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as far as I know a line impedance transformer is only valid for a frequency, but the attached one has a bandwidth from 2.5 to 10 GHz. Do I make a mistake?
as far as I know a line impedance transformer is only valid for a frequency, but the attached one has a bandwidth from 2.5 to 10 GHz. Do I make a mistake?
Yes, that is an incorrect assumption.
The line impedance value is valid over the frequency range for which the transformer is designed (has a flat frequency response).
Actually a transformer doesn't have an intrinsic line impedance, it's just the impedance that the input and output are designed for (such as 50Ω or 300Ω).
The transformer open-circuit impedance at its operating frequency is normally much higher.
A Ruthroff transmission line transformer doesn't utilize λ/4 or λ/2 stubs. The usual implementation uses a magnetic core to raise the common mode impedance which potentially shorts the signal to a sufficient high level.
In a coreless design, you need to analyze the impedances and electrical lengths of the coupled lines. There may be doubts if it's still a Ruthroff 1:4 unun.
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