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!