Analysing a 3-Loop RLC Circuit and Finding State Equations

In summary, the problem involves obtaining the state equations in matrix form for a two-input and one-output circuit where the output is i2. The relevant equations are Ohm's Law, KVL, and KCL. The currents i1, i2, and i3 are assumed to be clockwise, and there is a need for help with writing the loop equations and choosing state variables. The thread was marked as "solved" by the original poster, though the button for doing so may not be visible for all users.
  • #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].

aCEoLBZ.jpg


Homework Equations


Ohm's Law, KVL, KCL

The Attempt at a Solution


VuAVw22.jpg

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
 
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  • #2
Your first loop equation is incorrect. Notice that the current in the branch with the inductor is ##i_1 - i_2##, so you would instead have ##-L \frac{d}{dt} \left(i_1(t) - i_2(t)\right)##.
 
  • #3
My professor has posted the solution now. This thread may be deleted.
 
  • #4
Captain1024 said:
My professor has posted the solution now. This thread may be deleted.
Threads are not deleted unless there is some extraordinary reason. You may mark it "Solved", however. See the "MARK SOLVED" icon at the top of the thread.
 
  • #5
gneill said:
Threads are not deleted unless there is some extraordinary reason. You may mark it "Solved", however. See the "MARK SOLVED" icon at the top of the thread.
I don't think marking a thread "solved" is an option anymore. I looked at the top of the thread and didn't find anything. Then, I searched the site for "mark solved" and found a thread from last year that mentioned that feature is gone. Thanks anyway.

-Captain1024
 
  • #6
The feature is back. Go to the top of this page and look to the right of the thread title (all the way to the right of the page). Find the black icon:

upload_2016-1-30_21-40-24.png


Just hit that and it marks the thread "Solved".
 

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  • #7
gneill said:
The feature is back. Go to the top of this page and look to the right of the thread title (all the way to the right of the page). Find the black icon:

View attachment 95097

Just hit that and it marks the thread "Solved".
zYRfhTr.jpg


I logged in with Chrome, FireFox, and IE and I did not see that button next to my thread title. Is it possible this is a moderator only feature?
 
  • #8
Captain1024 said:
zYRfhTr.jpg


I logged in with Chrome, FireFox, and IE and I did not see that button next to my thread title. Is it possible this is a moderator only feature?
No, it's supposed to be available to all.

Leave it with me, I'll report the issue. Thanks for pointing it out.
 

FAQ: Analysing a 3-Loop RLC Circuit and Finding State Equations

1. What is a 3-loop RLC circuit?

A 3-loop RLC circuit is an electrical circuit that contains three components: a resistor (R), an inductor (L), and a capacitor (C). These components are connected in a loop, and the circuit can be used to control the flow of electrical current.

2. How do you analyze a 3-loop RLC circuit?

To analyze a 3-loop RLC circuit, you will need to use Kirchhoff's laws and Ohm's law. First, you will need to determine the values of the components in the circuit. Then, you can use these values to calculate the total resistance, inductance, and capacitance of the circuit. Finally, you can use these values to find the state equations, which describe the behavior of the circuit over time.

3. What are state equations?

State equations are mathematical equations that describe the behavior of a system over time. In the context of a 3-loop RLC circuit, state equations can be used to predict the voltage and current at any given time in the circuit.

4. How do you find state equations for a 3-loop RLC circuit?

To find state equations for a 3-loop RLC circuit, you will need to use the differential equations that describe the behavior of each component (resistor, inductor, and capacitor) in the circuit. Then, you can combine these equations using Kirchhoff's laws to find the overall state equations for the circuit.

5. What are the applications of analyzing a 3-loop RLC circuit?

Analyzing a 3-loop RLC circuit is useful in many practical applications, such as designing electronic circuits, predicting the behavior of electrical systems, and troubleshooting circuit problems. It is also a fundamental concept in the study of electrical engineering and physics.

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