finite differences method and TEM transmission line parameters

[musilj]

hi all,
I need to work out the the voltage distribution in the dielectric material and TEM transmission line parameters.

The cross section has 0 V at the boundary AND unbalanced conductors at 10 V as illustrated on attachment. I need to write a matlab code that automatically sets up a matrix from the difference equations using Laplacian equation and solve for the nodal voltages using the format AV=B hence V=A\B. Apart from the initialised known node voltages, I am stuck on how to come up with a matlab matrix which would include the unknown node voltages, preallocation of the matrix fills the other nodes with zeros, hence gives false additions when i start scanning the meshes.

I do not intend to use SOR or iterative fdm, but rather set up a matrix and solve as pointed above.

i hope this make sense

thanks
musilj

 

[electricpete]

For a rectangular geometery, the simplest approach is rectanglar mesh.

Looks like you have no variation in dielectric constant and no space charge. Piece of cake (except for the details !?)

A difference equation which can easily be derived:

Vcenter = 0.25(Vleft+Vright+Vtop+Vbottom)
where Vcenter Vleft, Vright, Vtop, Vbottom describe the voltages adjacent to any position.

Every unknown point generates an equation. The adjacent points are either other unknowns or known boundary conditions. It should be easy to realize the number of equations is the same as the number of unknowns, so all the remains is to solve n equations in n unknowns.

N equations in N unknowns... all that remains is bookkeeping to put it into matrix form.

There are of course a wide range of strategies for solving the problem and not all of them require solving NxN matrix.

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[musilj]

hi electricpete

thanks for the reply, I understand that i have to come up with a rectangular mesh as you rightly point out, my real issue is in the Matab implementation- maybe i am just not thinking hard enough! I have solved the problem before by hand calcs taking a few nodes and set up a matrix, then inputted into matlab and solve for unknowns. I can not figure out a way of automatically generating the required matrices in matlab- as I need to increase the number of nodes to plenty for accuracy, which will be beyond realism of hand calcs.

How can I come up with a system written in the form AV=B?.

I hope this all makes sense.