Pressure sensor experiment

AIMS AND OBJECTIVES

The aim of this laboratory is to understand the importance of statistical distributions in the operation of measurement equipment Involves

1 The measurement of the offset voltage and offset current from a large collection of operation amplifiers

2 The analysis of the distribution of the measured data3 The use of an operation amplifier to increase the signal level of a pressure sensor

selecting the amplifier from the statistical population of amplifiers4 Calibration of the pressure sensor

PART ONE MATERIALS USED IN THE EXPERIMENT

The operational amplifiers LF353 TL072 and LM358 Op- amp tester to measure the offset voltage and the offset current A Multimeter used for measuring the voltage output

METHOD USED IN THE EXPERIMENT Connect the Multimeter to the banana plug and set the meter to the voltage range

required The operational amplifiers used in this lab have amplifiers on two physical sides on

the chip (the left and the right) The Switch S4 (in Figure 1) selects either the left side or the right side of an

operational amplifier Once the left (or right) op amp is selected using Switch S4 ‐switch S1 on the left (or S2 on the right) selects the offset voltage or the offset current When the offset voltage is selected the output voltage can then be measured at the banana plug

SAMPLE CALCULATIONS

To calculate the voltage offset we used this calculation when the offset voltage is selected

V0 = -( R2

R1)Voffset = -100Voffset V offset=

minusV 0

100 Example

for 1 V 0=minus00496V Therefore V offset=minus(minus00496)

100=iquest04960mV

To calculate the offset current when the offset voltage and offset current is selected the output voltage (V0) is given by

v0=iquestiquest2R3 I offset iquest) ndash(R2

R1

iquestV offset=202times107 I offsetminus100V offsetiquest

iquest

I offset= V 0+100V 0 ffset

202times107 Example for 1 V 0=minus00496V V offset=iquest04960mV

Therefore I offset= minus00496+100times04960

202times107 = 24530microA

The mean x = 1nsumi

n

Xi and the standard deviation S=radic 1nminus1sumi=1

n

x iminusx

The Gaussian distribution f(z)= 1radic2 π

eminus1

2z 2

where z=( x - x)s

The uncertainty was Uc = kUx where the Ux= the experimental standard deviation of the mean and k=217 For example the LF353 op-amp the sample mean for the Voffset was 026mV and the S= 1978 and the number of samples n=13 therefore Ux=Sradic n= 1978radic 13 = 0549 Uc= 217 times0549 = 119 therefore the mean and spread of the mean is 026mVplusmn119Mv This was calculated using the ISO guide to the expression of uncertainty in measurement and is expressed by the stated interval which is estimated to contain the measurand with 95 probability The coverage factor for the interval is 217 (from the student t distribution)

GRAPHS

Offset voltage represented as Voffset

Offset current represented as Ioffset

Figure 1Measured values and normal distribution for offset voltage for the LF353 op-amp

Figure 2 Measured values and normal distribution for offset current for the LF353 op-amp

Comment on the graphs for LF353 op-amp

After calculating the Voffset and Ioffset of various samples on the right and left side of the op-amp and plotting it on the graph it was observed that there was a random distribution of values about the sample mean The sample mean here was calculated to be 026mV and -129microA for the Voffset and Ioffset respectively The Voffset and Ioffset on the right were observed to have all its measured values above the mean while the Voffset and Ioffset on the left of the measured values were below the sample mean The spread or imprecision of the mean in the graph is a plusmn119mV for the Voffset on the right and left while that of I offset has a spread of plusmn591 microA about the mean

Figure 3 The distribution of measured data of offset voltage in the LM358 op-amp

Figure 4 The distribution of measured data on the offset current of the LM358

Comments on the graph of the Voffset and Ioffset of the LM358 op-ampAfter calculating the Voffset and Ioffset of various samples on the right and left side of the op-amp and plotting it on the graph it was observed that there was a random distribution of values (spread) with about two values of both the Voffset and Ioffset coming off the sample

mean The sample mean here was 015mV and 073microA for the Voffset and Ioffset respectively The Voffset and Ioffset on the right were observed to have most of its measured values above the mean with at least two of the values exceeding the sample meanwhile the Voffset and Ioffset

on the left of the measured values was below the sample mean with two of its measured data also above the sample mean The spread or imprecision about the sample mean is plusmn069mV for the Voffset on the right and left while that of Ioffset is spread is plusmn343microA about the sample mean

Figure 5 The distribution of measured data of offset voltage in the TL072 op-amp

Figure 6 The distribution of measured data on the offset current of the TL072

Comments on the graph of the Voffset and I offset of the TL072 op-ampAfter calculating the Voffset and Ioffset of various samples on the right and left side of the op-amp and plotting it on the graph it was observed that there was a random distribution of values (spread) with the Voffset and Ioffset spread below the zero point with the sample mean being -251mV and -1243microA for the Voffset and Ioffset respectively The uncertainty and spread about the mean was plusmn136mV for Voffset and plusmn674microA for Ioffset

