9:1 transmission line transformers (TLT) BalBal Balun Ruthroff

[Lambda_]

This Excellent LDMOS build sparked my interest in this kind of Impedance matching transformer.
https://qrpblog.com/2019/10/a-600w-broadband-hf-amplifier-using-affordable-ldmos-devices/
https://qrpblog.com/wp-content/uploads/2019/10/circuit-schematic.png
I head to think about this for a while to understand how the output impedance matching transformer works.

And im still not fully convinced i get it right so let me explain.
The Transformer is in the build is just keeping the Transmission line short and ignores the added delay.(right?)
it works like a "Ruthrof autotransformer"

simplified and rearranged it looks like this:

 "As this is a 1:9 transformer and the output has to be 50ohm, the input impedance works out as 50/9 = 5.56ohm and the coax characteristic impedance is sqrt(50*5.56) = 16.67ohm."

For some TLT this is somewhat intuitive since the transmission lines outputs are in parallel and the outputs are in series or vice versa.
for example 50Ohm to 12,5Ohm

Here the 2 25Ohm Transmission lines are in series at the input to form a 50Ohm input and in parallel to form a 12,5Ohm output.

Can i Analyze this by looking into the Transformer replace the Transmission line ends with resistors of the characteristic impedance?
this seams to work for the 4:1 version but not the 9:1 version?

But the 9:1 Version only uses 2 transmission line with a 1/3 of the impedance of 16.667Ohm

 

Also if i would want to add the Delay line to correct the phases shift (like in the linked video) what would be the Ideal impedance for the Delay line?
If i draw it like this it starts to makes sens... (?)

For the version with the third delay line it would add up to 50Ohm on the output if all 3 lines have 16.66Ohm and to 5.56ohm on the input.

For the Balanced version with 4 lines the delay lines would need to have 16.66/2 Ohm?



List of resources about this topic:
https://www.mikrocontroller.net/attachment/217383/Trask_TLT_Tutorial.pdf
http://k5tra.net/TechFiles/Transformers.pdf
https://www.jstage.jst.go.jp/article/elex/7/8/7_8_534/_pdf
https://www.highfrequencyelectronics.com/Feb04/HFE0204_Sevick.pdf