Talk:Image impedance

Definition

"The definition of image impedance for a two-port network is the impedance, Zi 1, seen looking in to port 1 when port 2 is terminated with the image impedance, Zi 2, for port 2." This definition contains the word which is being defined. Kmpw (talk) 19:24, 13 January 2009 (UTC)

While your statement is true, it is not a logical fallacy. A definition of x as x²-2 contains the term being defined but has a well known analytical solution of "2". In the case of image impedance there are two unknowns and two equations (the inverse condition of Zi 2 looking into port 2 while port one is terminated with Zi 1 must simultaneously be true) and is therefore amenable to an arithmetic solution. SpinningSpark 22:40, 14 January 2009 (UTC)

I can't make head or tails of the lead paragraph. One simple question: why "image"? I can't find anything that relates to a normal meaning of image. Also isn't this definition much clearer: One of the impedances that, when connected to the input and output of a transducer, will make the impedances in both directions equal at the input terminals and at the output terminals.[[1]] Bhny (talk) 21:08, 31 August 2014 (UTC)

No, in general, the image impedances are not equal (and it says this in the lead). Also there is no transducer. Perhaps the definition in the lead assumes something that needs to be stated explicitly, or perhaps it contains an ambiguity. If I break the idea down into a series of statements perhaps you can identify what the present definition fails to capture:

• We are considering an electrical network with two ports, each consisting of a pair of terminals.
• The impedance presented by the network at a port can be measured by applying a voltage between the two terminals and observing the resulting current; we call this the impedance looking into the port.
• In use, each port will be connected either to a signal source with a certain internal impedance or simply to a passive load impedance.
• We would like to arrange it that each port is connected to a load or source with an impedance equal to (matching) the impedance looking into that port (which in general will be different between the two ports).
• But the impedance looking into either port depends on what load or source impedance is attached to the other port.
• So we seek a pair of impedances Z_i1 and Z_i2 which satisfies two conditions.
• The first condition is that if port 2 is terminated with the impedance Z_i2, then the impedance looking into port 1 is Z_i1
• The second condition is that if port 1 is terminated with the impedance Z_i1, then the impedance looking into port 2 is Z_i2
• Since Z_i1 depends on Z_i2 and Z_i2 depends on Z_i1, and it is necessary to solve for them simultaneously.

Hope that wasn't too much detail. I assume these are called image impedances because each is the image of the other seen looking through the lens of the network (but this is only my personal interpretation). --catslash (talk) 23:26, 31 August 2014 (UTC)

I can now interpret your proposed definition in a way that does make it correct (so perhaps you did understand), but only after four or five readings, so sorry but the existing definition is far clearer, to me at least. --catslash (talk) 23:38, 31 August 2014 (UTC)

Yes, in both directions in that definition means towards the port and towards the load connected to the same port. It is a correct definition, but I can't see that that makes it any clearer. It unnecessarily introduces a new concept and, at least with that phrasing, is ambiguous on at least two counts. SpinningSpark 23:45, 31 August 2014 (UTC)

I see that now. To meet Kmpw's objection, perhaps the definition could be extended ...where the image impedance Z_i2 is that seen looking into port 2 when port 1 is terminated with Z_i1? This may not help Bhny though. I had thought that Bhny did not understand, but this is not the case. --catslash (talk) 00:21, 1 September 2014 (UTC)

To answer the original question, according to [2] image impedance is so called because it is an image of the externally connected load at the same port. This actually says something for Bhny's suggested definition and is the one used in the book. SpinningSpark 18:41, 1 September 2014 (UTC)

Wrong!

A two port network loaded by an impedence, which then appears at the input terminals, is called an iterative impedence. Similarly a generator at the input terminals whose thevenin impedence appears at the outut terminals is also an iterative impedence. Thus we have Zit1 and Zit2. For a symetrical network (ie where A=D and AD-BC =1), then Zit1 = Zit2 = Zit. If a 2 port network has an input impedance which is the complex conjugate of the thevenin scource impedence, this is called an image impedance Zim1. Similarly if a 2 port network has an output impedance such that the impedance is the complex conjugate of the load impedence, then this is also called the image impedance of the load Zim2. For a symetrical network (ie where A=D and AD-BC =1), then Zim1 = Zim2 = Zim. If for a symetrical 2 port network, Zit = Zim then this is called Zo, the self impedence or characteristic impedence or eigenimpedance of the network. Phil Robinson UK — Preceding unsigned comment added by 94.72.252.35 (talk) 10:56, 20 October 2016 (UTC)