Designing low-Z (10, 12, 16, 18, 25 ohm etc) coax transmission line transformers

[wb0gaz]

VHF (50 and 144 MHz) push-pull ham radio power amplifiers often use pairs of short length (10-20 cm seems common) low impedance (often 10, 12, 16, 18 or 25 ohms depending on design) coaxial cable to transform the low impedance device drains to 50 ohms.

My question is this - given frequency, Vp (velocity of propagation) and the relevant impedances (drain, coax, and system), how is the length of the pair of low-impedance coax cables calculated/determined? Over what frequency range (say as % of center frequency) can these be expected to work properly (or conversely, what precision is required when actually preparing the coaxial cable pair?)

I am not able find any description of how the length of the (typically) short lengths of low impedance coaxial cable are calculated. When alternate impedance coaxial cable is used in radio antenna impedance transformation, a quarter wavelength (inclusive of Velocity of Propagation) is often chosen. At 144 MHz, quarter wave would be about 30-40 cm (assuming Vp of ~60-70%), yet the lengths used in these transformers seem to be much shorter (10-20 cm).

Any advice, references, or requests for clarification greatly appreciated!

[ZigmundRat]

As I recall, it’s a quarter wave where the characteristic impedance is the geometric mean of the two impedances to be matched. The physical length may change due to capacitance. For example I n tube amps with stripline tank circuits, 1/2 of the theoretical length was in the tube itself. Similar idea. Whether the actual length is determined empirically or just calculated I don’t know. If you have a real example you could calculate it backwards and see just how shortened it is.

See if you can find a copy of “Reference Data For Radio Engineers”. You should be able to find more related info in there.

[wb0gaz]

Thank  you ZigmundRat, that provides very valuable clues - mainly that 1/4 wavelength would be an upper limit (length), which also lights the path towards the other question (what is the operating frequency range?) If I then begin with 1/4 wavelength sections and sweep the amplifier, I'd suspect I'll end up with a cut-off problem at the intended frequency, but would then work backwards (shortening the sections).

Reference data for radio engineers - thanks for the pointer!

[LM21]

Old  Motorola had some push-pull amplifiers, and instructions how  to build their coaxial transformers. That data is on the net today. By the way, 25 coaxial is 2 50 ohm coaxials in parallel and so on. But this my own knowledge. Motorola used a different idea.