Question

Question 1 8 pts Use Nodal Analysis to complete the elements of the Amatrix of the equation A*V=S, where A is the nodal matrix, V is the nodes vector and Sis the sources vector for the circuit below: 2.12 21 2/0° A 12%ºv vil V2 V3 + Is Vs 22-12.12 Z3j42 24221 v. . Copy the Gxx and paste below then complete. G11= G12= ; G13= G21= G22= ; G23= G31= G32= ; G33= .


CIRCUIT ANALYSIS!
Electrical engineering!
Knowledge of MATLAB required!!!!
Professionals only!
Please be clear and concise.
MUST ANSWER ALL PARTS OF QUESTION!!!!!!!! Credit only awarded to all complete answers
Please circle answers

FILL IN THE MATRIX G11 G12 G13 and etc.....
I need all three values for S [ ---, ---, ---]
i need v0 in rectangular form
i need v0 in polar form

Answer 1

Solution : For the given circuit shown , first we need to assign the reference ground node then by Nodal analysis approach by using KCL at node 1 and KCL at supernode 2 and 3 we can obtain the three set of equations for the unknown node voltages such that the obtained equation can be setup in matrix form to obtain the unknown parameters ,then entering the values in the MATLAB script to determine the required output voltage in rectangular and polar form as shown below-

souding for the circuit shown infigure 212 Z1 (node 3 node 2/0° 12/0° V vill V2 V3 node 1 O + IS Vs 22-22 23] 14 24322 v. 0 ground node node Taking 'o'as ground Apply Kel At Node 's' we get It 1 Is Vo Z It Mit -引 2 - from eq? (2) 4,105 +0.5j) - 0-5V, = 2 ) =(0.5 +0.5j) GI G12 | GB C

Apply Kee At Sapronode & and 's' we get *[ 3 ] + v3+.) - V -35 > + V2 + V3 (+2) 1) + = -2 + Vollt 2 slor 기 j4 o 17 - 05v; -Jo.25 V + V₂ from egn (4) we we get 1 G21 0.5 1/4 G22 Ž joas Ga3 = (1 + 24 1 an and the two nodes are KNL separated by independent retrage source 'l' cling va tus - Vg Vg -v2 - Vs from eq? (5) G31 G32= -1 5 =0 G33=1

now using the equation &, 3 and 5 6*3.)V, +0.ve - Ny = 2 *** + žg Ve +68+) Vy = -1 va + V₂ Put the equation in MATRIX FORM *** **** - ON Vs 22 Is 2/4 12 -35 VIP Vz Vs 0 1 [A] [V] [3] MATRIX FORM as The equation represented in [A][v] - [S] cohere [AJ the nodal conductance malinis V] is the node vector matrix [s] is the source water MATRIX

therefore values of conductance elements of matrix [A] is equal to - GIMI G12 0 G13 ort NI G21 6122 G33 À - Ti o e will Ку 6131 G32 633 Gil 4) =(0.5 +0.5j) G12 =0 G3 NI G122 -I = -0.5 G22 = 1 / 3 = -jous G23 = 1/2 + 1/2 1 G3) = 0 G32= -1 G33=1 and the elements of Source matrix [S] is equal to - Is [S] = -Is Vs i.e. [S] -2 Now, entering the obtained data into the given MATLAB SCRIPT to obtain the required node voltages and the output voltages 'Vo' as shown below-

MATLAB CODE FOR SOLUTION %nodal analysis clc; clear all; close all; Z1=2; Z2=-2*j; z3=4*j; Z4=2; Vs=12; Is=2; G11= ((1./21) + (1./22)); G12=0; G13= (-1./21); G21=(-1./21); G22=1./23; G23=((1./21)+(1./24)); G31=0; G32=-1; G33=1; A=[G11 G12 G13; G21 G22 G33; G31 G32 G33]; % Conductance Nodal matrix S=[IS;-IS;Vs]; % Souce vector Matrix V=A\S % Voltage at different node in rectangular form Vo=V (3); % Voltage at node 3 is equal to Output voltage. % Amplitude of Output voltage. R=abs (Vo); theta=phase (Vo) *180/pi; % Phase of Output voltage disp(['Vor', num2 str (Vo)]); disp(['Vor', num2 str (R),'/_', num2 str (theta)]);

Command Window V = -1.3333 - 4.0000i -13.3333 5.3333i -1.3333 5.3333i Vo=-1.3333-5.3333i x Output voltage obtained in rectangular form as- Vo=- 1.333 - 35.333 Volt Vo=5.4975/ -104.0362 Output voltage 'Vo' obtained in polar form from the script Run which is approx. equal to : Vo = 5.5_-104.03° Volt