As many of you know, I am a ride along participant in the SolderSmoke Podcast ably chaired, directed and a brainchild of Bill, N2CQR. Often the podcast participants which now for several years has also included Dean, KK4DAS get a question in the "In Box". Such a question arrived yesterday.
The person submitting the question had to change locations and that involved a new space constrained antenna now fed by coax versus open wire feedline like at his old QTH. Sticker shock arrived with the current cost of high quality 52 Ohm coax. Back on life support, he said that 75 Ohm coax was a lot less expensive.
Thus, the question: "What if I used 75 Ohm coax as there is an obvious mismatch problem?" Most of our modern gear has a fixed output at 50 Ohms and typically safety circuitry to scale back the power when the SWR exceeds 3:1.
Several blog readers would do an analysis and likely conclude that that the mismatch would fall under the 3:1 radar so just git_er_done. [If you do that calculation, you will find the SWR is 1.5:1. No biggie but the 1.5 number is significant (perhaps coincidence) a bit later on.]
But just suppose you did want to match the 50 Ohm output of your radio (I call it a radio and not a rig since most likely it is an appliance box.) to the 50 Ohm input to the antenna with 75 Ohm coax stuffed in between.
My response was to use Ferrite core matching transformers at each end. We have a 50 to 75 Ohm match at the coax output of the radio and a 75 to 50 Ohm at the antenna. 75/50 = 1.5 and thus the turns ratio squared of the matching transformer has to equal 1.5.
Luckily if we use a large ferrite core like a FT-200-43 this would be good for a conservative 100 watts. You can stack these cores for those running a KW. BTW you will need wire bigger than #26. Like #12 or #10 for the higher power. The type 43 would work over the HF Bands.
Just because I have done this a lot, I know that 11 Turns on the 75 Ohm side and 9 Turns on the 50 Ohm side is a 1.5:1 match.
If we do the math 11^2 = 121 and 9^2 = 81. Thusly, 121/81 = 1.49382716 which is close enough to 1.5:1. So, you would need two such cores and you have a match to a 50 Ohm antenna using 75 Ohm coax over 2 -30 MHz.
Now suppose you have a 450 Ohm input antenna and the same 75 Ohm Coax. On the transmitter side our 11 and 9 turn winding will work but really a mismatch at the antenna end. The antenna is a 450/75 or a 6 to 1 match.
A bit of noodling yields a 22 Turn to 9 Turn match which gets us pretty close to 6 to 1.
Thusly, 22^2 = 484 and 9^2 = 81, where 484/81 = 5.975308642. Let's just call it 6.
BTW don't let this escape from you as there was a reason why my 2nd calculation picked 22 Turns. The answer is Turns Ratio Squared. In going from the 50 to 75, it was 1.5 and the 75 to 450 was 6. Shazam 6 is 4 Times bigger than 1.5. Since we are squaring that means that the 450 side has to be twice the number of turns as the squaring makes that number 4X. So, 11 Turns is now 22 Turns. Thank You Mr. Boyer my 8th Grade math teacher.
As a sanity check on my hairbrained scheme I asked copilot about my answer and the conclusion was that what I said was true. Copilot did suggest that if you were running some power you would need stacked cores. It also suggested the use of a choke balun to keep RF off of the shield. You can see that Here.
Them that know can make things go.
I guess we are still shut down as a government. For those on furlough our thoughts and prayers are with you. Recent polling has excluded Joe Biden as being responsible for the shutdown. The Fickle Fat Finger of Fate is tilting toward a specific responsible group, and it isn't Joe. Another year without the Nobel Prize... someone is pissed today.
73's
Pete N6QW