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In the Ebers-Moll Model of a BJT we have 4 Parameters.

The following images are taken from U. Tietze Ch. Schenk, "Halbleiter Schaltungstechnik" ("Semiconductor Circuit Technology") 11th Edition, 1999

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Totally clear until here. Now it is said that due to the reciprocal network theorem we must have

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So the model reduces from 4 to three parameters. Unfortunately, I can't follow – why is that?

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  • \$\begingroup\$ What do I_{S,N} and I_{S,I} stand for? \$\endgroup\$ Commented Oct 26 at 19:40

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A google search very quickly turned up this

https://ieeexplore.ieee.org/document/1484062

which I confess I have never read. The Roulston book, generally a good reference on bipolar transistors, just shows that reciprocity holds when the currents are written out in terms of doping, dimensions, etc.

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    \$\begingroup\$ Since the transformation between the injection (earlier) and transport (later, but not 1984 later) version is what I believe the OP's textbook is discussing, I don't believe that paper addresses the question. The transport version dealt with diffusion capacitance. But one of the more important things it did was to turn the injection version's 2 saturation currents, one for each PN junction, into 1 saturation current -- which everyone loved because it made the making of models was easier. \$\endgroup\$ Commented Oct 26 at 19:41
  • \$\begingroup\$ My book simply says that "from the theorem on reciprocal networks, one obtains a binding for the parameters". That' s all . So I thought that it follows from more general principles instead from semiconductor theory. According to 2-port theory, we know, that passive networks are always reciprocal and so the statement follows directly. But is it applicable also to a BJT? Not immediately clear. \$\endgroup\$ Commented Oct 26 at 19:43
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    \$\begingroup\$ @MichaelW : The diagrammed model you show is the original injection version from Ebers & Moll in their 1954 paper. It's easy to understand, as you say. Later, diffusion capacitance was added, not important here, but also the desire by computer programmers (and users) for a single saturation current led to the entirely equivalent transport version, which I believe is what you are talking about. \$\endgroup\$ Commented Oct 26 at 19:45
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    \$\begingroup\$ @MichaelW The transport version also directly leads to the small-signal T-model. I write about that here. And the entirely equivalent hybrid-\$\pi\$ version then made the small-model linearization still nider by combining the two current generators into one current generator. \$\endgroup\$ Commented Oct 26 at 19:47
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    \$\begingroup\$ @MichaelW Also, it might be helpful to go here where all three versions are laid out for you. But the reciprocity relationship (observed experimentally) is readily proven, at least for low-level injection cases, by using Green's theorem. \$\endgroup\$ Commented Oct 26 at 19:49

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