CK , so using a 1/4 wave length of coax ( physical length or electrical length ?) 50 ohm coax the amp would need a 200 ohm input to the amp to to show 50 ohms to the radio ?
Sorry Booty, electrical length. My bad on that. I NEVER talk in physical lengths as it means absolutely nothing unless you plan on using it as a clothesline or to tell someone how much cable I need to reach from point A to point B. A 200 ohm load on the end of 1/4 electrical wavelength of cable will present an impedance of only 12.5 ohms at the radio end. It's a simple ratio as referenced to 50 ohms. 200 is four times 50 so the other end will have 50/4 or 12.5 ohms. Now remember, that is with a 1/4 wavelength of cable which kind of has a special relationship just like a 1/2 wave does. Other ratios are possible with different lengths. If the amp did have a 200 ohm input impedance it could be matched to 50 ohms by some odd ball length of cable hence the trial and error method most often used.