# ECE207 Electrical Engineering Fall Lab 1 Nodal Analysis, Capacitor and Inductor Models

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1 Lab 1 Nodal Analysis, Capacitor and Inductor Models Objectives: At the conclusion of this lab, students should be able to: use the NI mydaq to power a circuit using the power supply and function generator use the NI mydaq to take measurements using the multimeter and oscilloscope verify nodal analysis by examining a resistive circuit derive a model for a capacitor derive a model for an inductor Equipment: Laptop with NI mydaq software installed NI MyDAQ breadboard resistor resistor 1-1 k resistor resistor F capacitor 1-33 mh inductor Procedure Part 1 - Introduction to the NI mydaq 1. You should become familiar with the NI my DAQ instruments by reviewing the documentation in the box and the tutorials at the following links: Introduction to NI mydaq: DMM ohmmeter: Analog Output and Input: 2. Launch the NI ELVISmx Instrument Launcher from the National Instruments folder and you should see the toolbar appear on your desktop. Click on the DMM on the Instrument Launcher and use the NI mydaq to measure the actual values of the 120, 200, 300 and 1 k resistors (see Figure 1) CAB Lab1.docx 1

2 Figure 1: DMM Measurements with the NI mydaq 3. For all of the labs in this course, you will record your data, analysis and observations on a worksheets which will be due at the end of class on Thursday. The worksheet will be available at the end of the lab procedure. 4. For each of the resistors, record the measured value, nominal value and % error in the appropriate space on the worksheet. Recall that the % error formula is Part 2 - Nodal Analysis 1. Build the circuit in Figure 2 on your breadboard by laying it out neatly such that it looks exactly like it does on the paper. Turn the breadboard to be horizontal so that the red line is across the top and the blue line is across the bottom. The ground of the circuit should be on the blue line at the bottom which represents a ground buss. 2. Connect the lead from the +15V terminal on the NI mydaq to v 1 on the circuit and connect AGND to the ground buss. Connect the lead from the +5V terminal on the NI mydaq to v 3 on the circuit. Connect the DGND terminal on the NI mydaq to the ground buss. CAB Lab1.docx 2

3 Figure 2: nodal analysis circuit Figure 3 provides an example of a properly wired circuit. Figure 3: properly wired circuit 3. Measure the 3 node voltages and record them on the provided worksheet. 4. Measure the 3 labeled branch currents and record them on the provided worksheet. Don t forget that you have to break the circuit and put the ammeter in series with the element! 5. For the circuit in Figure 2, use nodal analysis to solve for the labeled node voltage and branch currents. You should use the measured values of the resistors in your calculation. You must show your work on the provided worksheet. 6. Complete Table 2 by comparing the measured data to the calculated data. Part 3 - Capacitor Model 1. In this part you will build an RC circuit with a sine wave source. You will use the voltage across the capacitor and current through the capacitor to estimate the capacitor s impedance. Lastly, you will separate the impedance into the resistance and reactive components, R C and C. CAB Lab1.docx 3

4 2. The frequency of the sine wave will be 1 khz and was so chosen so that the RC circuit has a phase angle in the neighborhood of 45, thereby making the impedances of the 1 k resistor and capacitor approximately the same. 3. Use the DMM on the NI mydaq to measure the resistance of the capacitor. 4. Use the RLC meter provided in the room to record the capacitance of the 0.1 F capacitor and record the error on the table. 5. Build the circuit in Figure 4 and remember to lay it out on the breadboard, the way it looks on the paper. Connect the function generator (AO 0, AGND) to the input of the circuit. Connect channel 0 of the oscilloscope (AI 0+, AI0-) to the input of the circuit to measure the source. Figure 4: capacitor model circuit 6. Click on the Scope and FGEN to launch the oscilloscope and function generator on the NI MyDAQ. Set the function generator to a sine wave, 3.5 V pp and 0.00V offset, 1 khz. Confirm that the signal route is AO 0 and click run to provide the source to the circuit. 7. Set the oscilloscope Chanel 0 settings to Source: AI 0, 500 mv/div and Timebase of 100 s/div. Set the oscilloscope Channel 1 settings to Source AI 1, 500 mv/div and set the Trigger to Edge and the Chan 0 Source. Make sure to enable both channels and click run to run continuously. 8. Your function generator and scope output should look similar to the image in Figure 5, if it does not go back and check your work. CAB Lab1.docx 4

