2CI4_AD2_HW2_400480022_400480720

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AD2 HOMEWORK 2 By Aditya Hura and Mohammed Zeeshan Ansari ELECENG2CI4

AD2 HOMEWORK 2 Student 1: Aditya Hura Student 2: Mohammed Zeeshan Ansari Date: 09/11/2023 Date: 09/11/2023 Mac ID: huraa Mac ID: ansarm23 Student #:400480022 Student #:400480720 SET#4 Given the following circuit, theoreƟcally calculate V1, V2, V3, IT, I1, I2, I3, I4 using nodal analysis. Show your work in the report. Figure 1: The circuit SoluƟon:- We recognise the 3 main nodes, V1, V2 and V3. Using Nodal analysis at V1 via KCL 𝑉 ଵ 1𝑘 + 𝑉 ଵ − 𝑉 ଶ 10𝑘 + 𝑉 ଵ − 𝑉 ଷ 100𝑘 − 𝑉 ଵ − 5 1𝑘 = 0 Applying KCL at V2 𝑉 ଶ − 𝑉 ଵ 10 + 𝑉 ଶ − 𝑉 ଷ 1𝑘 + 𝑉 ଶ 100𝑘 = 0 Applying KCL at V3 𝑉 ଷ − 𝑉 ଶ 1𝑘 + 𝑉 ଷ − 𝑉 ଵ 100𝑘 + 𝑉 ଷ 10𝑘

AŌer forming a system of equaƟons with 3 unknowns and using the McMaster Standard Casio FX-991 MS calculator, we get- We get, 𝑉 ଵ = 2.435𝑉 𝑉 ଶ = 1.270 𝑉 𝑉 ଷ = 1.165 𝑉 The final calculated values are summarised as following – 𝑉 ଵ 2.435 V 𝑉 ଶ 1.270 V 𝑉 ଷ 1.165 V 𝐼 ଵ 2.43 mA 𝐼 ଶ 0.0127 mA 𝐼 ଷ 0.116 mA 𝐼 ସ 0.0126 mA 𝐼 ௧ 2.5646 mA Q2: Using the Analog Discovery 2, measure the voltages and currents in the circuit and compare them to the theoreƟcal values from part i. [Refer to Example Part (ii) on Page 19 to see how to measure currents.] SoluƟon- Figure 2: V1 and V3 are 2.448V and 1.178V respecƟvely. Figure 3:V1 and V2 are 2.444V and 1.278V respecƟvely. The measured values are as follows- 𝑉 ଵ 2.444 V 𝑉 ଶ 1.278 V

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𝑉 ଷ 1.178 V 𝐼 ଵ 2.444 mA 𝐼 ଶ 0.0278 mA 𝐼 ଷ 0.1178 mA 𝐼 ସ 0.01266 mA 𝐼 ௧ 2.55 mA Q3: What is the raƟo of input voltage (5V) to V1, V2, and V3? Input voltage raƟos: 𝑉 ଵ 𝑉 = 2.448 5 = 0.4896 𝑉 ଶ 𝑉 = 1.278 5 = 0.2556 𝑉 ଷ 𝑉 = 1.178 5 = 0.2356 Q4: Change the input from the 5V DC source to a triangular waveform, with a frequency of 2.5kHz, amplitude of 2.5V, and an offset of 2V. Using the oscilloscope, plot the input voltage on channel 1, and the voltage V1 on channel 2. Include a screenshot in your report with both channel 1 and channel 2 enabled. Figure 4:C1 and C2 as required. Q5. ConƟnuing with the circuit of Part (iv), add a custom math channel in the oscilloscope to measure the raƟo of the input waveform to the waveform at V1. How does this raƟo compare to the raƟo computed for V1 in Part (iii)? Include a screenshot in your report with only the math channel enabled.

