Understanding Wheatstone Bridge Properties with Resistance Measurements

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. You will build this bridge … Variable Decade Resistor Known Precision 100  resistors • You will Balance this bridge … Using R3 To determine R4 Unknown Resistor

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 Vex So that power dissipated in R1, R2 ~ 1/40 watt Vex

4. Resistance Bridge Summary (see Appendix) • .. Infinite Meter Impedance

5. Power Supply

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. Wheatstone Bridge on Breadboard

8. Your Circuit Decade resistance Power supply 100  100  Unknown resistance Rx • You will adjust decade resistance until Meter reads zero voltage (balance) Meter

9. Balancing Technique • Good way to sense An unknown resistance Vex • Solve for unknown resistance • Adjust R3 until IM = 0 R3 variable resistance … decade box

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

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. 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. 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. 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? 20 samples 80 samples

15. Precision Uncertainty Analysis (1) • Sample Mean, Standard Deviation Estimates • Sample Standard Deviation Estimates

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

17. Precision Uncertainty Analysis (3) Area under curve = 0.95

18. Precision Uncertainty Analysis (4) • precision uncertainty ….in mean estimate Area under curve = 0.95

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 R1 and R2 (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. Uncertainty Analysis (6) • How do you account for the fact that the meter only has two digits of precision

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

22. Uncertainty Analysis (8) • Meter resolution … 0.01 Volts

23. Uncertainty Analysis (9) • Meter resolution … 0.01 Volts • …. R1/R1 = R2/R2 =1% • Vex ---> voltage for 1/4 watt, {R1, R2} ~ 0

24. Types of Resistors (1) Fixed resistors Surface Mount Resistors

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. Types of Resistors (3) •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. • 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.

27. Types of Resistors (4) • 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%). Metal Film resistors

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. • 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. 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. Types of Resistors (7) • 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. • 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. Fixed resistors Surface Mount Resistors

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 marked resistance).

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

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. 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. 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 101, if the number is 2, you add two zeroes, or multiply by 102, etc.)

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. 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. Resistor Color Code (6) Look for gap

39. Resistor Color Code (7) • Another Color Coding Example

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

41. Color Code Quiz 106 5% 5% 91 5% 3300

42. Using Labview for Histogram Plot (1)

43. Using Labview for Histogram Plot (2)

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