5 a. function generator b. oscilloscope Figure 5: V S and V c on the NI MyDAQ function generator and oscilloscope 9. Record the RMS magnitude of V S and V C on the worksheet. 10. Assume the phase angle of the source is 0 and we will now use the oscilloscope cursors to estimate the phase angle. Click Cursors On and put C1 and CH 0 and C2 on CH 1. Put C1 at the zero time crossing for V s. Put C2 at the 0 time crossing for V c. Use the following formula to calculate the phase angle: = t = (dt) [rad] Note that the phase angle can be positive or negative, how do you decide? In this case, since V c crosses the time axis after V s, the waveform is lagging and the angle is negative. The phase should be in the range of -30 to -50 Record the phase angle in degrees of V S and V C on the worksheet at the end of the lab procedure. 11. Calculate the phasor current, I, using the measured value of the 1 k resistor. Note that you can calculate the phasor voltage across the resistor by using V S and V C. 12. Transform the three phasors into the time domain or sinusoidal steady-state as v S (t), v C (t) and i(t). Remember that you need to convert the magnitudes from RMS to peak for the sinusoid. 13. Use the following formula to determine C and R C for your capacitor. Recall that the admittance, Y C, is the reciprocal of the impedance which is the parallel model of the capacitor. Make sure that you use the complete phasor with the angle. Record these values on the provided worksheet. 14. Draw and label the capacitor s parallel model in the space provided. CAB Lab1.docx 5

6 Part 4 - Inductor Model 1. In this section, you will derive an inductor model similar to the procedure used for the capacitor model. Note that the capacitor model was in parallel with a resistance and did not appear to be very ideal. The inductor is a coil of wire and since wires have some resistance it will appear to be in series with the inductor. 2. Use the NI mydaq multimeter to measure the DC resistance of the 33 mh inductor. 3. Use the RLC meter provided in the room to record the inductance of the 33 mh inductor and record the error on the table. 4. Build the circuit in Figure 6 on the breadboard and connect the function generator (AO 0, AGND) and Ch. 0 of the oscilloscope (AI 0+, AI 0-) to the input resistor and ground. Connect Ch. 1 of the oscilloscope (AI 1+, AI 1-) across the inductor to ground. Figure 6: Inductor model circuit 5. Set the function generator to 3.5 V pp, 0.00V DC Offset, 5 khz. 6. Enable both channels on the oscilloscope and set the source on Channel 0 to AI 0 and the source on Channel 1 to AI 1. Set the Volts/Div on both channels to 500 mv. Set the Time/Div to 20 s. Set the trigger type to Edge, Chan 0 source, Rising edge, Level 0. You may want to press the Stop button to get an accurate measurement of V s and V L. Record the magnitude in Vrms and phase angle of Vs and VL on the provided worksheet. 7. Use the voltage across the source and the inductor to calculate the current through the resistor. This is similar to what you did in Part Calculate the impedance of the inductor by using Z L = V L /I = R L + j L. Don t forget that these values are phasors and you have to use the angle to find those values. Record the inductance and resistance on the worksheet. 9. Draw the inductor circuit model on the worksheet. CAB Lab1.docx 6

7 Lab 1 Nodal Analysis, Capacitor and Inductor Models WORKSHEET NAME: NAME: Part 1: Introduction to the NI MyDAQ Table 1: Resistor measurements (you must include units) measured nominal %error Resistor 1 Resistor 2 Resistor 3 Resistor 4 Part 2 - Nodal Analysis Table 2: Node voltage and branch current measurements (you must include units) measured nominal %error v 1 V 2 v 3 i a i b i c Nodal Analysis Calculation CAB Lab1.docx 7

8 Part 3: Capacitor Model R capacitor = C measured = V S = V S = V C = V C = Calculate the current, I: I = Time-domain values: v S (t) = v C (t) = i(t) = Derivation of Y C and calculation of C and R C : CAB Lab1.docx 8

9 Model values from Y C : C = R C = Draw and label the R-C parallel model of the capacitor: Part 4 - Inductor Model R inductor = L measured = V S = V S = V L = V L = Calculate the current, I: I = CAB Lab1.docx 9

10 Derivation of Z L and calculation of L and R L : Model values from Z L : L = R L = Draw and label the R-L series model of the inductor: CAB Lab1.docx 10

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