- #1

Captain1024

- 45

- 2

## Homework Statement

Obtain the state equations in Matrix form for the two-input and one-output circuit shown in the figure below where the output is [itex]i_2[/itex].

## Homework Equations

Ohm's Law, KVL, KCL

## The Attempt at a Solution

Currents i1, i2, i3 assumed clockwise. Is there a better assumption I could have made?

Nodes:

a: ##i_1=i_2+i_\mathrm{L}##

b: ##i_3=i_2+C\frac{\mathrm{d}v_C(t)}{\mathrm{d}t}##

Loops:

l1: ##v_1-\mathrm{R}_1i_1-\mathrm{L}\frac{\mathrm{d}i_1(t)}{\mathrm{d}t}=0##

l2: ##v_C-\mathrm{?}-\mathrm{R}_2i_2=0##

l3: ##v_2-v_C-\mathrm{R}_3i_3=0##

Before I start solving for unknowns, I need a little help writing the loop equations. After that, I'm not sure how to choose my state variables.

-Captain1024