Transmission zeros of driving point impedance functions

[1yen]

Hello all,

This question might be at the same time both general and very specific. Admittedly, it has been over 10 years since I really thought about circuit analysis, but I hope I might get some help here! So, thanks in advance!

I will ask a few questions here to make the presentation easier.

• Are there general properties of the transmission zeros of a driving point impedance function? (i.e., is it always minimum phase?)
• If I have a transfer function that is in a partial fraction expansion form, is there a method to realize a circuit from it? i.e.,
  $$P(s) = \sum_{i=1}^n\frac{\alpha_i}{s+\lambda_i}$$
  $$\lambda_i \geq 0 , \sum_i\alpha_i = 0$$

I can say a little more about the coefficients in the transfer function. They come from the eigenvectors of a graph Laplacian matrix, used to describe the interconnections of the network. I can give more details if needed.

From some quick digging around, I found that drive point impedance functions can be synthesized using an RLC ladder. But what happens if I want to measure my output between 2 arbitrary nodes in the ladder? Is there a good way to construct that transfer-function?

I hope this question makes sense. Open to anyh ideas! Thanks again

 

[anorlunda]

But what happens if I want to measure my output between 2 arbitrary nodes in the ladder? Is there a good way to construct that transfer-function?

Your question is, how to derive the transfer function between any two arbitrary points in a circuit? The answer is to write the differential equations of the circuit first, then convert to laplace. That is the subject of most undergraduate differential equations courses, and too much to answer in a thread.