Lab #6 Accuracy and Precision

ECE 170 Lab #6 Accuracy and Precision

Lab #6 Accuracy and Precision

In this experiment, you will become acquainted with the terms accuracy and precision. You have used several different measurement devices in the past few labs. The precision of some measurements and the accuracy of these measuring devices will now be investigated.

First however, let's look at some definitions.

ERROR

Error is defined as the difference between the true value and the measured value. Except in artificial cases, the true value is never known. Therefore, the value of an error is never known. In laboratory work, it is better to refer to the difference between two values, perhaps measured and theoretical, rather than "error" in a measurement. Sometimes the term error is used, perhaps inappropriately, to mean inaccuracy in the measuring instrument or mistakes in reading the instrument.

ACCURACY

Accuracy is defined as the closeness to the true value and, like an error, is never known in practical cases. When the accuracy of an instrument is specified, it is the manufacturer's claim of how close the measurement will be to the actual value.

PRECISION

Precision is the closeness of grouping of data. It is related to the repeatability of a measurement or to the number of significant figures that a measuring device is capable of producing.

Precision and accuracy do not necessarily go together. A measuring device may be very accurate but not precise, or it may be very precise but not accurate. To illustrate this point, consider the following experiment: We want to use two instruments to measure the resistance of a 10k resistor. To make sure of the measurement, several readings are taken with each.

The readings from one meter are

10.8 k

9.3 k

9.9 k

10.1 k

10.7 k

The readings from a second meter are

15.11461 k

15.11462 k

15.11461 k

15.11460 k

15.11461 k

What can we say about the accuracy and precision of the two instruments? Accuracy is the closeness to the true value. The true value is not known, but it seems reasonable that the manufacturer of the resistor has labeled the resistor as a 10k resistor because the resistance is somewhere around 10k. Therefore the first instrument gives reasonable results, although the readings jump around quite a bit. However, the second instrument gives results that are very repeatable, but we know that the results do not seem reasonable. By comparison, the first meter is accurate but not precise and the second meter is precise but not accurate. Figure 6.1 provides a visual explanation about accuracy and precision using three dartboards as an example.

Lack of accuracy and precision in a measuring device always leads to an uncertainty in a measurement. One method to indicate the uncertainty in a measurement is to include a range. For example, a data entry of VAB = 14 ± 1 Volts indicates that the experimenter has read 14 volts from the measuring device, but the voltage may be as low as 13 or as high as 15 volts. The range of uncertainty may result from lack of accuracy, lack of precision, or both.

Another method of indicating the uncertainty in a measurement is in the number of significant figures in the data entry. A measurement of 14.0 volts indicates something different than 14 volts. There is an implied range that goes along with data entries, and that is  half of the place value of the last digit. For example, a recording of 14.0 volts implies 14 ± 0.05 volts, and 14 volts implies 14 ± 0.5 volts.

For the digital multimeter (DMM), the manufacture states the accuracy to be ±0.01% of the displayed reading when measuring DC voltage. The precision is based on how many significant figures are displayed.

For the oscilloscope, the stated accuracy is ±3%. The precision is based on how many significant figures can be read from the scope display.

For some analog meters, the precision is based on how many significant figures are read from the scale. The accuracy is stated by the manufacturer, but this accuracy is usually based on the full-scale deflection of the needle. When the deflection is less than full scale, the range is still based on the full-scale deflection. For example, if the full-scale value of a voltmeter is 25 volts and the stated accuracy is 5%, the range of a reading is ± (.05)(25) = ± 1.25 volts. A reading anywhere on the scale has a range of ±1.25 volts. If the reading is low, say 5 volts, this means that the measurement is 5 ± 1.25 volts. Readings low on the scale of analog meters may produce a range that is a large percentage of the reading.

Sometimes the precision of a device exceeds the accuracy, although this is not good engineering design practice. If this is the case, you should not record a measurement such as 84.5847 ± 0.5. The range indicates that a better representation is 85. The implied range of this value is consistent with the accuracy.

