Sinusoidal Steady-State Analysis (Nodal Analysis)

NODAL ANALYSIS

Given the  circuit below i(t) = 5sin(1000t) A. Find Vo(t) and io(t)

a

Solving this kind of problem using nodal analysis is just the same on the DC analysis.

Steps for solving the problem:

1. Analyse the problem first and simplify it (if possible).

2. Solve only for what is being asked.

3. Convert first the passive elements into a frequency domain.

a

where:

L is for Inductor and C is the capacitor element

4. Label the nodes and the reference node. (See figure below)

a

5.  Solve the circuit using your own convenient.

@ node 1

a

@ node 2

a

Simplifying it:

a

Matrix the given equation and solve for V1 and V2 using cramer’s rule. The result will be :

a

Now we have the values of V1 and V2, we can solve the Io (using the Current division):

a

and Vo will be

a

 

In this topic, nodal analysis, is very useful to solve for unknown if only there are two or more sources( voltage or current) in the given circuit. In analyzing the AC circuit, this is just the same in the DC circuit. The rules, KCL and KVL, basic formulas. The only differ is in the values used or the parameters.

 

Leave a comment