Figure 5:Vin/V1 raƟo waveform. This raƟo aligns with my calculaƟons for the voltage raƟos in part 4. The verƟcal asymptotes signify division by 0 as the input waveform touches 0 periodically. CIRCUIT SETUP FOR SET#4

END OF SET #4

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SET#5 ObjecƟve • Apply the mesh analysis technique to solve circuits with mulƟple resistors. • Understanding the uƟlity of variables in circuit equaƟons. • GeneraƟng matrices to solve for unknown currents in the circuit Given the following circuit, use mesh analysis to theoreƟcally generate a 4x4 matrix for the 4 loop currents in the circuit. Choose the loops and their direcƟons yourself. Include a redrawn circuit diagram in your report indicaƟng your 4 loop currents chosen. Show your work in the report. Note: You will not use specific values for resistors in this part. See the example earlier in this Set Q2. Given that Vsource = 4V, R1 = 220Ω, R2 = R3 = R5 = 1kΩ, R4 = R6 = R7 = 10kΩ, and Ro = 24.9kΩ, theoreƟcally calculate the loop currents using your matrix from part i. Show your work in the report. I would have used word’s equaƟon script for this, but it is simply too long, instead I will provide a handwriƩen soluƟon followed by a screenshot of octave online which I used to solve the matrix. Hopefully it is understandable. I would also like to point out that I’ve used two 4.99K ohm and two 10 ohm resistors as I lack a third 10k ohm resistors. Discrepancy in any measured values may be because of that.

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Q3. With the source and resistor values given in Part (ii), build the circuit on the breadboard and use the Voltmeter tool on the Analog Discovery 2 to check your answers from Part (ii) by measuring the 4 currents in the circuit. Record the calculated and measured currents in the table below and include it in your report. [Note: To measure the current through a resistor, you can find the voltage across the resistor using the Voltmeter tool on the Analog Discovery 2 and then use Ohm's Law to find the corresponding current.] I (calculated) (mA) I (measured) (mA) 𝐼 ଵ 2.23 mA 2.14 mA 𝐼 ଶ 0.534 mA 0.536 mA 𝐼 ଷ 0.408 mA 0.397 mA 𝐼 ସ 0.1 mA 0.1 mA In order to measure the currents we need to first measure the node voltages. The screenshots of the measurements are as follows- Figure 6: V0 voltage Figure 7:V4 voltage Figure 8: V1 Voltage Figure 9: V2 Voltage

Figure 10: Current CalculaƟons Q4. Calculate Vo, and then use the Voltmeter tool in the Waveforms soŌware to measure and confirm your calculaƟons. State both the calculated and measured values of Vo. We know by Ohm’s law, 𝑉 ଴ = 𝐼 ∗ 𝑅 Here 𝐼 = 𝐼 ସ and 𝑅 = 24.9 𝑘Ω So, 𝑉 ଴ = 0.1 𝑚𝐴 ∗ 24.9𝑘Ω = 2.49 𝑉 This value aligns very closely with my measured value for 𝑉 ଴ . Q5. ConƟnuing with work done in part iv, use measurements already done through the Analog Discovery 2 to calculate the power dissipated in Ro. 𝑃 = 𝐼 ∗ 𝑉 For Power dissipated through 𝑅 ଴ = 24.9 𝑘Ω , 𝐼 = 0.1𝑚𝐴 and 𝑉 ଴ = 3.092 𝑉 So, 𝑃 = 0.1 𝑚𝐴 ∗ 3.092 𝑉 𝑃 = 0.3092 𝑚𝑊

Q6. Change Ro to 1kΩ and redo parts iv and v. Q4. Calculate Vo, and then use the Voltmeter tool in the Waveforms soŌware to measure and confirm your calculaƟons. State both the calculated and measured values of Vo. Here we have 10k and 1k ohm resistors in series. We can use voltage division to calculate the new value for 𝑉 ଴ . 𝑉 ௢௨௧ = 𝑉 ௜௡ ∗ 𝑅 𝑅 ௘௤ 𝑉 ௢௨௧ = 4 ∗ 1000 220 + 10000 + 1000 𝑉 ௢௨௧ = 0.3565 𝑉 Figure 11: New measured value of V0 The discrepancies here may be because of the fact that I have used two 4.99k ohm and two 10 ohm resistors as I lack a third 10k ohm resistor. This value aligns somewhat closely with my measured value for 𝑉 ଴ . 𝑃 = 𝐼 ∗ 𝑉 For Power dissipated through 𝑅 ଴ = 24.9 𝑘Ω , 𝐼 = 0.1𝑚𝐴 and 𝑉 ଴ = 3.092 𝑉 So, 𝑃 = 0.1 𝑚𝐴 ∗ 0.3565 𝑉 𝑃 = 0.03565 𝑚𝑊 ConƟnuing with the Ro selected in Part (vi), change Vsource to a sine wave with a frequency of 2 kHz, amplitude of 3 V, and zero offset. Show Vo on the oscilloscope in the Waveforms soŌware and include a screenshot in your report. Make sure that the Vo waveform is adequately visible.

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