When doing computations based on laboratory measurements, do not write answers that will mislead the reader into believing that your measurements have a smaller uncertainty than they really do. For example, if you measure a voltage of 5.0 Volts and calculate the current using Ohm's Law with a resistor of 4.7k, do not write the answer as 1.0638298mA. A standard practice is to use the same number of significant figures in the final value as the measurement with the least number of significant figures. In that case the answer is best represented as 1.1mA.

The range of measured values is also important when adding or subtracting numbers. In subtraction in particular, misleading results can be obtained if the numbers are relatively close together. For example, the potential difference between two points in a circuit is obtained by subtracting the voltage at one point from the voltage at another point. If V1 = 6.4 V and V2 = 6.3 V, subtraction yields V1 – V2 = 0.1 volt. The implied ranges of the numbers are  0.05 volts, so the answer to the subtraction could be as high as 0.2 volts or as low as 0 volts. (This is determined by taking the extremes of V1 and V2) The result might then be expressed as 0.1 ± 0.1 volt, so the uncertainty in a calculation could be as large or larger than the answer.

Instructional Objectives

6.1Explain the difference between accuracy and precision.

6.2Determine the range of uncertainty of a measurement due to the stated accuracy of an instrument.

6.3Determine the range of uncertainty of a measurement based on the implied precision of a reading.

6.4Determine the best instrument to use for a particular measurement.

Procedure

1. Construct the circuit of Figure 6.2. Measure the voltages V1, V2, and V3 using the HP DMM. Since the instantaneous voltage is constantly changing, we use an averaging figure of merit called the root-mean-square or RMS voltage. This value stays relatively constant for periodic voltage waveforms. The calculation of this value is beyond the scope of this course but the equipment is designed to determine it automatically. Record your measurements in Table 6.1. The values will likely jump around a little. Record high and low values and use the average in your calculations.

Figure 6.2 Basic measurement circuit

Note an unchanging voltage over time is called the DC voltage and is represented as VDC.

1. Measure the same voltages using the digital oscilloscope display. For each voltage, take a measurement for the largest sensitivity setting (volts/div) possible to get the entire magnitude of the waveform on the display. Decide on the number of significant figures that are appropriate when recording voltages from the display with the oscilloscope. You will have to read the maximum and minimum values of the waveform, find the difference and then multiply the value by .3535 to get the same units as the DMM provides. You will learn about this factor of ..3535 when you take ECE 230.

NOTE:

V1 can be measured with the digital oscilloscope only if the circuit is NOT referenced to earth ground due to the scope’s single ended probes. Therefore you need two probes to display this voltage. Put one probe on one side of the resistor and the other probe on the other side of the resistor and then use the subtraction function of the scope. Then if you turn off both channels, you should still have the difference displayed on the scope to take your measurements.

1. Now measure the same voltages a third time using the voltage measurement functionality of the digital oscilloscope. For each voltage, take a measurement for the largest sensitivity setting (volts/div) possible. Use the “Measure Voltage” feature and select "rms voltage" to get your readings. The values will likely jump around a little. Record high and low values and use the average in your calculations.

Again we need to handle V1 a little differently since V1 is being calculated within the scope. You will need to use the cursors function of the scope to get this reading. Assuming that only the difference between the two channels is displayed, select cursor V1 to the top of the waveform and V2 to the bottom of the waveform. V will give you V2-V1 that you will again need to multiply by 0.3535. Also note V2 and V1 on the scope are coincidentally the same as the variable names in our circuit.

1. Record your data in Table 6.1.

1. From each of your measurements, calculate the voltage difference V1– V2. Include a range with your result. Use the average values of V1 and V2 from Table 6.1 for your calculations. Place your results in Table 6.1.

1. From each of your instruments, add the voltages V1and V2and call it V3’. Once again use the average values of V1 and V2 and place your results in Table 6.1.

