Lab report #5. Oscilloscope and Function Generator Operation Theory, Transformers Basics

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Lab report #5. Oscilloscope and Function Generator Operation Theory, Transformers Basics Objectives: 1. Obtain values of the period, frequency and amplitude by the use of oscilloscope.

2. Investigate the principle of transformer’s work.

3. Compare theoretical and experimental results.

Experimental data: Part I

Figure 1. The photo of the signal in step C. Table 1. Results for horizontal scale.

Time sensitivity, ms/div

Number of divisions (calculatedd)

Number of divisions (masured)

Error , ms/div Period T, ms

Error of period Δ T, ms

0.05

2

2

0.025

0.05

1

Table 2. Results for calibration.(steps f-g) Time sensitivity, ms/div

Number of divisions (calculated)

Number of divisions (masured)

Error , ms/div Period T, ms

Error of period Δ T, ms

0.5

2

2

0.05

1

0.1

1

1

1

0.1

1

0.02

Table 3. Horizontal sensitivity and its error(step H)

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Horizontal sensitivity, ms/div

0.2

0.5

1.0

Error, ms/ dv

0.02

0.05

0.1

Table 4. Results for vertical scale.(steps j-k) Vertical sensitivity, ms/div

Number of divisions (calculated)

Number of divisions (masured)

Error , ms/div Voltage V, V

Error of Voltage Δ V, V

2

1.6

1.6

0.02

0.8

0.2

0.5

0.4

0.4

0.02

0.8

0.05

Part II Primary coil turns = 400 Voltage from generator =5 ± 0.05V Period T=2ms Table 5. Voltage for two 400 turn coils.

Coil turns

Voltage V, V

Error of Voltage

400

1.2

0.05

Δ V, V

Table 6. Voltages for different coil turns.

Coil turns (secondary) N

Voltage V, V (calculated)

Voltage V, V (measured)

Error of Voltage V, V

200

2.5

1

0.05

400

5

0.8

0.05

800

10

0.4

0.02

Δ

Table 7. Voltage and frequency values for secondary coils. f, Hz

100

200

300

400

500

600

700

800

900

1000

V, V

1.1

1.3

1.4

1.5

1.5

1.5

1.5

1.5

1.5

1.5

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Figure 2. Voltage vs. Frequency.

Data analysis: Part I. Theoretical part: Oscilloscope is an irreplaceable tool for designing, manufacturing and repairing electronic equipment. With this tool, we can measure all kinds of phenomena due to the presence of proper sensors. These sensors can create an electric signal as a response to physical stimuli such as sound, mechanical stress, light, pressure, heat. The oscilloscopes can visually display the voltage signal which can show a lot of information about the circuit or system that simple standard multimeter could not. In our case, we use oscilloscopes to measure the frequency, period and amplitude of sinusoidal signal. (Lab 5. Theory) Formula to calculate the period, according to the lab manual: T t h eoretical=

1 f

(1)

Variable description for (1): T is the period (s); f is the frequency (Hz).

Number of horizontal divisions required to display full cycle of f =1000 Hz can be calculated by the following formula, according to the lab manual: Number of d ivisionst h eoretical=

T t h eoretical h orizontal sensitivity

According to our lab manual, Amplitude of signal voltage=Voltage sen s itivity (V /¿ .) Deflection (¿ .)

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(2)

(3)

Period of signal voltage=Horizontal sensitivity (V /¿ .) Deflection (¿ .)

(4)

Part II. Transformers are 4-terminal devices that transfers electrical energy from one circuit to another by electromagnetic induction. The electrical energy is always transferred without a change in frequency, but may involve changes in magnitudes of voltage and current. A transformer usually consists of two closely coupled coils that are designed to transfer energy between its winding circuits. One of the coils is referred to as the primary (containing Np turns), while the other coil is called the secondary (containing Ns turns). (Lab 5 Theory) Formula which shows the relationship between the voltage in the primary and the secondary coils: N V 2=V 1 × 2 (4) N1 Variable description: V 2 - voltage in the secondary coil; V 1 - voltage in the primary coil; N 2 - number of coils in the secondary coil; N 1 - number of coils in the primary coil; Error propagation: ΔV 1 2 Δ N 1 2 Δ N 2 2 Δ V 2=V 2 ( ) +( ) +( ) V1 N1 N2

√

Δ N 2 and

(5)

