2E04 H2

docx

School

McMaster University *

*We aren’t endorsed by this school

Course

2E04

Subject

Electrical Engineering

Date

May 1, 2024

Type

docx

Pages

Uploaded by AgentDonkeyPerson1068

H2 AC Circuit Analysis Short description of the circuit: For this circuit I have included the internal resistance of the inductor as R1 to lower disparity between the results. In this circuit, there is a parallel combination of capacitors and resistors (C1, R2 and C2, R3) in series with the inductor and its internal resistance. Step 1: Solve for the voltage and phase (with respect to the source) at nodes A, B and C, and the current through the inductor analytically. Step 2: Solve the circuit for the same values using MultiSim. Do your results agree with Step 1? Step 3: Recreate the circuit physically and make the necessary measurements, make sure to account for the uncertainties of the measurements. Use the uncertainty values of the Hantek. ANALYTICAL ANALYSIS

My method for solving this analytically will be to convert the source to the phasor form as well as convert the inductors and capacitors to their impedances, then do the necessary equations of parallel and series impedances as well as making use of the voltage divider. Zpar is the impedance value of the parallel combination, and Ztot is the total impedance of the circuit.

We found Vb and Vc using the voltage divider equation, Va is across to the total impedance and Vb is parallel to just Zpar so Vb/Zpar=Va/Ztot. In addition to this we found the magnitude and phase of Vb and Vc as well as the differences in time with respect to the source to help with relating the phases to the MultiSim and the physical measurements. The current through the inductor is dependant on the total inductance of the circuit which was previously found to be slightly inductive which explains the slight lag it has. Table 1 Amplitude Phase(rad) Δt (μs) Va 1.00 V 0 0 Vb 1.72 V -1.218 -110.8 Vc 1.26 V -0.474 -43.1 Il 1.48 mA -0.051 -4.66 Discussion: We can see that we should be seeing Vb, Vc and Il all lag the source voltage. The whole circuit is slightly inductive meaning that the current would be lagging the source voltage. For Vb, the equation we used was Zpar/(Ztot)*Va and Zpar/Ztot was capacitative which means that the voltage would definitely lag the source. However, it can be noticed that Vc lags the source but not as much as Vb because the equation we used was R3/(Zc2+R3) *Vb where R3/(Zc2+R3) has a positive phase which explains why Vc lags the source voltage less.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

MULTISIM ANALYSIS Va and Vb shown here with their peak values. Va=999.410 mV Vb=1.660V Va and Vb shown here with their difference in time. ΔT=-109.677 Microseconds.

Va and Vc with their peaks shown here: Va = 999.410 mV Vc = 1.188 V Va and Vc shown with their time difference: ΔT=-41.935 Microseconds. Ilrms=1.048 mA Il=1.048*sqrt(2)=1.482 mA

The phase can be found using the formula: phase = 2 ∗ π ∗ f ∗ Δtf = 1750 Hz For the phase and time difference of Il I could not figure out how to measure it, so I calculated it using the value of Va found (named Vtry). Amplitude Phase(rad) Δt (μs) Va 0.99V 0 0 Vb 1.66 V -1.205 -109.6 Vc 1.19 V -0.461 -41.9 Il 1.48 mA -0.051 -4.66 Comparison of MultiSim to analytical analysis: Our values in the analytical analysis and the MultiSim are very close and have only slight differences such as a maximum of ±0.07 V in the amplitude. The time differences do agree as well within a maximum of 1.2 microseconds. The phase may seem to vary a lot but that is because the small differences in time are multiplied by omega which is around 10995 rad/s which can greatly magnify the small differences in time. PHYSICAL MEASUREMENTS Circuit: Values:

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

L1=0.1 mH, R1=219 ohm, C1=50 nF, R2=219 ohm, C2=50nF, R3=1976 ohm. R1 is the resistance of L1 that I included in the circuit. I am unsure whether this resistance changes as the voltage signal goes through the inductor which might be a source of error. Vb C2 Vc L1+R1 R3 R2 C1 Va DISCLAIMER: The values for the amplitudes of Va and Vb are going to be different than the pictures provided because I have taken the average value, the values were fluctuating. Measurements:

Amplitudes: Va=1.00 ± 0.05 V Vb=1.70 ± 0.05 V Time difference: Δt= -104.0 ± 8.5μs Note: 8.5=8(smallest division) + 0.5(specified uncertainty) Amplitudes: Vc=1.24 ± 0.05 V Time difference: Δt = -40.0 ± 8.5μs Ilrms=0.877 mA which is Il=1.240 ± 0.018 mA (±1.3%+2) [Note to TA: I do not understand why I measured 0.877 would you please include what you think is happening in your feedback?] Table 3

Amplitude Phase (rad)[Δt*ω] Δt (μs) Va 1.00 ± 0.05 V 0±0.09 0.0± 8.5μs Vb 1.70 ± 0.05 V -1.14±0.09 -104.0 ± 8.5μs Vc 1.24 ± 0.05 V -0.44±0.09 -40.0 ± 8.5μs Il 1.240 ± 0.018 mA Undetermined Undetermined Discussion: As we can see the values of the amplitude are close to the values found in the other two methods. I did not include the phase of the current because the purpose of this lab is just to measure its amplitude. Speaking of the current Il, you can see that its value is not even close to the values measured in the other two methods, there is an error involved with its value that I could not figure out. In terms of lags and leads, the voltages Vb and Vc do lag the source, just like the other two methods have shown. ANALYSIS Amplitude Table 4: Physical Multisim Analytical Va 1.00 ± 0.05 V 0.99V 1.00 V Vb 1.70 ± 0.05 V 1.66 V 1.72 V Vc 1.24 ± 0.05 V 1.19 V 1.26 V Il 1.240 ± 0.018 mA 1.48 mA 1.48 mA For Va, Vb and Vc the values all agree within uncertainty. The physical measurements values deviate from our Multisim and physical measurements slightly, however this may be due to random errors as well as the errors of the measurement devices themselves. On the other hand, the value for Il in the physical measurement greatly differs from the Multisim and analytical values for Il. This may be because of the inductor’s resistance is changing; however, I do not have a clear idea as to why this value deviates so far from the other two methods. It can be noticed that the physical values of Va, Vb and Vc all agree within uncertainty with the Multisim and Analytical values. Phase Table 5: Physical Multisim Analytical Va 0±0.09 0 0 Vb -1.14±0.09 -1.205 -1.218

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Vc -0.44±0.09 -0.461 -0.474 Il Undetermined -0.051 -0.051 For Il, I struggled with finding its phase using measurement tools without involving analytical formulae, so I have left it undetermined, although, the multisim and analytical values of the phase of Il do in fact agree. While the physical measurements of the phase may deviate from the multisim and analytical values, they are still well within the uncertainty range. In addition, the signs of the phases all match up, further verifying the presence of lags and leads with respect to the source. REFLECTION The objective of this experiment was to analyze the effects of different combinations of inductors and capacitors on the phase and amplitude of an incoming AC Voltage wave. We know that a purely inductive circuit results in a current lag, and a purely capacitive circuit results in a voltage lag, when inductors and capacitors are used in combination, we can create different phase differences that may be needed for different devices. Knowledge of these effects can help with making devices like filters which only allow a certain frequency to pass through can be created. In this experiment, I faced a difficulty with my current measurements for an unknown reason I was getting a current much lower than the Multisim and Analytical analysis. I think that the resistance of the inductor might be changing which resulted in this or that I made an error in my measurements that I could not pinpoint.