab Report Summary (1) When you are finished, get together with the other 4 groups in your section and make a text file containing all 80 samples.. … Using all the data, compute an estimate of the normalized mean and the standard deviation for the pool of 80 resistors, your 20 resistors. “sample mean” “sample Std. Dev.”

12. MAE 3340 INSTRUMENTATION SYSTEMS 12 Lab Report Summary (2) Down Load and Open Histogram Code … http://www.neng.usu.edu/classes/mae/3340/section6/resistor_data_histogram.llb Make a histogram of the data with all 80 samples and attach it to this lab (Labview makes this easy). … A VI has been built for this purpose … there is a link on Web page … http://www.neng.usu.edu/classes/mae/3340/section6/resistor_data_histogram.llb

13. MAE 3340 INSTRUMENTATION SYSTEMS 13 Lab Report Summary (3) A histogram divides the range of possible values up Into “bins” and plots the % of occurrences of values within that bin Histogram data

14. MAE 3340 INSTRUMENTATION SYSTEMS 14 Lab Report Summary (4) What is the precision uncertainty of the mean based on all 80 resistors? (95% confidence)? Using only your 20 resistors, estimate the normalized mean, and the precision uncertainty of the mean to 95% confidence. Which one would you expect to have the best precision uncertainty? 80 samples 20 samples

15. MAE 3340 INSTRUMENTATION SYSTEMS 15 Precision Uncertainty Analysis (1) Sample Mean, Standard Deviation Estimates Sample Standard Deviation Estimates

16. MAE 3340 INSTRUMENTATION SYSTEMS 16 Precision Uncertainty Analysis (2) Confidence Interval for Sample Mean Estimate Standard Error of the Sample Mean 95% Confidence Interval --->

17. MAE 3340 INSTRUMENTATION SYSTEMS 17 Precision Uncertainty Analysis (3) Area under curve = 0.95

18. MAE 3340 INSTRUMENTATION SYSTEMS 18 Precision Uncertainty Analysis (4) Area under curve = 0.95 precision uncertainty ….in mean estimate

19. MAE 3340 INSTRUMENTATION SYSTEMS 19 Error Analysis (1) Given the relationship between the known resistors and the unknown resistors, find the uncertainty in your measurement that is due to the uncertainty in the values of R 1 and R 2 (100 , +1%). Assume that the decade resistor is exact. (no error)… Hint … How do you account for the fact that the meter only has two digits of precision in voltage?… see next page Compare this calculated value to the standard deviation you computed based on your 20 resistors based on all 80 resistors Comment on the manufacturer’s claim as to the accuracy of these resistors.

20. MAE 3340 INSTRUMENTATION SYSTEMS 20 Uncertainty Analysis (6) How do you account for the fact that the meter only has two digits of precision

21. MAE 3340 INSTRUMENTATION SYSTEMS 21 Uncertainty Analysis (7) How do you account for the fact that the meter only has two digits of precision But ….

22. MAE 3340 INSTRUMENTATION SYSTEMS 22 Uncertainty Analysis (8) Meter resolution … 0.01 Volts

23. MAE 3340 INSTRUMENTATION SYSTEMS 23 Uncertainty Analysis (9) Meter resolution … 0.01 Volts ….  R 1 /R 1 =  R 2 /R 2 =1% V ex ---> voltage for 1/4 watt, {R 1, R 2 } ~ 0

24. MAE 3340 INSTRUMENTATION SYSTEMS 24 Types of Resistors (1) Fixed resistors Surface Mount Resistors

25. MAE 3340 INSTRUMENTATION SYSTEMS 25 Types of Resistors (2) Carbon composition resistors consist of a solid cylindrical resistive element with embedded wire leadouts or metal end caps to which the leadout wires are attached. Resistive element is made from a mixture of finely ground (powdered) carbon and an insulating material (usually ceramic). The mixture is held together by a resin. Resistance is determined by the ratio of the fill material (the powdered ceramic) and the carbon.

26. MAE 3340 INSTRUMENTATION SYSTEMS 26 Types of Resistors (3) Resistive coating is peeled away in an automatic machine until resistance between ends rod is within tolerance Metal leads and end caps are added and resistor is covered insulating coating and painted with colored bands to indicate the resistor value. Carbon film resistors are cheap and easily available, with values within 10% or 5% of their marked, or 'nominal' value. During manufacture, a thin film of carbon is deposited onto a small ceramic rod.

27. MAE 3340 INSTRUMENTATION SYSTEMS 27 Types of Resistors (4) Metal Film resistors Metal-film resistor is a common type of high precision axial resistor today is referred to as a Metal Film resistors are usually coated with nickel chromium (NiCr) Resistance value is determined by cutting a helix through the coating rather than by etching. The result is a reasonable tolerance (0.5, 1, or 2%).

