Citation for those interested:
https://patents.google.com/patent/US8392495B2/enThe branches are ordinary filter sections, or maybe give or take tweaks once coupled together, so normal filter analysis applies.
You don't mention what Zo and bandwidth you're looking at. I'm going to guess bandwidth is much too low, and you've fallen into the common trap: calculators normally give the ladder equivalent diagram, whether it is reasonable to do so or not. The calculation is perfectly fine, but often the values are a physical impossibility, like -- not only a 15nH inductor (which is at least plausible, if not very stable as much of its value will be due to PCB dimensions and thus sensitive to FR4 expansion rate), but somehow being able to make a connection to a 300pF cap that has only a tiny fraction of 15nH in its loop -- but the average 0805 chip starts at ~2nH, not a very "tiny" fraction. Conversely, you might have fairly reasonable values of 800nH for the series branches, but paired with 5pF, and when trace/pad capacitance to ground is itself a modest fraction of that... you won't have a pure series resonator anymore.
The solution is to transform series branches to parallel branches, and match the impedance to something reasonable.
The resulting topology has a chain-of-resonators motif. Parallel-resonant tanks are coupled between using small capacitors (gives shallow HF asymptote, C's shift F down), or tapped coils (for low k, or L divider, gives shallow LF asymptote, low F shift depending), or mutual inductance (balanced asymptotes, no F shift).
Then you can use, say, 220nH || 20pF, or 18pF plus a small trimmer, Z is nominal, losses are low, strays are distant, and instead of the impedance ratio compared to Zo (higher for series branches, lower for shunt branches, in the ladder network), you have the coupling factors, from input to first, first to second, etc.
I don't have the exact formulas, though this may be a good enough start to do the adjustments in a simulator, but you can refer to classics like Zverev for more detail.
The motif lends itself well to mechanical designs: at UHF+, resonators might be coaxial elements carved into cavities, with gaps between cavities adjusted to give desired (mutual) coupling factor. In the microwaves, resonators might be hollow cavities joined by waveguide, or microstrip elements: if you've ever seen what looks like a stack of slashes -////- on an RF board, the "slashes" are 1/2-wave resonators, edge coupled to each other, and to the input/output 1/4-wave segments. Microstrip coupling is quite modest even for spacing at design rules (say, 4 or 7 mils gap vs 20 mils trace width on 10-15 mils substrate height, giving, I think less than 10% coupling?), so it's an effective design for narrowband (<10% BW) filters.
Obviously, whatever the route, you'll need to prepare both "even" and "odd" forms, match their tuning, then link them together for this filter.
I think I would be more than happy to just put a little extra gain and an R pad in front, or a buffer, instead of solving and trimming all that. When it's solvable in an as-built no-adjustment form (like the chip component example given at end of patent) that's fine, give or take availability of standard values, but if you don't have that benefit, it's a lot of adjustment to bring a complicated filter together.
Tim
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