Discussion of the findings for part 1

The sample mean of the Voffset and Ioffset for the LF353 op-amp was obtained as 026mV plusmn119mV and -129microA plusmn591 microA respectively This reveals that the op-amp has a low input offset voltage and an internally trimmed offset voltage and they also a low offset and bias current with little drift from the required zero input Voffset and Ioffset The same mean of the Voffset and Ioffset for the LM358 op-amp is 015mVplusmn069mV and 073microA plusmn343microA respectively This reveals that the op-amp has a very low input offset voltage closer to zero and it also has a very low offset and bias current (lower than that of LF353 op-amp with a very little drift from the required zero input Voffset and Ioffset The sample mean of the Voffset and Ioffset for the TL072 op-amp was obtained as -251mV plusmn136mV and -124304microA plusmn674 microA respectively Though little offset voltage it was larger than the other two op-amp and with a large offset or drift of current from the zero point than the other two op-amp The random spread of values in the measured data was due to several sources of error which made the reading very different from the expected input offset voltage and input offset current which was expected t be zero in an ideal state This uncertainty in measurement was due to a lot of errors which we had no control over such as calibration uncertainty in the equipments the ambient conditions such as the changes in the pressure temperature and humidity calibration factor and ageing of the equipments furthermore errors such as taking just a few samples of the op-amp could have resulted into such deviation and drift from the actual readings

PART TWO MATERIALS USED

The MPX 2102A pressure sensor is used which is a silicon piezoreisitive pressure sensor providing a highly and linear voltage output

A printed circuit board with a specially designed breadboard Two Resisitors with colour bands resistor 1- 15kΩ and the resistor 2- 680kΩ A short and a long tube multimeter scale ruler and a syringe We chose the best and worst offset voltage for LF353 op-amp as analyze below

Figure 6 The best and worst offset voltage for the LF353 op-amp

THE CIRCUIT USED TO AMPLIFY THE PRESSURE OUTPUT

Figure 7The circuit used to amplify the pressure output MPX2102 pressure sensor converts pressure change into micro voltage changes as output signal As seen in the datasheet the voltage gain of LF353 is given as 100 VmV which means 1 mV change in input voltage from the pressure sensor will result in 1 V voltage change in final output This is equivalent to 105 times the input voltage The amplifier used to amplify the pressure output is a differential amplifier and amplifies the difference between two voltages but does not amplify the particular voltage and has the advantage of having a very high common mode rejection ratio (CMRR) which rejects the noise sources

present on both V1 and V2 However the gain in the amplifier used is given as G = R2

R1 =

68015

=

453 METHOD USED FOR CALIBRATION

Connect the circuit correctly as indicated as indicated in figure 7 using the best and the worst voltage gotten from the LF353 op-amp

We selected a long tube and measured the length of the tube as L1=1930mm and the inner diameter of the tube D1=4mm the volume = 24253cm3

We connected one end of the tube to one sensor inlet and measured voltage V1 we filled the syringe with water and then connect it to the other end of the tube and measure voltage V2

We marked the length of the rise of the water in the tube and placed the tube horizontally along a ruler and measure the length of water pushed into the tube at various increments (by pushing slowly on the syringe)

Measure the voltage V(L) at each value of water length L pushed into the tube We determined the pressure change in the tube which results from the

compressed volume of air in the tube SAMPLE CALCULAIONSTo calculate pressure we use P0V0 = P1V1 P0 = 1atm =1013kPa V0 =volume of the tube

Vwater = π r2L V1= V0- Vwater P1= P0V 0V 1

Gauge pressure (pressure differential) Pgauge=P1-P0

To determine the output voltage from the the data sheet we used the formula

Vouput (mV) = mX+bG

times1000 where m= slope b= intercept G=gain

UNCERTAINTY ANALYSIS FOR THE MEASURED DATA2 Left (Worst) 0 1 2 3 4 5 6

Voltage1 -1417 -0773 -0217 0372 0848 1440 2110Voltage2 -1412 -0790 -029 0295 0892 1436 2090Voltage3 -1410 -0780 -0259 0306 0834 1413 2080Voltage4 -1438 -0789 -029 0301 0900 1385 2020Voltage5 -1410 -0772 -026 0312 0887 1401 2090Voltage6 -1408 -0786 -0239 0263 0861 1409 2207

Voltage7 -1425 -0766 -0223 0341 0841 1505 2070Voltage8 -1419 -0808 -027 0298 0870 1459 2080Voltage9 -1432 -0789 -0284 0254 0840 1428 2060

Voltage10 -1410 -0812 -0282 0363 0835 1344 2060Measurand (mV) -142plusmn001 -079plusmn001 -026plusmn002 03plusmn002 086plusmn002 142plusmn00

3208plusmn003

12 Right(Best) 0 1 2 3 4 5 6

Voltage1 -01537 0515 1049 1685 223 289 358Voltage2 -01866 0424 1024 1683 227 291 364Voltage3 -01558 0474 1056 1651 229 285 358Voltage4 -01607 0519 1107 1679 23 28 35Voltage5 -01634 0446 11051 1631 218 274 351Voltage6 -01746 0499 1024 1624 217 287 35Voltage7 -018 0505 1101 1717 233 285 358Voltage8 -0174 0475 1057 1673 226 292 359Voltage9 -0163 0549 1114 1708 227 284 355

