Worryingly, there are comments here: http://www.eham.net/articles/24502 that are simply wrong, and cause a lot of confusion to people trying to understand this topic.
“In order for Z0 to matter, in the TEM mode, one must use a relatively long transmission line. For eample, a 2:1 transformation point is roughly 1/4 wavelength of a transmission line with a Z0 which is the geometric mean of the two.. For example, to transform 100 ohms to 50 ohms, 1/4 wavelength of line with a 75 ohm Z0 is used. At 7 MHz, that’s about 25 feet long. 25 feet of bifilar transmission line as two 12 AWG wires wrapped about a core? Good luck. “
The above is not true. Any length of transmission line functions as a transmission line. Reflections will be overlaid, but nevertheless it still behaves as a transmission line. And in fact a shorter transmission line is used in real transmission line transformers. For example, a 2008 paper (i.e. recent) used 30cm length of transmission line for a balun (in a Ruthroff configuration) that was usable up to 150MHz. According to the struck out comments, this would have used conventional transformer action since 30cm is too short in that case!
Cores function as transformers. Conventional broadband current and voltage transformers, not transmission line transformers that are unique lengths for unique frequencies!!!!
The above is not true. The core could be removed, and it would still function as a transmission line. The core serves for a purpose though..
Core material and permeabilities are very important. So is self impedance of each winding. Windings should have at least five and preferably ten times the source impedance to minimize winding losses.
And, transformer designers of any consequence know that you must have sufficient self impedance to prevent heavy winding losses when connected as a voltage transformer.
The TLT does not use the core like a conventional transformer. Actually, the core is needed so that any secondary waveforms (i.e. those caused not because of the twisted pair wire interactions or coax core-to-screen interactions, but interactions between the wires and ground have a sufficiently high impedance, i.e. this is inductance, not a conventional transformer action. The action is not great at high frequencies with ferrite, so this only applies to lower frequencies, and at higher frequencies the secondary waveforms are reduced by the air-core (ferrite will look like an air core at high frequencies), so the number of turns is important for that reason.
So, since this conclusively shows that the core is certainly not being used for conventional transformer action at neither low nor high frequencies, then one can deduce that it can be possible to have multiple transmission lines on a single ferrite core in certain cases.