Nodal Analysis Lab Name Section Prelab (Must be completed before lab.) Nodal analysis is a method of solving for the node voltages in a circuit. A node voltage is the voltage of a node with respect to ground. In other words, it is the voltage between that node and ground. Nodal analysis can be used even when all other circuit solution methods will not work. Once node voltages are found, the voltages across each circuit element are found easily. 1. Use nodal analysis to calculate the node voltages V1 and V2 in Figure 1. Record to datasheet. 2. Use nodal analysis to calculate the node voltages V1, V2, and V3 in Figure 2. Record to datasheet. 3. Use a MULTISIM simulation to find the node voltages V1 and V2 in Figure 1. Include a printoff of your simulation circuit. Record values to datasheet. 4. Use a MULTISIM simulation to find the node voltages V1, V2, and V3 in Figure 2. Include a printoff of your simulation circuit. Record values to datasheet. Note: most circuit simulation software does not like two voltage sources connected together directly, as in Figure 2. Most circuit simulators use nodal analysis at their core and ideal voltage sources have an indeterminate current through them, subject only to the nature of the circuit to which they are connected. You can fool the software by connecting the voltage sources together using a VERY small resistor, on the order of 1 milliohm. This value is small enough to not perturb the simulation but large enough to be non-zero. 5. Compare your simulation results with your calculated values for both circuits.
R1 V1 1 3k 6.2k 11k 2 3 V2 9.1k V1 DC = 7.5V 1.1k Figure 1 1 R1 2 V1 5.1K DC = 5V 2k 6.2K 3 V2 R6 2K DC = 8V 9.1K 4 5 4.7K Figure 2 V3 Lab Session A Measure the actual values for the resistors in Figure 1, and record them in the Data Sheet. Use these values to calculate the nodal voltages V1 and V2. Use the Multimeter to measure V1 and V2 for this circuit. Compare your measured values with your calculated values. Explain any discrepancies.
Use your measured node voltages to calculate the voltage drops across each resistor. See Figure 3. Lab Session B Figure 3 Measure the actual values for the resistors for the circuit of Figure 2, and use these to calculate the nodal voltages. Use the Multimeter to measure V1, V2 and V3 for this circuit. Compare your measured values with your calculated values. Explain any discrepancies. Calculate the resistor voltage drops using the measured nodal voltages. See Figure 3.
Figure 4 Now, we will measure the node voltages, using the superposition principle. Zero the 8V power supply by setting it to V. Measure the voltages V1, V2 and V3 in Figure 5 and record these into the data sheet. 1 R1 5.1K V1' DC = 5V 2k 6.2K V2' R6 2K 9.1K 4.7K Figure 5 V3' Now, measure the voltages V1, V2 and V3 in Figure 6.
1 R1 5.1K V1'' 2k 6.2K V2'' R6 2K DC = 8V 9.1K 4.7K Figure 6 V3'' The superposition principle states that the system response to all sources can be determined by summing the systems response to each source acting alone, with all other sources zeroed. This strategy only works for linear systems. Calculate the node voltages V1, V2, V3, by zeroing all but one source and calculating V1, V2, and V3. Repeat this process until all sources have had been accounted for and then sum each response. Remember that you must be consistent in your choices of polarity. Compare the superposition results to the measurement results. Is there any difference?
Post lab 1. Can these circuits be solved by other methods than nodal analysis? 2. What was the easiest/hardest part of this lab? Hand in: Datasheet Prelab calculations Prelab simulations Lab calculations Answered questions from prelab, lab and postlab. NO LAB REPORT required for this lab.
Datasheet: Nodal Analysis Lab Name: Section: Prelab Fig 1 Calculated: Fig 2 Calculated: Fig 1 Simulated: Fig 2 Simulated: V1 V2 V1 V2 V3 V1 V2 V1 V2 V3 Lab Session A Actual Resistor Resistor voltages: Values: R1: V R1 : : V : : V : : V : : V : Calculated node voltages: V1: V2: Measured node voltages: V1: V2: Lab Session B Actual Resistor Resistor voltages: Values: R1: V R1 : : V : : V : : V : : V : R6: V R6 : Calculated node voltages: V1: V2: V3: Measured node voltages: V1: V2: V3: Superposition: V1 : V2 : V3 : V1 : V2 : V3 : V1: V2: V3: