ANSYS Maxwell Impedance Matrix

Hello everybody,

Three conductors are being simulated in Maxwell with a peak current. From Maxwell I extract the impedance matrix (3x3 matrix) of the three conductors. Conductors are placed on top of each other so there will be mutual inductances and resistances. The documentation on the impedance matrix (2 by 2 matrix) from ANSYS is shown here:



3x3 example is not available.

How do you calculate the total resistance and reactance or impedance of a single conductor from the matrix? I was told you add R11 + R12 + R13 (same idea for reactance add across) to get total resistance of a conductor but I believe that is wrong. Reason is because you have two different currents I1 and I2 in these terms.

These conductors are being represented (Maxwell simulation) as 3 loops. Similar to what is shown in the documentation.

• The diagonal resistances are the self resistances due to DC component and skin effect as well as proximity effects. The off diagonal resistance is the result from proximity effect currents.

• The diagonal inductance are the self inductance of each coil and the off diagonal inductance are the mutual inductance due to coupling.

Here I derived (2x2 matrix only meaning 2 conductors) where each equation comes from and how the impedance matrix is built.



Now I believe the components in Z11 represent the total resistance and reactance of one conductor. Then Z22 represents the total values for the second conductor, and so on for n condcutors.

I cannot find a source to back this up. Does anyone know if what I defined is true? or provide a documentation based on calculating total impedance of a single conductor with mutual resistances and inductance? I cannot find anything online.

Thank you, and let me know if there are any questions.

Welcome jcesar203,

I've been working a fair bit with MTL theory lately so this looks familiar. However, I'm not sure what you mean by "the total resistance and reactance or impedance of a single conductor". One conductor by itself does not mean anything in transmission line theory, are you looking to extract the input impedance seen at a specific port (set of two conductors)? As in one of your loops?

You are correct that the other currents (I1, I2, etc.) will affect the results... this is why the solution is a matrix and not a number. Therefore, if you are looking for a particular result, you need to specify what the boundary conditions are on every port. Keep in mind that the definition of Z-Parameters requires that every other port is open-circuited!

If you are looking at the impedance of a single loop (say, #1) then, when the rest of the ports are open-circuited, then the input impedance is simply Z11.

Hope this helps,
PlanarMetamaterials

PlanarMetamaterials said:

Welcome jcesar203,

I've been working a fair bit with MTL theory lately so this looks familiar. However, I'm not sure what you mean by "the total resistance and reactance or impedance of a single conductor". One conductor by itself does not mean anything in transmission line theory, are you looking to extract the input impedance seen at a specific port (set of two conductors)? As in one of your loops?

You are correct that the other currents (I1, I2, etc.) will affect the results... this is why the solution is a matrix and not a number. Therefore, if you are looking for a particular result, you need to specify what the boundary conditions are on every port. Keep in mind that the definition of Z-Parameters requires that every other port is open-circuited!

If you are looking at the impedance of a single loop (say, #1) then, when the rest of the ports are open-circuited, then the input impedance is simply Z11.

Hope this helps,
PlanarMetamaterials

Click to expand...

Thank you for your response.

The three conductors are just three busbars. I want to find the electrical characteristic of each busbar which are its resistance and reactance at a given rated current.

Like you said at the end of your post, the input impedance is simply Z11 which is what I am thinking it is.

Based on what I said on top, does it still hold true that Z11, Z22 and Z33 are the input impedance of each bar? It seems that maxwell calculates these values based on magnetic field.

Hi jcesar203,

If you're working with busses (i.e., single conductors), then you of course need to specify which is your "ground" or "return". If you're looking to extract the series impedance from a Z-matrix, there is a process for that (see Pozar 3rd ed. Page 188 for an *effective* 2-port network).

Yes, Z11, Z22 and Z33 are the input impedance of each bar under the condition that the other ports are open-circuited. If all loops are active simultaneously, this will not be true.