Δ N 1 are equal to 0, because we have exact values for them.(number of turns) Voltage loss=

√

ΔVoltage loss= (

V t h eoretical −V experimental × 100 % V t h eoretical 2

2 V exp −1 × Δ V ) +( × Δ V ) t heo exp 2 2 (V t h eo) ❑ (V t h eo ) ❑

Calculations: Voltage loss for 200-turn coil: V= V ❑loss =

(6)

5 V❑ ×

200 400

= 2.5V

2.5−1.2 ×100 %=52 % 2.5

2 2 1.2 −1 ΔVloss= ( ×0.01) +( 2 ×0.05) = ± 19.2% 2 (2.5) ❑ (5) ❑ Voltage loss for 400-turn coil:

√

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(7)

V= V ❑loss =

√

Δ Vloss= ( Voltage loss for 800-turn coil:

V ❑loss =

√

400 400

= 5V

5−0.8 × 100 %=84 % 5

2 2 0.8 −1 ×0.01) +( ×0.05) = ± 16.5% (5)2❑ (5)2❑

V=

Δ Vloss= (

5 V❑×

5 V❑×

800 400

= 10V

10−0.4 ×100 %=96 % 10

2 2 0.4 −1 × 0.01) +( × 0.02) = ± 12.5% 2 2 (10) ❑ (0.4) ❑

Discussion: We could observe that by increasing the horizontal sensitivity of the oscilloscope, we get smaller divisions for the same period. Error is directly proportional to the horizontal sensitivity, which means that by increasing sensitivity, we increase the error, too. So, to get less errors we need to use a low sensitivity and the device will become more sensitive to small deviations.

In step H, we increased the horizontal sensitivity from 0.2 ms/dev to 0.5 ms/dev and then 1.0 ms/ dev, the pictures of waves that we get change significantly, it is because the frequency of the wave increases. The graph that we observed became more tighter as we increased the sensitivity. However, as we said before it is better to observe the wave with low value of sensitivity, because by that we get less errors in values.

We also could see the trends in vertical sensitivities. By decreasing from 2.0 V/dev to 0.2 V/dev, we could observe that more sensitivity is, the less becomes the amplitude. It is because graph becomes closer to x-axis.

Experimental and theoretical values of the voltages, which were obtained from oscilloscope and frequency generator respectively, differ from each other. The difference could occur because of these factors: Material Losses, Hysteresis losses, Eddy Current losses, Sensitivity of Oscilloscope, human errors. Eddy current losses could occur due to the fact that the core is a conductor, while other currents could be induced. Material losses due to resistance of the winding. Human errors could occur because our eyes could see the results from the picture of the wave incorrectly or less precisely than it could be and which could affect the results.

In Part 2, we could calculate the secondary voltage by given formula 4. Even though we did everything step by step as it was told in the manual, the difference in predictions and experimental results was significant. In theory, increasing the windings increases the secondary voltage, however, practically we get vice versa trend, which means our results were abnormal.The difference in results could occur because of the errors that we discussed before.

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From figure 2 and table 7, we see the trend which explains the dependence of voltage on frequency. It is linear dependence at first three points, but after them the voltage did not increase as the frequency was increasing. It satisfies both our predictions and obtained results. The reason why the voltage was not changing can be due to limitations of the device, which can be less sensitive. The slope we obtained was 0.0003 V*s.

Conclusion: The main goal of the experiment was to understand the principles of transformer and osciloscope’s work. The goal was achieved as we obtained values and errors from the oscilloscope.. All other objectives were achieved. Higher the horizontal sensitivity, the higher frequency of the wave is. Lower the vertical sensitivity, the lower amplitude is. By increasing the sensitivities, the less divisions become. In the second part of our experiment, we could work with a transformer, which can change the voltage. However, we got different practical results than the calculated voltages. The errors that we discussed were affecting the trend that was not the same for practical and theoretical results.

References: Nazarbayev University (2020). Lab 5: Oscilloscope and Transformers Basics . PHYS 162.

Obtained from https://moodle.nu.edu.kz/pluginfile.php/201755/mod_resource/content/1/Lab %205.%20Procedure.pdf Nazarbayev University (2020). Lab 5: Oscilloscope and Function Generator Operation Theory, Transformers Basics. PHYS 162. Obtained from https://moodle.nu.edu.kz/pluginfile.php/201756/mod_resource/content/1/Lab %205.%20Theory.pdf

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