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In a recent post:

How can the transfer function of an infinite ladder network be used to solve real world problems?

I reference how one can solve the transfer function (impedance) of an infinite ladder network. In what I've researched the techniques and solutions apply to the input impedance (looking at the network input). So from that perspective, and as an example one could solve what the input voltage response is for say a step current input.

But a long network model (transmission line for example) also has an output terminal. When using the same (infinite elements + just one more element = infinite elements) technique I'm unable to formulate a solution (transfer function) that relates the input with the output.

Can I use the same technique or is there another trick that applies?

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  • The impedance is not the transfer function. An impedance is a property of a two-pole (i.e. one-port), a transfer function is a property of an electrical four-pole (two-port). If you want to learn how to calculate transfer functions of two-port circuits, I would start here: https://en.wikipedia.org/wiki/Port_(circuit_theory) and https://en.wikipedia.org/wiki/Two-port_network. It's not too complicated and basically boils down to matrix products. – CuriousOne Nov 01 '15 at 22:50
  • @CuriousOne Take a simple series RC circuit with input current and input voltage as the 'output' The impedance is $$\frac{V}{I}=\frac{j\omega RC +1}{j\omega RC}$$ You are telling me that I can't call this a transfer function? – docscience Nov 01 '15 at 23:07
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    @CuriousOne Impedance is a transfer function sure as you're born. I think you might be thinking about the difference between an impedance matrix and a scattering matrix (often called "S-matrix"), which differ by the boundary conditions assumed in their construction/measurement. However, distinguishing by the number of ports/wires is not the critical distinguishing factor. docscience, you are correct to think of impedance as a transfer function. – DanielSank Nov 01 '15 at 23:09
  • @DanielSank: Irrespective of choice of term all of these are linear. I don't know where docscience got the idea that they aren't. :-) – CuriousOne Nov 01 '15 at 23:14
  • @CuriousOne I have completely lost your line of discussion here. When did docscience say anything at all about linearity? – DanielSank Nov 01 '15 at 23:19
  • @DanielSank: In his previous question. – CuriousOne Nov 01 '15 at 23:19
  • @CuriousOne Yikes, that's confusing. Also, it's super-duper confusing that when I made a counterpoint about your statements regarding "transfer function" you abandoned that discussion entirely. For the sake of other readers I think we ought to come to some sort of agreement. ...or not. I guess people can consult the literature themselves. – DanielSank Nov 01 '15 at 23:23
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    @CuriousOne Just so you realize I'm not just trying to be a needle in your side, I am up-voting several of your comments regarding linearity. – DanielSank Nov 01 '15 at 23:27
  • @DanielSank: Yes, I think he was a bit confused when he wrote that. Nothing that can't be rectified by him looking at the two-port theory. That should set it straight. And, by the way: I think we are somewhat past the personal animosity stage, aren't we? I didn't take your comments personally, don't worry. You are correct about my use of language, I should be more careful. If you feel like writing an answer, I am more than happy to delete all of my comments. At this point I think docscience can look it up himself, though. – CuriousOne Nov 01 '15 at 23:30
  • If you have an output terminal, you need tot specify the load on that terminal. If you don't, then you haven't given enough information for there to be a well defined impedance. – DanielSank Nov 01 '15 at 23:55
  • @DanielSank it just occurred to me this morning - regarding a 4 port network. Since it has a physical 'beginning' and 'end' and considering your answer to my other question regarding relative size of wavelength and ladder rung 'size' , does it make any sense to consider an infinite 4 port network? – docscience Nov 02 '15 at 15:48
  • @docscience I usually think of "infinite" as a limit of something. So yeah, I can make a 4-port network with $n$ sections and then take $n$ to infinity. – DanielSank Nov 02 '15 at 16:00

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