Lab 5 Final

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EE 220L Sec)on 1006 Lab 4: Nodal and Mesh Analysis October 4, 2023 <Nicholas Eastwood> <Andrew Hardwick>

EE 220L Sec)on 1006 Objec)ve: The objec)ve for this lab is to calculate given circuits using nodal and mesh analysis and compare results to simulated values from Mul)sim and measured values obtained using circuit components on a breadboard. Equipment Used: Breadboard Resistors: AC/DC Power Supply Two 1k Ω Digital Mul)meter with Clips Connected 1.8k Ω Power Supply Clips 2k Ω Breadboard Jumper Cables 4.7k Ω Alligator Clips 10k Ω Two 20k Ω 30k Ω The power supply is a device that provides a stable and adjustable DC (Direct Current) voltage to your circuits. The tolerance of error of +0.5% means that the voltage output of your power supply may deviate from the set value by up to 0.5%. For example, if you set the power supply to provide 5 volts, the actual output voltage can vary between 4.975 volts and 5.025 volts. Theory: Nicholas Eastwood For this lab, we analyzed two electrical circuits by comparing calculated values derived from using Nodal analysis and mesh analysis, comparing these values to values found via simula)on using Mul)sim and measured values found through measurements taken from building the circuit on a breadboard. Theore)cally, the values of all three should be the same, with the calculated values and simulated values being near iden)cal with a margin of error being allowable for the measured values. For the first circuit, we were tasked with analyzing Circuit 1 (figured below) using nodal analysis at point A, B, and C.

EE 220L Sec)on 1006 To perform nodal analysis, we find the node voltages at the requested points. Nodes are the point between circuit elements. Nodal analysis uses the applica)on of Kirchhoff's current law to create a series of node equa)ons that can be used to solve node voltages. This is the ideal method to analyze this circuit, as opposed to mesh analysis, because the amount of meshes in the circuit makes this method cumbersome. Ohms laws are used to find these node voltages and circuit currents. I = V R The general forms of the nodal analysis equa)ons we will use is as follows: V ! − V " R # + V $ − V " R % = V " R & We can use these equa)ons and our knowledge of circuit analysis to calculate the currents delivered by each power supply in our system. We will use MatLab for the matrix calcula)on. We can then use Mul)sim to simulate the results that our circuit provides. Theore)cally these values should be iden)cal. Finally, we will build the circuit using a breadboard. Then we will measure the current delivered by each power supply. These values should be the same as the simulated and calculated values within an allowable percent difference. We can find this percent difference by using the percent difference equa)on. Using these values, we can calculate the power consumed by the circuit. %Difference = expected − measured expected × 100% For the second circuit, we are given the same task of calcula)ng, simula)ng, and measuring the node voltages at A, B, C, and D. For this circuit(Figure 2).

EE 220L Sec)on 1006 For mesh analysis, we use Kirchoffs Voltage law to find the node voltages at the four nodes. We then repeat the same process as from the first circuit by simula)ng the circuit in Mul)sim and building the circuit on the breadboard. We then use the percent difference equa)on as before with the measured and calculated values. The simula)on and calcula)on should be iden)cal, and the measurements should be within an allowable error. Theory (Andrew Hardwick) Nodal analysis, also known as the node-voltage method, is based on Kirchhoff's current law (KCL) and Ohm's law. Nodes are points in the circuit where two or more elements meet. Assume voltages for each node with respect to the reference node. The reference node voltage is usually taken as 0V. KCL equa)ons for each non-reference node. The sum of currents entering a node is equal to the sum of currents leaving the node. Mesh analysis is based on Kirchhoff's voltage law. A mesh is a loop that does not contain any other loops within it. Assume currents for each mesh. Choose a direc)on for each current, and assign a variable. Write KVL equa)ons for each mesh. The sum of voltage drops around any closed loop is zero. Nodal analysis focuses on the currents ﬂowing into and out of nodes, while mesh analysis relies on the voltages around loops. Procedure Circuit 1 We first start by performing the calcula)ons for nodal analysis. We will the put these values in a matrix in MatLab. V ! − 5 1000 + V ! 1800 + V ! − V " 1000 = 0 V ! 23 9000 − V " 1 1000 = 1 200

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