Voltage10 -0169 0519 1073 1646 222 287 359Measurand (mV)

-0168plusmn002

049plusmn003 107plusmn002

1669plusmn003

2282plusmn002

286plusmn002

354plusmn003

Table 1 Showing the measured voltages in the circuit with uncertainty

This was calculated using the ISO guide to the expression of uncertainty in measurement and is expressed by the stated interval which is estimated to contain the measurand with 95 probability The coverage factor for the interval is 2

CALIBRATION PLOT

Figure 8 the voltage output vs pressure from the measured values

Figure showing the measured value in respect to the true value from the data sheetThis graph above was plotted using the indicated pressure which is obtained from our measurement while the true pressure was calculated from the figure 3 Output voltage vs pressure data sheets to obtain the formula to calibrate the pressure sensor The formula Y= 16605x +04249 was used Pressure calibrated = (pressure indicated -04249 )16605The calibrated pressure when compared to the one in the datasheet is as shown below

COMPARISON OF THE SENSITIVITY OF THE DATASHEET AND THE EXPERIMENTAL ONE

To get the actual sensitivity of the pressure sensor the experimental value by the Gain ieKa = K G

The gain of the op amp was given by R2R1 which is equal to 45333To obtain the sensitivity of the pressure sensor can be evaluated as

Ka=KGtimes1000mVKPa

Hence the sensitivity is obtained as 02426 mVKPa using the best op-amp meanwhile the sensitivity given in datasheet is typically at 04 mV Kpa which is almost two times higher than our group`s experimental result This shows that the typical pressure sensor is more sensitive The sensitivity of the pressure sensor was not that accurate when compare to the datasheet

Problems observed with the calibration method

It wasnrsquot easy using water as there was bound to be the leakage of water when it was put into the tube

Statistical uncertainty in parameters affects a measurement

There are several uncertainties due to the number of readings that were taken Uncertainty due to the conditions of pressure temperature humidity and any drift

since factory calibration There was also uncertainty associated with the calibration which is from the

manufacturers data

The uncertainty of input resistance may change the voltage gain of an op-amp and thus brings systematic errors to the measurement with different amplifiers Also may increase the noise to the output signal

There could be Uncertainty in the Common-Mode Rejection Ratio leading to a very minimal reading in the output voltage

There was error due to resolution which is as a result of the readability of the data Uncertainty as a result of the sensitivity to the changes in conditions of the room

However we tried to minimize the Type B error by not putting it in autoranging and also by using the same multimeter to measure the values

Contribution of each team member

Thomas Aremu the analysis of part one and the taking applying the pressure during the lab he was involved in typing the report was his contribution

Buxin Teng Set up circuits reading the multimeter and recording in the lab together with and carrying out calculations and analyzing part two was his contribution We both had equal percentage contribution

REFERENCES

Adrian keating (2013) Measurement and Noise course note University of western Australia

Operational amplifiers last updated 7082013 httpenwikipediaorgwiki Operational _ amplifiers last viewed 28092013

APPENDIX

The Gaussian distribution f(z)= 1radic2 π

eminus1

2z 2

where z=( x - x)s

The uncertainty was Uc = kUx where the Ux= the experimental standard deviation of the mean and k=217 For example the LF353 op-amp the sample mean for the Voffset was 026mV and the S= 1978 and the number of samples n=13 therefore Ux=Sradic n= 1978radic 13 = 0549 Uc= 217 times0549 = 119 therefore the mean and spread of the mean is 026mVplusmn119Mv This was calculated using the ISO guide to the expression of uncertainty in measurement and is expressed by the stated interval which is estimated to contain the measurand with 95 probability The coverage factor for the interval is 217 (from the student t distribution)

GRAPHS

Offset voltage represented as Voffset

Offset current represented as Ioffset

Figure 1Measured values and normal distribution for offset voltage for the LF353 op-amp

Figure 2 Measured values and normal distribution for offset current for the LF353 op-amp




















R1 =

68015

=











Vouput (mV) = mX+bG






3208plusmn003

12 Right(Best) 0 1 2 3 4 5 6



-0168plusmn002


1669plusmn003

2282plusmn002

286plusmn002

354plusmn003



CALIBRATION PLOT






Ka=KGtimes1000mVKPa







manufacturers data








REFERENCES



APPENDIX




















R1 =

68015

=











Vouput (mV) = mX+bG






3208plusmn003

12 Right(Best) 0 1 2 3 4 5 6



-0168plusmn002


1669plusmn003

2282plusmn002

286plusmn002

354plusmn003



CALIBRATION PLOT






Ka=KGtimes1000mVKPa







manufacturers data








REFERENCES



APPENDIX



3208plusmn003

12 Right(Best) 0 1 2 3 4 5 6



-0168plusmn002


1669plusmn003

2282plusmn002

286plusmn002

354plusmn003



CALIBRATION PLOT






Ka=KGtimes1000mVKPa







manufacturers data








REFERENCES



APPENDIX






Ka=KGtimes1000mVKPa







manufacturers data








REFERENCES



APPENDIX








REFERENCES



APPENDIX

Pressure sensor experiment

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