NODAL ANALYSIS
The basis of nodal analysis is Kirchoff's current law. Since KCL is valid for phasors, we can also analyze ac circuits using nodal analysis.
This are some steps to analyze AC circuits:
1. Transform the circuit to the phasor or frequency domain.
2.Solve the problem using circuit techniques (nodal analysis, mesh analysis, superposition, etc)
3. Transform the resulting phasor to the time domain.
Example:
Example:
Find Ix in the circuit using nodal analysis
We first convert the circuit to the frequency domain:
20cos4t => 20∠0 , Ѡ=4rad/s
1H => JѠL=J4
0.5H => JѠL=J2
0.1F => 1/JѠC= -j2.5
The frequency domain equivalent circuit is as shown in figure
Applying KCL at node A
20-Va/10= Va/-j2.5 + Va-Vb/J4
or
(1+J1.5)Va+J2.5Vb=20
At node B
2Ix+Va-Vb/J4=Vb/J2
Ix=Va/-j2.5 then substitute
2Va/-j2.5+Va-Vb/J4=Vb/j2
By simplifying, we get
11Va+15Vb=0
Then Equation 1 and equation 2 can be put in matrix form as shown
|1+j1.5 j2.5| |v1|=|20|
|11 11 | |v2|=|0|
where delta =15-j5 as i computed using matrix form
and Delta1 equals to -220 as i computed using cramers rule.
where v1=delta1/delta=300/15-j5=18.97angle18.43 V
v2=delta2/delta=-220/15-j5=13.91angle198.3 V
The current Ix is given by
Ix=V1/-j2.5=18.97angle18.43/2.5angle-90
=7.59angle108.4 A
Transforming this to the time domain,
ix=7.59cos(4t+108.4) A
No comments:
Post a Comment