Elec Sys Lab 4

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Electrical Engineering

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Apr 3, 2024

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Lab #4: Nodal Analysis ELEE 2317 – 01 Ever Acosta Gerardo Zapata 02/23/2024

OBJECTIVES To demonstrate the validity of the nidal analysis technique through experimental measurements and grain further familiarization with PSpice simulations of electric circuits. EQUIPMENT & PARTS  HP-3631A DC Power Supply  Digital Multimeter (DMM)  Prototype Board  Device Test Leads and Cables  Desktop Computer  1⁄4 Watt Resistors: 1 kΩ, 1.2 kΩ, 2x 2.2 kΩ, 2x 3.3 kΩ  Hook-up Wires IN THE LAB Built circuit shown in Figure 1 and measured R1, R2, R3, and R4 to be 1.1741kOhms, 3.258kOhms, 0.984kOhms, and 2.178kOhms respectively. Figure 1 Used the measured resistor values to determine the nodal voltage which resulted in 5.726V.

Used the following calculations to determine I R1 and I R3. I R1 = (15 – V4)/1.2K = 7.7375 mA I R3 = (V4/1K) = 5.715 mA Then, measured the values of I R1 and I R3, 7.910mA and 5.825 mA respectively. We turned on the power supply and measured value of Va was 5.578V giving us a percent difference of 0.67% for Va and 2.36% and 1.35% for I R1 and I R3 respectively. For the Bridge Network the following calculations were conducted to find the desired values and their corresponding real measured values are noted as well.

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The following is also the work for the percent difference calculated using the theoretical and experimental values. AFTER THE LAB : 1.) What is the procedure of nodal analysis? Explain the steps in the procedure with as many details as possible! Nodal analysis is a systematic approach to electrical circuit analysis that involves several key steps. First, nodes are identified in the circuit—points where two or more elements are connected—and assigned unique reference numbers, designating one as the ground node. Voltage variables are then assigned to each node relative to the ground, forming the basis for subsequent calculations. Applying Kirchhoff's Current Law (KCL) at each non- reference node, which dictates that incoming currents equal outgoing currents, forms the foundation for the analysis. Ohm's Law is then utilized to express currents in terms of node voltages and resistances. These equations are combined to create a system of simultaneous linear equations, representing the nodal analysis model. Solving this system—often done through methods like Gaussian elimination—yields the voltage at each non- reference node. Validation is crucial, involving checking the solution by calculating branch currents and verifying power dissipation. With the node voltages known, additional circuit parameters such as branch currents and component power can be determined. Nodal analysis is particularly effective for circuits with voltage sources, though modifications may be required for circuits with current sources or increased complexity.

2.) When is a supernode necessary to be defined? A supernode is defined in nodal analysis when there is a voltage source connected between two non-reference nodes. This situation creates a constraint that prevents directly applying Kirchhoff's Voltage Law (KVL) to the enclosing loop, as the voltage source introduces a fixed potential difference. To address this, the two non-reference nodes and the voltage source are grouped together as a supernode, treating the voltage source as an internal element within the analysis. The procedure for defining a supernode involves creating a single equation for the supernode that considers the voltages of both non-reference nodes and the voltage source. This equation is then incorporated into the overall nodal analysis equations. In summary, a supernode is necessary when a voltage source spans two non-reference nodes, requiring a special treatment to account for the constrained voltage relationship within the nodal analysis framework.

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