Bandstop Filter using microstrip lambda/4 resonator

[Georgi]

Hi all,

Currently I am preparing for my Microwave components and Systems exam, I am struggling to understand something about Microstrip bandstop Filters:

Here is a page from my textbook, where a microstrip bandstop filter using lambda/4 resonators is shown. I can understand why the resonators
are lambda/4 long (Because they will transform the open end into shortcircuit for the needed frequency). What i cannot understand is why the spacing between two resonators needs to be also lambda/4. I will be very thankful if some could explain this to me.

Thanks in advance and wish you all a nice week!

Georgi

[T3sl4co1l]

Why wouldn't it be?

Or, what would happen if the spacing were zero, or lambda/2, or anything else?

Tim

[Georgi]

I personally don't see any difference if its lambda/2 or lambda/4 or something else, maybe in the coupling factor, which will influence the Q, but I cannot think of anything else.

Georgi

[T3sl4co1l]

Well, if it were N*lambda/2, it would be the same as zero (i.e., including N = 0).  The segments would simply be in parallel, so the impedance would stack up, but not the poles.

With lambda/4, each stub is a transformer, that is itself transformed.  A stub is open at the end, so it acts as a short at the junction.  Which acts like an open, 1/4 wave from that; but that next node is also shorted by another stub, and so on.

So the whole thing acts like a thick brick wall at the right frequency.

If the spacing were any other (non integral) length, the transformation would be incomplete, and reactive; all the stubs would have to be weird, and the frequency response would simply be wrong.

A more accurate explanation requires understanding each trace length as a resonator itself; you get coupling from one to the other and so on.  The coupling factor, and therefore the bandwidth (given the limitations that the maximum bandwidth has to be fractional, because the stubs and segments still need to look largely 1/4-wave-ish for it to work), is determined by the ratio of impedances.  Thus you get fatter traces acting to short out the signal, and narrower traces acting to open up the signal, with the geometric average of those two impedances being equal to the system impedance Zo = sqrt(Zfat * Zthin).

(The coupling can, of course, be by proximity rather than direct connection, and hence you get narrow band filters made from 1/2 wave strips.)

Also... isn't that a lowpass filter?  Well, I suppose it'll have harmonic pass bands, so it would be a band stop of sorts.  But the other band edges may not be as well controlled as the fundamental cutoff edge.  Dunno, depends?

Tim

[Georgi]

Thank you very much for your explanation.
No I get it (I think I do).
ps: I think the filter could also act as a lowpass at certain  lower frequencies where the stub length will be much smaller than lambda/4. In my textbook it is also written, that these kind of filters are often very hard to manufacture, because the stubs have to have high impedance. I do not know why we have to have chapter about them, but as you explain it to me, I find this idea of using these resonators as bandstop filter interesting.
Georgi

[kridri]

Wich textbook are you Using?
I am interested in a introductionary course text on stripline design.

[Georgi]

The picture was taken from script that was made by my professor, and  I just used the word textbook for the sake of the question, because here in Germany the professor almost never use a textbook for the lectures and just make their own scripts. Since I don't know how professors in other countries do it, i have just used the word textbook instead of script. Nevertheless I did a project this Semester designing and implementing a Microstrip Lowpass filter and i have mainly used the book "Microstrip Filtersfor RF/Microwave Applications" by JIA-SHENG HONG and M. J. LANCASTER for the project. I find it a very useful book giving you a guide on how to go when designing such a filters.

Georgi

[kridri]

The picture was taken from script that was made by my professor, and  I just used the word textbook for the sake of the question, because here in Germany the professor almost never use a textbook for the lectures and just make their own scripts. Since I don't know how professors in other countries do it, i have just used the word textbook instead of script. Nevertheless I did a project this Semester designing and implementing a Microstrip Lowpass filter and i have mainly used the book "Microstrip Filtersfor RF/Microwave Applications" by JIA-SHENG HONG and M. J. LANCASTER for the project. I find it a very useful book giving you a guide on how to go when designing such a filters.

Georgi

Here in Belgium we have the same with most of our professors. There course notes is a collection of various sources
The book you proposed is a nice introduction. Thanks !