28. MAE 3340 INSTRUMENTATION SYSTEMS 28 Types of Resistors (5) Wirewound resistors are commonly made by winding a metal wire around a ceramic, plastic, or fiberglass core. The ends of the wire are soldered or welded to two caps, attached to the ends of the core. The assembly is protected with a layer of paint, molded plastic, or an enamel coating baked at high temperature.enamel For higher power wirewound resistors, either a ceramic outer case or an aluminium outer case on top of an insulating layer is used. Wirewound resistors

29. MAE 3340 INSTRUMENTATION SYSTEMS 29 Types of Resistors (6) Metal Oxide resistors are non-inductive and substitute for carbon comp in most cases. They have a resistance element formed by the oxidation reaction of a vapor or spray of tin chloride solution on the heated surface of a glass or ceramic rod. The resulting tin-oxide film is adjusted to value by cutting a helix path through the film. Metal Oxide resistors

30. MAE 3340 INSTRUMENTATION SYSTEMS 30 Types of Resistors (7) Fixed resistors Resistors are manufactured in values from a few milliohms to about a Gigaohm Only a limited range of values from the IEC 60063 preferred number series are commonly available. IECpreferred number These series are called E6, E12, E24, E96 and E192. The number tells how many standarized values exist in each decade (e.g. between 10 and 100, or between 100 and 1000). So resistors confirming to the E12 series, can have 12 distinct values between 10 and 100, whereas those confirming to the E24 series would have 24 distinct values. Surface Mount Resistors

31. MAE 3340 INSTRUMENTATION SYSTEMS 31 Types of Resistors (8) E12 preferred values: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 Ohms Multiples of 10 of these values are used, … 0.47 , 4.7 , 47 , 470 , 4.7 k , 47 k , 470 k , and so on ….. E24 preferred values, includes E12 values and: 11, 13, 16, 20, 24, 30, 36, 43, 51, 62, 75, 91 Ohms In practice, the discrete component sold as a "resistor" is not a perfect resistance, as defined above. Resistors are often marked with their tolerance (maximum expected variation from the markedtolerance resistance).

32. MAE 3340 INSTRUMENTATION SYSTEMS 32 Types of Resistors (9) ▪ Rheostat: variable resistor with two terminals, one fixed and one sliding. It is used with high currents.Rheostat ▪ Potentiometer: a common type of variable resistor. One common use is as volume controls on audio amplifiers and other forms of amplifiers.Potentiometeraudio amplifiers Variable resistors Construction of a wire-wound variable resistor. The effective length of the resistive element (1) varies as the wiper turns, adjusting resistance.

33. MAE 3340 INSTRUMENTATION SYSTEMS 33 Resistor Color Code (1) A resistor is device whose only purpose it is to offer resistance to current flow. Nominal resistance of a resistor is printed onto the resistor in code. Pattern of colored rings is used. Most resistors have three rings to encode the value of the resistance, and one ring to encode the tolerance (uncertainty) in percent.

34. MAE 3340 INSTRUMENTATION SYSTEMS 34 Resistor Color Code (2) Ring Colors are internationally defined to as integers 0 -- 9. First band is the band closest to one end of the resistor. First and second band together make a two-digit integer number. Multiply number represented by the color of the first band by 10 and add the number represented by the color of the second band. Result is a two-digit integer number.

35. MAE 3340 INSTRUMENTATION SYSTEMS 35 Resistor Color Code (3) Ring Colors are internationally defined to as integers 0 -- 9. Number represented by the color of the third band is the number of zeroes that must be appended to the number obtained from the first two bands to get the resistance in Ohms. (If this number is 1, you add one zero, or multiply by 10 1, if the number is 2, you add two zeroes, or multiply by 10 2, etc.)

36. MAE 3340 INSTRUMENTATION SYSTEMS 36 Resistor Color Code (4) Ring Colors are internationally defined to as integers 0 -- 9. The next band, (i.e. the fourth band), is the tolerance band -- typically either gold or silver. A gold tolerance band indicates actual value will be within 5% of the nominal value. A silver band indicates 10% tolerance.

37. MAE 3340 INSTRUMENTATION SYSTEMS 37 Resistor Color Code (5) Ring Colors are internationally defined to as integers 0 -- 9. If the resistor has one more band past the tolerance band it is a quality band. Read the number as the % failure rate per 1000 hours, assuming maximum rated power is being dissipated by the resistor.

38. MAE 3340 INSTRUMENTATION SYSTEMS 38 Resistor Color Code (6) Look for gap

39. MAE 3340 INSTRUMENTATION SYSTEMS 39 Resistor Color Code (7) Another Color Coding Example

40. MAE 3340 INSTRUMENTATION SYSTEMS 40 Precision Resistor Coding 5-band axial resistors5-band identification is used for higher tolerance resistors (1%, 0.5%, 0.25%, 0.1%), to notatetolerance the extra digit. The first three bands represent the significant digits, the fourth is the multiplier, and the fifth is the tolerance.tolerance

41. MAE 3340 INSTRUMENTATION SYSTEMS 41 Color Code Quiz 10 6 5% 91 3300 5%

42. MAE 3340 INSTRUMENTATION SYSTEMS 42 Using Labview for Histogram Plot (1)

43. MAE 3340 INSTRUMENTATION SYSTEMS 43 Using Labview for Histogram Plot (2)

44. MAE 3340 INSTRUMENTATION SYSTEMS 44 Using Labview for Histogram Plot (3) “double click” Set bin intervals And min/max On front panel