How can I design a Twin Lead Transformer of impedance 180 ohms? I need this impedance transformer between coaxial cable and my Spiral antenna. Please guide me.
You can use the so-called 1/4-lambda impedance transformer to attain your goal, if the antenna is of narrowband. If you think the 1/4-lambda strucutre is too long to your limited space, you can use lumped elements to realize the impedance matching with the Smith chart or the ADS software.
As stated earlier the quarter-wave stub matching is a well-known solution for matching the transmission line to the antenna etc.
However, you can look for some ARRL stuff that has excellent information on the impedance transformations as most of the HAM Radio operators do use or make their own transmission lines and antennas and use such odd-value matching to standard transmission lines such as the 50, 75 and 300 ohms one. Therefore you should have no difficulty in getting the one to suit your need.