Topological analysis for a network

[Uhm]

Hi,

I was set a piece of work for a module and it is asking me to do a topological analysis of a network. The question is:

For the network shown below, take n1 as the reference node and write down the incidence matrix. For the same network, write down the independant node equations in matrix form.

I've attached the circuit picture from the work below.

The problem is that I've looked through my lecture notes and I cannot seem to find anything on this type of analysis. We have stuff on the node voltage analysis, branch current method and some other theorems. I really need help understanding what it is they're asking for and if there's a name for the way to calculate the answer.

Any help would be really appreciated

 

[Harald Kapp]

Hello,

Incidence matrices are explained here:
http://mathworld.wolfram.com/IncidenceMatrix.html

Independent node equations are explained here:
http://fourier.eng.hmc.edu/e84/lectures/ch2/node2.html

Matrix equations are explained here:
http://www.math.utah.edu/~gustafso/matrix-eqn.pdf

Harald

 

[Uhm]

Thank you for replying!

I am still struggling a bit with the incidence matrix stuff, the rest understandable but I was hoping you would be able to explain it?

 

[Harald Kapp]

Look at the example on the Wolfram page.
Each matrix has
- as many columns as there are connections between nodes.
- as many rows as there are nodes
You can directly correlate this with your diagram:
- there are 7 connections (=components incl. voltage source)
- there are 5 nodes
A matrix element is 1 if the corresponding node (row) is endpoint of the respective connection (column). All other matrix elements are 0.
Label your nodes and connections from 1 to 5 and 1 to 7 respectively. Set up the matrix and find the nodes that are part of connections. Set the corresponding matrix elements to 1, the rest to 0.

That's as far as I'm going to detail this.

Regards,
Harald

 

[Uhm]

Thank you! That has been very helpful!