I have found this doctoral thesis:

Article On-board health monitoring of power modules in inverters dri...

where in chapter 3.3 this conversion is explained. The example in appendix 2 seems to give same answers as this matlab code linked above.

I just still dont get the idea of this. How is Y_i and Z_i derived for i:th term?

Hello Aku Forsström ,

The transformation between the Foster and Cauer RC circuits is a staple of books on network synthesis, see,

M. E. Van Valkenburg; Introduction to Modern Network Synthesis; John Wiley & Sons, Inc.; 1960; pp. 140-160, Chapter 6 - RC and RL Networks.

I am curious, though, why do you need to perform the transformation? If you have an RC ladder network, representing a material of finite spatial extent with thermal conductivity, mass density, and heat capacity at constant pressure, why can't you just solve this problem in Simulink? The Simulink solution would, of course, not be exact as it requires discretizing of the spatial portion of the parabolic PDE (Partial Differential Equation). I mean, I am assuming you are going to solve your heat transfer problem using the Matlab SMT (Symbolic Math Toolbox) using dsolve() so the problem is solved algebraically, however, still not exactly, but is this approach necessary?

Can you tell us a little more about the actual statement of the problem or would that disclose propiertary information?

Regards,

Tom Cuff

http://arxiv.org/ftp/arxiv/papers/0801/0801.0817.pdf

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1084459&abstractAccess=no&userType=inst

http://ieeexplore.ieee.org/xpl/abstractAuthors.jsp?arnumber=1084459

Helllo everyone! Thank you for your answers. I am still pondering this problem for now.

Thomas Cuff: I am trying to derive the Cauer model to then plot the cumulative capacitance and cumulative resistance. This should give me a look of the structure in question.

Repeating this plot during the lifetime of the system should then give the changes in the structure during its lifetime.

For now I dont know how the transformation will be done. The m-file linked above gives good results even without Matlab SMT part. I dont know what happens when I input ~100-200 RC stages however.

https://en.wikipedia.org/wiki/Admittance https://electronics.stackexchange.com/questions/488011/converting-a-lithium-ion-model-from-a-foster-network-to-a-cauer-network

Hello Aku Forsström ,

Forgive me, but I am still not clear on what you are trying to do. It appears that you are considering a 1-dimensional heat transfer situation, which can be modelled as an RthermalCthermal ladder network based on the duality between the RC telegrapher's equation and the heat diffusion equation. I have attached a document I wrote describing how to derive this duality and showing the ladder network. From what you have said, it appears that you believe that with use the RthermalCthermal sections of the ladder will experience a change in their parameter values (thermal conductivity, heat capacity at constant pressure, and/or mass density, see pp. 4-5 of my document for the relationships amongst these parameters and Rthermal and Cthermal), and that the driving point impedance or admittance will allow you get the cumulative values ∑Rthermal and ∑Cthermal from all sections of the ladder. Do I have that correct?

The reason I am asking is that I am unaware of any heat transfer problem requiring the Foster to Cauer transformation. Please, can you provide a citation to such a thermal analysis? Note, I have tried to obtain the document entitled "On-board health monitoring ...", which you mentioned, but I have been unsuccessful so far.

Regards,

Tom Cuff