So, I need to design an impedance transformer from 50 to 250 ohms. Should I design a 50 ohm power splitter and then design a transformer from 50 to 250 ohms? Because, in power splitter, I am going from 50 to 70 and then again 50 ohms as the result of splitter. Getting confused, why I am going from 50 to 70 and then 50 and again go from 50 to 250? Is there any trade off I can do?
Please advise.
Thank you
Up to UHF frequency you can design transformer with tapped impedence.
You do not seem to understand microwave components at all. You need to be very careful, or else things will not do what you expect them to. You need to read about microwave components.
A transformer that uses a 70 ohm section I expect is a quarter wave transformer which will match 100 ohms at one end to 50 ohms at the other. The splitter sees two lines going away from it in parallel. For the 50 ohm line to be matched the two lines need to be 100 ohms each so that in parallel they are 50 ohms.
A 70 ohm line quarter wave long is a standard inverting transformer which looks like 100 ohms at one end if there is 50 ohms at the other, so if it has a 50 ohm line going out it presents the 100 ohms at the other end that the single input line needs at the split.
To get from one 50 ohm line to a 250 ohm line you need a quarter wave long line of impedance square root of 12500 ohms, which is close to 111 ohms.
The lines are almost never exactly a quarter wave long because the steps in size look like capacitors which have a similar effect to extra line length, so the line lengths are usually shorter.
If the transformer doesn't work at the frequency you want, find out which frequency it does work at, then if that frequency is too high or low, make the quarter wave section longer or shorter by the ratio of the two frequencies, which will get you very close.