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This report covers an experiment in which a function generator is connected to a CRO and DMM. Data is obtained from the CRO display to calculate the Vrms of the AC waveform from the function generator. The DMM also displays a value for Vrms, and by varying the frequencies it is possible to identify ...

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School of Computing, Engineering and Mathematics

Engineering Report

FY003 – Alternating Current and Oscilloscope

Abstract This report covers an experiment in which a function generator is connected to a CRO and DMM. Data is obtained from the CRO display to calculate the V rms of the AC waveform from the function generator. The DMM also displays a value for Vrms, and by varying the frequencies it is possible to identify a range

of

frequencies

at

which

the

DMM

is

able

to

respond.

The findings are that the DMM only gives a reliable reading up to 10KHz, frequencies higher than this give a large percentage error from the Vrms calculated from the CRO. All the results are represented in a table and also graphically. This report also covers the way in which a CRO works using a cathode ray tube and how the displayed trace can be controlled. Date: 11/10/16

Table of Contents International System of Units................................................................................................................3 Abbreviations........................................................................................................................................4 List of Figures.........................................................................................................................................5 List of Tables..........................................................................................................................................6 List of Graphs.........................................................................................................................................7 List of Equations....................................................................................................................................8 1.

Introduction...................................................................................................................................9

2.

Theory...........................................................................................................................................9

3.

Risk Assessment...........................................................................................................................10

4.

Method........................................................................................................................................10

5.

Tables...........................................................................................................................................11

6.

Figures.........................................................................................................................................12

7.

Graphs.........................................................................................................................................15

8.

Calculations.................................................................................................................................16

9.

Conclusion...................................................................................................................................16

10.

References...............................................................................................................................17

International System of Units Quantity Voltage Time period Frequency

Unit Volts Seconds Hertz

Symbol V S or sec Hz

Abbreviations Lab CRO DMM AC DC Vrms VPk VPkPk

Laboratory Cathode Ray oscilloscope Digital Multi Meter Alternating Current Direct Current Root Mean Square Voltage Peak voltage Peak to peak voltage

List of Figures Figure 6-1 Diagram of the setup..........................................................................................................12 Figure 6-2 CRO(HAMEG HM400).........................................................................................................13 Figure 6-3 Signal Generator (GWINSTEK SFG-2104).............................................................................13 Figure 6-4 DMM (Rapid 318B).............................................................................................................14 Figure 6-5 Diagram of a CRO [2]..........................................................................................................14 Figure 6-6 Deflection of an electron beam [3].....................................................................................14

List of Tables Table 5-1 Results for test 1...................................................................................................................11 Table 5-2 Results for test 2...................................................................................................................11 Table 5-3 Results for test 3...................................................................................................................12

List of Graphs Graph 7-1 CRO Vrms reading against frequency..................................................................................15 Graph 7-2 DMM voltage reading against frequency............................................................................15 Graph 7-3 Percentage error of the DMM against frequency...............................................................15

List of Equations 2-1.........................................................................................................................................................9 2-2.........................................................................................................................................................9 2-3.......................................................................................................................................................10

1. Introduction The aim of this test is to obtain data from a CRO about the wave form produced by a Function Generator and to also compare the accuracy of the DMM reading for different frequencies. A CRO is used for displaying the AC waveform from the function generator. CRO means Cathode Ray Oscilloscope. This is an analogue piece of equipment, the accuracy is down to the person taking readings from the screen as it does not give exact figures like a digital piece of equipment would. The way in which the CRO displays the waveform will be discussed in the theory section of this report. The AC signal from the function generator is connected to the input of the CRO, which displays a sine wave. From the sine wave a reading for time period can be obtained and used to calculate the frequency from the function generator. The time period is the time taken for the wave to complete one full cycle. Peak voltage can also be read off the CRO’s display and using Equation 2 -2 the Vrms can be calculated. By connecting a DMM to the function generator this will give a reading for V rms, the DMM is digital so will give an exact value. This may not be more reliable than calculating it from the data taken from the CRO because the DMM may not respond to the signal at higher frequencies giving a false voltage reading. By using both a DMM and CRO to find values of Vrms the data can be compared to find a range at which the DMM works reliably, this is in the form of percentage error. All results can be tabulated and plotted on a graph.

2. Theory The formula below is used to calculate the frequency of a wave by using the time period. Time period is the time taken for one full cycle of the wave.[ CITATION Pop87 \l 2057 ]

f= Where: f= Frequency T=time period

1 T

2-1

The waveform from the function generator is a sine wave, or AC wave. The voltage level of the AC wave changes between positive and negative. The equivalent DC voltage is Vrms, it is the average of the AC wave, and it is calculated with the following equation.

