Why adding microstrip coupled filter elements in series increases filter bandwidth?

[Terminator3]

Here is my dummy question. It must be some basics of electronic design, some simple math behind it. There is straightforward design procedure, which includes bandwidth, ripple, normalized frequency, choosing of filter order, etc.. Following design procedure calculations it is obvious, that realization of wider bandwidth requires more filter elements. For example, more microstrip half-wave resonators. But intuitively i can't understand one thing: why adding similar filter elements in series increases filter bandwidth? Intuitively i expect to see huge increase of insertion loss and very narrow bandwidth at resonators center frequency. But reality is that insertion loss increases not so drastically, and filter bandwidth become increased. And what is more confusing, S21 passband looks pretty flat. For example, if i take some filter "profile" curve and convoluted it with itself, i obtain more narrow-band profile.

 

[edf]

Here's my 2 cents. In the case of a multi-section quarter-wave (QW) transformer (XFMR), the bandwidth is broadened by adding additional sections (of the right impedances). These sections are QW at the center frequency, but when considered in subgroups their center maybe lowered or raised (at the subgroup harmonics) via their inter-impedance relationships. A 40 Ohm TLine loading a 50 Ohm TLine looks like extra capacitance via Zo=sqrt(L/C), a 60 Ohm like extra inductance. More resonances are required to fill in the amplitude ripples as the resonances are spread further apart.

 

[biff44]

it only seems that way. if you look at a 1 resonator bandpass filter, it will have a hump with one very small passband in the very middle. If you have more resonators, you can force it to have an EQUIRIPPLE bandwidth that, for example, stays below 0.1 dB of insertion loss ripple. There are more degrees of freedom by varying the resonator impedances and the coupling values so that you can form a chebychev response. BUT going from a 5 element filter to a 20 element filter will NOT increase the bandwidth at all.

 

[Warpspeed]

It depends on the coupling between the individual resonators.

Below critical coupling you will certainly get a further narrowed bandwidth with higher insertion loss.
At critical coupling there will be minimum insertion loss.
But extra coupling beyond critical, an interesting thing happens.
You get a double hump with perhaps a dip in the middle and steeper skirts.

These are not strip lines, but the same principle applies:

https://www.robkalmeijer.nl/technie...hniek/hambladen/qst/1991/12/page29/index.html