Matching circuits using non-50 ohm stubs and lines.

Complex matching is usually done using 50 ohm microstrip lines, open and closed stubs. But is it optimal? Real impedance is matched using quarterwave transformers (sqrt(z1*z2)). But if we have complex impedance which is far from 50 ohm, is it right to match it using 50 ohm stubs? But some designs do use microstrip lines with different characteristic impedance for matching. But which impedance must be chosen? The one which allows to get in desired location on Smith chart or something else?

For example, i design two matching circuit to put some complex impedance at the center of Smith Chart (50 Ohm). I can do this two ways: using 50 ohm lines, and using some N ohm lines (each line with different impedance). Will final design perform the same (i mean reflection). I think not. How to choose optimal impedance of matching stubs and phasing lines? The same resulting point on a Smith Chart can be obtained many ways, and now one more variable in this equation - characteristic impedance of matching lines...

Assuming the BW is achieved, I find the TL matching scheme that results in the shortest overall length of TLs.

who said it is "usually" done with 50 ohm lines? ONLY if you do not know how to use a smith chart, or use a modern computer simulation.

Generally speaking, you will get much more matching bandwidth using lines that are far away from 50 ohms as possible! Like 25 ohm or 130 ohm lines, because they approximate lumped elements better.

at least in many book examples. With lumped elements usually some R + L or R + C is used to achieve complex impedance. But with microstrip lines authors mostly use 50 ohm lines. Many papers on LNA and multiplier design, matching is done using 50 Ohm stubs. I feel that using non-50 ohm lines makes sense, but I am not sure where it comes from. On a Smith chart I have an intuitive feeling that choosing some impedance makes line more sensitive to phase error (dielectric constant deviation or line length deviation).

Obviously lossless impedance matching won't use resistors. TL stubs could be used to mimic reactances, but I don't see the particular advantage. It's still true that matching different impedances can be better achieved with non-50 ohms TL, similarly larger C or L value emulation asks for non-50 ohms, within the range of practical implementation.