Vrms= Where: Vrms=root mean square voltage Vpk =peak voltage

2-2

Vpk √2

The percentage error can be used to plot a graph to graphically show the deviation of the DMM from the true value of Vrms at different frequencies. The value calculated from the CRO data is the ‘expected value’ and the DMM reading is the ‘actual value’. % error =

expected −actual expected

2-3 x100

The CRO is short for Cathode Ray Oscilloscope. The CRO uses a cathode ray tube, this consist of an electron gun at one end and a fluorescent screen at the other end1. Figure 6 -5 shows a diagram of the components that make up the cathode ray tube. A beam of electrons are fired through an anode which accelerates the electrons towards the centre of the screen at the end of the cathode ray tube, the anodes also focus the beam to a point on the screen [ CITATION Pop87 \l 2057 ]

. Adjusting the focus control on the CRO adjusts the focus point on the screen. The grid, in between the

anode and the cathode, controls the intensity of the trace by changing the amount of electrons emitted from the gun. The spot on the screen which is hit by the electrons can be controlled by deflecting the electron beam. Two pairs of parallel plates (y-plates and x-plates) deflect the beam vertically and horizontally, shown in Figure 6 -6. A potential difference across the plates control the magnitude and direction of deflection. The resulting electron beam shows a trace across the screen, replicating the input waveform. The deflection in the x direction is controlled by changing the time base setting, the deflection in the y direction is controlled by changing the volts per division setting.

1 The fluorescent coating on the screen is zinc sulphide, this shows a bright spot when electrons hit it.

3. Risk Assessment Bags left in the way are a tripping hazard, all bags should be stored under the work bench and out of the way. Cables are also a trip hazard if they are left trailing across the floor, make sure cables are neatly stored away. Drinks must be kept away from the electrical equipment to reduce the risk of damage if spillages occur. When connecting the circuit make sure the Signal Generator output is turned off, this will avoid short circuits and potential damage to the equipment.

4. Method The equipment used in the experiment was as follows: a Function Generator, DMM and a CRO. The output from the Function Generator was connected to the input of the CRO. The DMM was connected in parallel with the output from the Function Generator [see Figure 6 -1]. The amplitude control was set to the midpoint and remained that way for the duration of the experiments. The Function generator was set to produce a sine wave. For the first part of the experiment the sine wave frequency was set to 1kHz. The time base on the CRO was set to 0.2ms per division2. The vertical scale of the CRO is set so that the amplitude of the sine wave occupies most of the screen vertically. The settings for time base where adjusted for different frequencies so that one complete cycle of the sine wave was shown occupying most of the screen, this made it easier to take readings for time period. The vertical scale of the CRO maintained the same because the amplitude of the wave from the function generator did not change. In the first part of the experiment the function generator frequency was set to 1khz, readings for time period were taken from the CRO and used to calculate frequency. The peak to peak voltage reading was used to calculate the Vrms, and a value for voltage was also taken from the DMM. All results were recorded in a table [see ]. For the second part of the experiment the process was repeated but with frequency set to 400khz, all the same readings were taken and recorded [see Error: Reference source not found].

2 0.2ms per division means that the time period is the number of divisions multiplied by 0.2ms.

In the third part of the experiment readings were taken over a range of frequencies and ultimately plotted on a graph to observe the frequency response of the DMM and percentage error [see Error: Reference source not found]. The frequencies used started from a minimum of 10Hz and increased to the maximum at 500KHz. Throughout the experiments the time base was changed on the CRO so that the sine wave occupied most of the screen, the vertical axis did not need to be changed because the amplitude of the wave was constant.

5. Tables Table 5-1 Results for test 1

Generator frequency/HZ 1KHz

CRO measured period /seconds 1ms

CRO CRO peak to Calculated peak Frequency/Hz Amplitude/v 1000Hz 6v

CRO RMS Amplitude/v 2.12v

DMM Voltage/v 2.30v

CRO peak to peak CRO RMS Amplitude/v Amplitude/v 6v 2.12v

DMM Voltage/v 0v

Table 5-2 Results for test 2

Generator frequency/HZ 400KHz

CRO measured period /seconds 2.5µs

CRO Calculated Frequency/Hz 400KHz

Table 5-3 Results for test 3

Generator frequency/HZ 10 20 50 100 200 500 1000 2000 5000 10000

CRO measured period /seconds 100ms 50ms 20ms 10ms 5ms 2ms 1ms 0.5ms 200µs 100µs

CRO Calculated Frequency/Hz 10 20 50 100 200 500 1000 2000 5000 10000

CRO peak to peak CRO RMS Amplitude/v Amplitude/v 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12 6.00 2.12

DMM Voltage/v 2.36 2.34 2.35 2.35 2.34 2.33 2.30 2.25 2.22 2.37

DMM % Error 11.32 10.38 10.85 10.85 10.38 9.91 8.49 6.13 4.72 11.79

20000 50000 100000 200000 500000

50µs 20µs 10µs 5µs 2µs

20000 50000 100000 200000 500000

6.00 6.00 6.00 6.00 6.00

2.12 2.12 2.12 2.12 2.12

6. Figures

Figure 6-1 Diagram of the setup

Figure 6-2 CRO(HAMEG HM400)

