If I have a load Z_L and a length of transmission line with impedance Z_0 I know how to compute the impedance at the input to the transmission line (using smith chart or using telegraph equation). But now suppose I attach a 4:1 Unun to the (input) end of this, what do I do here? Just divide the complex impedance at that point by 4? Is there some phase factor?
This is not a complete answer so I am not going to mark it, but I just did some testing with an MFJ-911 4:1 balun with fixed resistances connected to the output. (Metal oxide resistors). Using an antenna analyzer I got results consistent with assuming that the impedance was just 1/4 the resistance I connected, with no additional phase factor other then what I expected due to the cable connecting the balun to the analyzer.