Linear Algebra - Incidence Matrix of an RLC Ckt

In summary, the circuit has resistors, inductors, and capacitors, and the matrix is a vector consisting of the element jωL in the ith row and column.
  • #1
YoshiMoshi
226
8
<Moved from a homework forum. Template removed.>

I can't find any documentation on how to do this. I remember in linear algebra how to find the incidence matrix of an electrical network of purely resistors. Put how do I find it of a RLC circuit with resistors, inductors, and capacitors? I can't even find an example. Thanks for any help.
 
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  • #3
I'm not able to open that link
 
  • #4
YoshiMoshi said:
I'm not able to open that link
The link doesn't open here either. Looking for it in google gives the same link with the same result.

I think you can use complex impedances instead of the resistance. Inductor is jωL, capacitor is 1/jωC. Your matrix will depend on the frequency.
 
  • #5
Link won't open here either. It is apparently a closed educational network in Sri Lanka:

address: University of Peradeniya
address: Peradeniya (20400)
country: LK
 
  • #6
Today, I can't open the link either - using a different computer. The computer I used to read the pdf still opens it, but that may be because the pdf is cached on the machine.
 
  • #8
YoshiMoshi said:
<Moved from a homework forum. Template removed.>

I can't find any documentation on how to do this. I remember in linear algebra how to find the incidence matrix of an electrical network of purely resistors. Put how do I find it of a RLC circuit with resistors, inductors, and capacitors? I can't even find an example. Thanks for any help.
I do not think the nature of the elements matters, as far as the incidence matrix is concerned.
For an example of an RLC circuit and its incidence matrix, you can have a look at p 385 (Section 9.1) of Basic Circuit Theory by Desoer and Kuh, 1969.
 
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1. What is an incidence matrix in the context of RLC circuits?

An incidence matrix is a mathematical representation of the connections between different elements in an RLC circuit. It is a square matrix that contains information about the nodes and branches in the circuit, and how they are connected to each other.

2. How is an incidence matrix used in analyzing RLC circuits?

An incidence matrix helps in solving the equations that describe the behavior of an RLC circuit. It can be used to determine the voltage and current in each element of the circuit and to calculate the overall behavior of the circuit in response to different inputs.

3. What information does an incidence matrix provide about an RLC circuit?

An incidence matrix provides information about the topology of the circuit, including the number of nodes and branches, the connections between them, and the direction of current flow in each branch. It also helps in identifying any loops or meshes in the circuit.

4. How is an incidence matrix different from other types of circuit matrices?

An incidence matrix is specifically designed for RLC circuits and represents the connections between different elements in the circuit. It is different from other types of matrices such as impedance or admittance matrices, which represent the electrical properties of the circuit elements.

5. Can an incidence matrix be used to analyze complex RLC circuits?

Yes, an incidence matrix can be used to analyze even the most complex RLC circuits. It can handle circuits with multiple nodes, branches, and loops, making it a powerful tool for circuit analysis. However, for larger and more complex circuits, the matrix can become too large and difficult to manage, so other methods may be used in conjunction with the incidence matrix.

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