How to build a 75 ohm to 50 ohm converter

Question

I need help to build a simple converter to match a 75 ohm feed line to a 50 ohm antenna. Please help :-(

Answer 1

1. Use a transformer. At frequencies where 50 versus 75 Ohm impedance matters, it can be quite small. A few turns for each side around a ferrite is probably good enough. The impedance ratio is the square of the turns ratio. One problem with this method is that there will be some loss, and you have to be careful your core (ferrite usually) works at the intended frequency. There are quite a few flavors of "ferrite".
2. Look up something called a Smith Chart. It is a graphical means to give you values of reactive components to add to essentially change impedance. It's not intended for exactly this application, but it might give you some guidance. The theory and proper usage of a Smith Chart could fill a whole book, so I'll leave you mostly with the search term.
   

   The basic concept is that a network (usually just two or three) inductors and capacitors between two signals can change the apparent impedance of one signal as seen by the other. The advantage is that this method can be low loss, usually less loss than a transformer. The Smith chart is a graphical way to arrive at the component value, which can be quite complex mathematically. This is usually used at the feed point of a antenna so that the antenna looks just resistive and with the desired resistance. The downside is that this only works at a specific frequency. If your impedance matching has to work over a reasonable frequency range, then adding some capacitors and inductors won't work, and the Smith Chart method of determining them is unapplicable.

Answer 2

The Twelfth-Wave Transformer is often a more convenient alternative to the more well-known quarter-wave transformer. It has been around for at least 50 yrs, so I must point out to my less RF experienced colleagues that Hams have been using this to match cheap 75 Ohm feed line to standard 50 Ohm antenna for a long time. The theory is less useful to helping build this than the design tool offered previous in above answer.

This design tool can be applied to any frequency of choice and any coax. preferably large diameter cheap solid coax. surplus or scrap from the cable TV industry known as "hardline" in RF circles, such as gas filled solid coax or teflon filled solid coax.

My diligence indicates the requester has purchased a company in 2005 that sells RF antenna suitable for two way communication over a wide variety of application bands and power levels so choosing an inductor or a balun is not a trivial task.

I proposed using a line loss calculator to match hardline coax to feed a 50Ω antenna is an easier task with this calculator, now it seems other helpers need justification.

Given: Feed impedance line of 75Ω of unknown length, unknown source impedance and antenna of 50Ω for a rated power level and frequency range.

May I refer to the theory in Princeton's University paper, rather than plagiarise, but in short;

Conclusion:

Choose Coax and calculate 1/12 λ of 50Ω coax. and 1/12 λ of 75Ω coax. for chosen frequency.. This works from DC to 1.5 x center F chosen. These two cables will transform the impedance for maximal power transfer. Choose the lowest loss cable you have avail. and best connectors to achieve < 0.1dB loss for these short lengths.

Convenient calculator: http://vk1od.net/calc/tl/tllc.php#NoteModellingLoss Choose F, coax , 50 Ω load 1/12 λ option enter 0.083333 [wavelength], then calculate. Repeat for both 50Ω & 75Ω coax choosing type of coax as 1st entry.