1. For the data in Table 6.1(next page), determine the range due to accuracy and the range due to precision for each measurement as the example suggests.

/ Accuracy
/ Precision
/ Accuracy / 3.000  0.090
/ Precision / 3.0000.0005
/ Accuracy / 3.00000.0003
Precision / 3.00000.00005
Example (V) / V1 max / V1 min / V1 Average / V2 max / V2 min / V2 Average / V3 max / V3 min / V3 Average / V1 – V2 / V3’

1. Display the frequency of V3 with the digital oscilloscope using the measure time feature and select "frequency" to get your readings. Adjust the function generator to produce a sine wave and adjust the frequency dial for a frequency as close to exactly 1 kHz as possible using the 1 kHz scale and getting close to "1" on the dial.

1. Record the actual measured frequency of V3 in Table 6.2.

Frequency measured on X 1 scale / Frequency measured on X 0.1 scale / Frequency measured on X 10 scale

Table 6.2: Frequency Measurement Table.

10.Switch the frequency scale to 10 kHz. Adjust the frequency dial for a frequency as close to 1 kHz as possible using the 10 kHz scale (as close to ".1" on the dial as possible). Note that your reading for this case may vary from 600Hz up to about 2kHz. Record the frequency closest to 1kHz that your function generator can produce.

11.Adjust the frequency dial for a frequency as close to 1 kHz as possible using the 100 Hz scale (as close to "10" on the dial as possible). Record the actual measured frequency of V3 in Table 6.2.

Unless you were extremely lucky, your results should be closest to the target frequency of 1 kHz when you were on the 100 Hz scale and the dial was set at "10". If this is not the case, at least you should have seen that the function generator was less sensitive to small rotations of the dial working on the higher end of the dial (i.e. near "10") as opposed to the lower end (i.e. near 0.1-1). The explanation for these results is beyond the scope of this course but should be helpful to you in future labs.

1. Without changing the settings on the function generator, measure the frequency of the sine wave using the waveform displayed on the oscilloscope. This is not a direct measurement. You must measure the period (T) or time it takes to complete one cycle, and then find the frequency by dividing your result into 1. So frequency (f) = 1/T. Your results will be in Hz.

T ______f ______

13.We will now adjust the amplitude or peak-to-peak value. You need to use the measure voltage feature and select "Vpp" to get your readings. Adjust the amplitude of the waveform on the function generator so that the signal is reading about 2 Vpp.

14.Adjust the vertical scale and record the peak-to-peak voltagereading at each scale setting in Table 6.3. Do not adjust the amplitude of the function generator between readings.

15.With the largest waveform being displayed (on the 500 mV/div vertical scale), turn the vernier "on" and adjust the vertical scale so that the waveform is taking up almost the entire vertical scale. Record the value of Vpp. This should be your most accurate reading. As a general rule for the digital oscilloscopes, the more of the vertical scale you can use, the more accurate your voltage reading will be.

Vertical Scale (V/div) / Peak-to Peak Voltage Reading (V)
Vernier On _____mV/div
500mV/div

1V/div

2V/div
5V/div
10V/div
20V/div
50V/div

Table 6.3: Varying V/div Data.

Post LabQuestions

1.Explain in your own words the difference between accuracy and precision.

2.Discuss the advantages and disadvantages of each of the three measuring techniques/devices used to acquire the data in Table 6.1.

3.If your oscilloscope had a maximum scale of 5V per division, and there were 8 vertical divisions on the scope display, explain how you could measure a pure AC voltage of 62 Volts peak-to-peak.

4.For the circuit we used from Figure 6.2, the voltage between the two resistors should be exactly half the supply voltage value. What are some of the factors that affect the accuracy of this assumption?

5.If you wanted to know the value of the voltage from the wall outlet in the lab, what instrument in the lab would you use to measure it? Justify your decision by explaining why you would use that instrument. (please don’t try this using trial and error)

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