ELEC273 Lab report #1

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Concordia University *

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273

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Electrical Engineering

Date

Dec 6, 2023

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Abstract This experiment will allow us to become familiar with measuring instruments and other equipment used in the lab. These instruments include Digital Multimeters (DMMs), Function Generator (FG), Digital- Storage-Oscilloscope (DSO) and DC Power supplies. The experiment is divided into two parts. One in which DC (direct current) is used and Kirchhoff’s laws (KCL and KVL) will be proved. In other words, the sum of current running to a node would equal the current leaving the node. Therefore, AC (alternative current) is used in the second part of the experiment and will be useful for our sinusoidal waveform measurement. Through this waveform, we will be able to find the voltage gain and the phase shift once we vary the frequency. A significant change will occur in both voltage and phase-shift at a certain frequency and this frequency is called ‘series resonant-frequency’.

Introduction To start off, to measure the current (DC circuit), we will be using the Fluke 8010A as an Ammeter. As for the resistance and voltage, the Agilent34405A as a voltmeter. Afterwards, the results will serve to prove Kirchhoff’s laws ( voltage and current law). Finally, we are asked to determine the phase shift and the voltage gain through an AC circuit using the Function generator (FG) and the Digital-Storage-Oscilloscope. At the end of this experiment, we are expected to be able to measure the resistance, voltage and current of a circuit with the given instruments and to analyze their respective circuits. Procedure Part 1: DC voltage and current measurements: 1) Assemble the following connections in the picture below between the PSP and the R-Chassis

2) On the R-Chassis, set the R L to a value between 200 Ω and 300 Ω 3) Turn on the PSP and turn the ‘Vs ADJ’ and ‘Is ADJ’ knobs 4-8 turns from their extreme position 4) With the Fluke 8010A as an ammeter in the 200 mA DC range, measure the branch currents I 1 I 2 and I 3 while connecting it in series 5) With the Agilent 34405A set in DCV-Auto mode, measure the node voltages V E V A and V C Part 2: AC (sinusoidal) waveform measurements: 1) Build the following circuit between FG, the DSO and the RLC- Chassis

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2) With DC input coupling, set the DSO to display Channels 1 and 2 3) Set the FG output amplitude and frequency to display a sinusoidal Ch1 signal of about 2 volts RMS at a frequency of about 100 Hz (press AUTOSET to size the display optimally) 4) Observe the changes in the output voltage (Ch2) amplitude and the phase while varying the FG frequency over the range of 100 Hz to 10 kHz. (Changes will occur around 5kHz) 5) Once the ‘series resonant-frequency’ (around 5 kHz) is found, procure one printout at that frequency and another on x1.5 of that frequency. Results

Calculations: - DC Circuit: a) KCL equation: I 2 = I 1 + I 3 7.1 mA = -2.1 mA + 9.2 mA b) V EA = V E − V A = 5.2 − 1.8 = 3.4 V V AB = V A − V B = 1.8 − 0 = 1.8 V V AC = V A − V C = 1.8 − 1.1 = 0.7 V V CD = V C − V D = 1.1 − 0 = 1.1 V V EF = V E − V F = 5.2 − 0 = 5.2 V V EF = V EA + V AB = V EA + V AC + V CD 5.2 = 3.4 + 1.8 = 3.4 + 0.7 + 1.1 V AC + V CD + V BA = 0 0.7 + 1.1 − 1.8 = 0 I s = I 4 + I 2 = 1.1 100 + 0.0071 = 0.0181 A c) ¿ P del = V s I 1 + V c I s = 5.2 ∗ 0.0092 + 1.1 ∗ ¿ 0.0181) = 0.06775 Watts

d) P diss = I 1 V EA + I 2 V AB + I 3 V CA + I 4 V CD = 0.0092 ∗ 3.4 + 0.0071 ∗ 1.8 +− 0.0021 ∗− 0.7 + 0.011 ∗ 1.1 = 0.05763 Watts P diss isn’t equal to P del because of some internal resistance in one of the components that might have converted some of the energy into heat. - AC Circuit: a) And b) Voltage Gain and phase shift: Printout #1: A V = V out V ¿ = 17.26 1.453 = 11.88 Φ = 360 ∗ f ∗ ∆t = 360 ∗ 4851 ∗ 47 ∗ 10 − 6 = 82.08 o Ф Printout #2: A V = V out V ¿ = 1.633 1.955 = 0.835 Φ = 360 ∗ f ∗ ∆t = 360 ∗ 7260 ∗ 71 ∗ 10 − 6 = 185.6 o b) Theoretical results

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C = 22nF = 0.000000022 F L = 0.047 H R = 100 Ω w 1 = 2 ∗ π ∗ f = 2 ∗ π ∗ 4851 = 9702 π w 2 = 2 ∗ π ∗ f = 2 ∗ π ∗ 7260 = 14520 π A V Printout #1 = 12.85  7.5% A V Printout #2 = 0.865  3.5% Φ Printout #1 = − 59.6 o = 360 o − 59.6 o = 300.4 o  72.7% Φ Printout #2 = − 175 o = 360 o − 175 o = 185 o  0.3% AC circuit calculation: b) Effective frequency Printout #4 f = 1 T = 1 208 ∗ 10 − 6 = 4.807 kHz Discussion:

In the DC circuit (part 1), we managed to prove and confirm Kirchhoff’s voltage and current laws (KCL and KVL). For Kirchhoff’s current law, the currents added up perfectly even with their respective signs. On the other hand, Kirchoff’s voltage law was respected perfectly too. However, for the dissipated power of components and the power delivered by the source, their values don’t match and that is most probably because some energy was lost in form of heat in the components. Moreover, with printout #4, the voltage gain was obtained around the frequency 4851 Hz. That is where the voltage spiked really fast and hit its maximum. At 1.5x of that frequency the voltage gain was very small and decreased rapidly. In what concerns the theoretical values, most of the values matched very closely except for the phase shift in printout #1 where a big difference between the theoretical value and experimental value was clearly present. Conclusion

In conclusion, in order to get the hang of the instruments, the Kirchhoff’s laws of voltage and current had to be proven and the dissipated power and the power provided by the sources had to be calculated. For the second part of the experiment, the resonance frequency is the frequency where the voltage is the maximum. Once the frequency changed (to 1.5x of the resonance frequency), the voltage changes and reduces drastically.

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