foster's reactance theorem disproven?

[biff44]

foster theorem

Do the advent of metamaterials disprove foster's reactance theorem?

https://en.wikipedia.org/wiki/Foster_reactance_theorem

 

[LvW]

metamaterial smith chart

Do the advent of metamaterials disprove foster's reactance theorem?
https://en.wikipedia.org/wiki/Foster_reactance_theorem

Hi bif44,

I don´t know if I understood your question well - but, in fact, I cannot see any relation between Foster and modern metamaterials. Fosters theorem applies (of course! It was in the 1920th !) only to lumped elements L resp. C.
Therefore, I don´t think that this theorem can be disproved by such actual technological developments. Or did I misunderstand something. In this case it would be helpful to explain your question.
Regards

(I know the following example matches the problem not really, but nevertheless:
Do you think that Einstein has disproven Newton ? I don´t think so. But it can be discussed).

Addendum: Of course, one can ask if this theorem applies also for materials which did not exist as Foster formulated his sentence (e. g. if it applies to electrical fields or antennas, .....) ; but in this case only the application range of his theorem is touched but not the question "proven or disproven".

 

[biff44]

foster reactance

"passive networks have impedances and admitances that always rotate clockwise on a smith chart" is what I always thought, based on Foster's reactance theorem. But my (limited) understanding of metamaterials is that they can rotate counter clockwise on the smith chart. So, fosters reactance "theorem" is disproven?

https://books.google.com/books?id=w...esult&ct=result&resnum=4#v=onepage&q=&f=false

 

[LvW]

foster reactance theorem

"passive networks have impedances and admitances that always rotate clockwise on a smith chart" is what I always thought, based on Foster's reactance theorem. But my (limited) understanding of metamaterials is that they can rotate counter clockwise on the smith chart. So, fosters reactance "theorem" is disproven?

Do metamaterials constitute a passive network consisting of inductances and capacitances ?

 

[katko]

reactance fosters

A quick google turned up this:
https://repository.upenn.edu/cgi/viewcontent.cgi?article=1305&context=ese_papers
this is written by one of the authorities on metamaterials (Engheta) in response to one of the authorities on anti-metamaterials (Munk).

 

[LvW]

fosters reactance teorem

Thank you KATKO for pointing our attention to the document and to the link.
However, I am not surprised that there are some new materials which do not satisfy FOSTER´s theorem. He has developped it in the 1920th and he had only passive lumped reactances in his mind - not knowing that perhaps some other "stuff" (e. g. microwave materials) would match this theorem as well.
But, on the other hand, if there are some materials which do not satisfy this theorem I never would consider this fact as a "disproval" of the theorem.

 

[katko]

Conceptually I would say the difference comes in examining effective media versus simpler, lumped element models. This is basically the debate between metamaterial and anti-metamaterial researchers, considering how you can treat a system as effectively homogeneous and whether it is valid at all. An interesting topic for sure.

 

[biff44]

Thanks for the paper! Nice find!

I am curious because there are basic ideas I have about microwaves, and I leverage off of those ideas in all sorts of areas to develop new components/systems. In the past, I have been stymied by foster's reactance theorem. For example, in areas where you are trying to improve resonator Q, you can not simply connect two resonators together and get more reactance slope, because you might end up going from a short circuit to an open circuit, and then back to a short circuit in a very short frequency span, just to satisfy foster's reactance theorem. If it can be violated, maybe new types of higher Q resonators can be devised. Would be handy to have a microstrip resonator with a Q of 500 or so.

Rich

 

[katko]

I'm not as up on metamaterials as I should be, but I do recall seeing some resonator papers around. One problem is that common metamaterial elements (SRRs) are pretty lossy. I think higher frequency (THz+) versions of metamaterials are lower loss, but I don't know what kind of Q you can get from microwave/microstrip size metamaterials.

You might want to look into Eleftheriades' work, most of his metamaterial research focuses on T-line implementations, so it might be useful. I'm more familiar with volumetric metamaterials

 

[Abhishekabs]

I agree with LuW,
Insted of using term disproven can we use the term corollary for the theorem?

 

[biff44]

I do not like arguing about semantics, but when I hear the phrase "The sun always rises in the east and sets in the west", and one day I find it rising in the south, I tend to think about abandoning the whole phrase, lest I get lost in the woods someday!

 

[katko]

I'd say just revise the assumptions of the theorem, as in the Engheta paper. The theorem is still valid when considering a smaller subset of problems, that sort of thing.

The "diffraction limit" is a hard limit - if you neglect metamaterial effects, for instance. Imaging systems have overcome this "limit", but it still holds in many, many cases - just a smaller subset than was once thought.

 

[y7wu]

"passive networks have impedances and admitances that always rotate clockwise on a smith chart" is what I always thought, based on Foster's reactance theorem. But my (limited) understanding of metamaterials is that they can rotate counter clockwise on the smith chart. So, fosters reactance "theorem" is disproven?

https://books.google.com/books?id=w...esult&ct=result&resnum=4#v=onepage&q=&f=false

Can you provide some reference that claims metamaterial can rotate counter clockwise on the smith chart? If this were true, wouldnt the gain-bandwidth constraint be gone as you can now perfectly conjugate match a set of impedances on the smith chart?

I have a hard time linking the "negative refraction index", and negative e and u to impedances on the smith chart

I'm intensely interested in this topic as it can solve some serious problems in many wideband applications of power amps and antenna

any reference would be appreciated

Thanks!