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Selecting microstrip band-pass filter dimensions from Zo Ze realizability problem.

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Terminator3

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I started to design microstrip band-pass filters for 5 and 10GHz, currently using book "RF Circuit Design Theory and Applications, second edition" Reinhold Ludwig, Gene Bogdanov. Also several articles from internet. I did all calculations and cross-checked them with several paper examples.

My current problem is:

1) Final time-consuming step is selecting actual microstrip dimensions using Figure 5-45.
it is common practice to resort to a numerically computed impedance grid, such as the one shown in Figure 5-45
Is there any way to avoid it, some approximation formulas available?

2) Most important problem is: for my substrate height i obtain unrealizable dimensions. For example:
gap S<=0.1mm for Z0=50 Ohm.
when i choose Z0=100 Ohm, then width W is too tiny.
Of course there are some CAD software, for example QUCS can do coupled lines, and in theory there are some sweep available to make brute-force of design.
But while struggling with this boring stuff, found interesting references here:

https://surface.syr.edu/cgi/viewcontent.cgi?article=1000&context=eecs_thesis
2.3. Filter Bandwidth Improvement Techniques
2.3.1. Tapped Input
Wide band coupled line filters usually require a tight coupling at the input and
output coupled line sections. The tight coupling is usually not realizable for most
microstrip line filters. Tapping the input and output of a coupled line filter gives an
opportunity to remove the tightly coupled first and last coupler sections. See Figs. 2.9 and
2.10.
2.3.2. Impedance Transformation
A proper impedance transformation at input / output of a coupled line filter
improves the bandwidth of the transmission lines [12] as shown in Fig 2.11.
i found some similar references, but not too much information.

Tapped input is used in hairpin filters, and some designs on the internet. But it is unclear to me how to find tap position (for tap method)? How to calculate quarterwave transformer to "fix" tight coupling (for impedance transformation method)?

I came across some formulas, but unfortunately they use very different formulas, and important details are omitted (not enough for me to do the calculations).

So maybe someone can give some hints how to solve this problem.

What i have now:
all traditional formulas entered in SpeqMath, i calculate Zodd, Zeven, etc. for some ripple, pass band, attenuation.

What i want to achieve:
Slightly modify my calculations to solve tight coupling realizable dimensions problem (gap/width) or add some formulas. So all things are done numerically with formulas in a simple math calculator application SpeqMath.

Currently i see only one simple way to tune physical dimensions: modify Z0. My idea is to modify Z0 of system to shift Zodd Zeven, so physical sizes will shift too. But with that old-style impedance grid approach it is too time consuming. Can anybody confirm that it is a good approach? Shift Z0 of band pass filter to some other value, it can be 40 Ohm or maybe 70 Ohm, 100 Ohm, etc.. If sizes are good, add quarterwave transformation before and after filter, to match filter in 50 Ohm system. But it seems this approach is very different from:
A proper impedance transformation at input / output of a coupled line filter
improves the bandwidth of the transmission lines [12] as shown in Fig 2.11.
as in this approach tight coupling area is somehow replaced with quarterwave transformer.
 

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