2.87 2.86 0.56 0.02 0.00

35.38 34.91 73.58 99.06 100.00

Figure 6-3 Signal Generator (GWINSTEK SFG-2104)

Figure 6-4 DMM (Rapid 318B)

Figure 6-5 Diagram of a CRO[ CITATION Cat16 \l 2057 ]

Figure 6-6 Deflection of an electron beam[ CITATION Rev16 \l 2057 ]

7. Graphs 2.5

CRO Voltage/v

2.0 1.5 1.0 0.5 0.0 10

100

1000

10000

100000

1000000

Frequency/Hz

Graph 7-1 CRO Vrms reading against frequency 3.5

DMM Voltage/v

3.0 2.5 2.0 1.5 1.0 0.5 0.0 10

100

1000

10000

100000

Frequency/Hz Graph 7-2 DMM voltage reading against frequency

1000000

120

Percentage error

100 80 60 40 20 0 10

100

1000

10000

100000

1000000

Frequency/Hz Graph 7-3 Percentage error of the DMM against frequency

8. Calculations Frequency: The frequency of the AC wave from the function generator can be checked by using equation 2 -1. The value for time period in is 1ms, this is found by multiplying the time base (0.2ms) by the number of divisions which are covered by one full wave cycle(5 divisions).

1 T

The frequency , f = =

1 =1 KHz 1× 10−3

This same steps are reaped for Error: Reference source not found to take readings of time period and calculate the frequency. Vrms: The wave form on the CRO covered 3 divisions from peak to peak, the vertical axis was set to 2v per division, therefore it was 6vpkpk. The peak voltage is half the peak to peak voltage, this value is used to calculate the Vrms:

Vrms=

Vpk 3 = =2.12 v . This value is consistent throughout the experiment. √2 √ 2

Percentage error: At 10Hz the CRO calculated Vrms is 2.12v, the DMM voltage reading at this frequency is 2.36v. The expected value is 2.12v, and the actual value is the DMM value of 2.36v.

% error =

expected −actual expected

x100 =

2.12 −2.36 2.12

x100 = 11.32%

At a higher frequency of 100KHz the CRO calculated Vrms is 2.12v, the DMM voltage reading at this frequency is 0.56v. The expected value is 2.12v, and the actual value is the DMM value of 0.56. % error =

expected −actual expected

x100 =

2.12 −0.56 2.12

x100 = 73.58%

9. Conclusion The value for Vrms calculated from the CRO display is consistent throughout the experiment, this is as expected because the amplitude control on the Function Generator was not changed. This is the value which is used as the ‘expected value’ when calculating the percentage error. The amplitude of the wave on the CRO was consistent for all frequencies, therefore the results in Graph 7 -1 show that the Vrms, and therefore peak voltage, of the AC wave stay the same for all frequencies. Peak voltage is 6v, and Vrms is 2.12v. Connected to the same waveform as the CRO, the DMM had a greater percentage error for the V rms, this is because the DMM is digital and gives an exact value to two decimal points, whereas the CRO is only as accurate as the person taking readings from the screen. The displayed value for V rms was deviated by approximately 10% for frequencies ranging from 10Hz to 10KHz. At frequencies greater than 10KHz the percentage error noticeably increased until it displayed 0v at 500KHz, at which point the error is 100%. This is evident from the results in Graph 7 -2 and Graph 7 -3. From the results for the DMM voltage and percentage error at different frequencies it can be speculated that the DMM has a range of frequencies where it works accurately. From Graph 7 -3 it is clear that the percentage error is consistent up until 10KHz. Outside of this range it shows false readings because it cannot respond fast enough to the frequency change. This conclusion can be confirmed by checking the data sheet for the DMM. It states that the operating frequency range is up to 20KHz.[ CITATION Rap16 \l 2057 ] Obtaining a value for Vrms is easier to do with a DMM as long as the AC frequency is within the operating range for the equipment. Although more steps have to be taken to calculate the Vrms from the CRO this way is reliable for all range of frequencies.

10. References

[1] S. Pople, “Explaining Physics,” Oxford, Oxford University Press, 1987, p. 330. [2] “Cathode Ray Oscilloscope,” [Online]. Available: http://www.studyvilla.com/cro.aspx. [Accessed 8 December 2016]. [3] “Revision World,” [Online]. Available: https://revisionworld.com/a2-level-level-revision/physics/fields0/electric-fields. [Accessed 8 December 2016]. [4] “Rapid Online,” [Online]. Available: https://www.rapidonline.com/pdf/86-3181.pdf. [Accessed 30 November 2016]....