Home / Circuits with Matlab / Nodal Analysis using Matlab | Nodal Analysis using Matrices

# Nodal Analysis using Matlab | Nodal Analysis using Matrices

Want create site? Find Free WordPress Themes and plugins.

In this tutorial, we will find node voltages for a very simple resistive circuit using Nodal Analysis.

While applying KCL, we will assume that currents leaving the node are positive and entering the node are negative. Keeping that fact in mind, let’s write node voltages for each node in the circuit.

Node 1:

\begin{matrix} \begin{align} & \frac{{{V}_{1}}-{{V}_{2}}}{10}+\frac{{{V}_{1}}-{{V}_{3}}}{10}-5=0 \\ & 0.15{{V}_{1}}-0.1{{V}_{2}}-0.05{{V}_{3}}=5 \\\end{align} & \cdots & (1) \\\end{matrix}

Node 2:

\begin{matrix} \begin{align} & \frac{{{V}_{2}}-{{V}_{1}}}{10}+\frac{{{V}_{2}}}{50}+\frac{{{V}_{2}}-{{V}_{3}}}{40}=0 \\ & -0.10{{V}_{1}}+0.145{{V}_{2}}-0.025{{V}_{3}}=0 \\\end{align} & \cdots & (2) \\\end{matrix}

Node 3:

\begin{matrix} \begin{align} & \frac{{{V}_{3}}-{{V}_{1}}}{20}+\frac{{{V}_{3}}-{{V}_{2}}}{40}-2=0 \\ & -0.05{{V}_{1}}-0.025{{V}_{2}}+0.075{{V}_{3}}=2 \\\end{align} & \cdots & (3) \\\end{matrix}

Let’s combine all (1), (2), and (3) in Matrix form

$\left[ \begin{matrix} 0.15 & -0.1 & -0.05 \\ -0.1 & 0.145 & -0.025 \\ -0.05 & -0.025 & 0.075 \\\end{matrix} \right]\left[ \begin{matrix} {{V}_{1}} \\ {{V}_{2}} \\ {{V}_{3}} \\\end{matrix} \right]=\left[ \begin{matrix} 5 \\ 0 \\ 2 \\\end{matrix} \right]$

Now, we will write a small piece of Matlab code to compute all node voltages.

clear all;close all;clc
% Nodal Analysis using Matlab
Y_Mat = [ 0.15 -0.1 -0.05;
-0.1 0.145 -0.025; % Admittance Matrix (YV=I) obtain from Node equations
-0.05 -0.025 0.075];
I_vec = [5;
0; % Current Vector (again from Node equations)
2];
%% Node Voltages Calculation
fprintf('Nodal voltages V1, V2 and V3 are \n')
V_Node = inv(Y_Mat)*I_vec


Results:

Nodal voltages V1, V2, and V3 are

V_Node =

404.2857

350.0000

412.8571

Did you find apk for android? You can find new Free Android Games and apps.