RF transformer design rules

Question

I am reading a book about building a HF transceiver. This book gives instruction about how to build, but not so much about the theory behind. In particular, I am exploring the following balanced modulator circuit:

In the instructions there is the following sentence: "T1 and T2 are each 7 turns of trifilar wound 0.375mm [...]. The toroid cores are FT37-43 or similar medium to high permeability ferrite toroids."

I would like to understand how the author came to this conclusion. What are the steps for designing such a transformer, and to choose the right toroid?

Carrier in is a 10.7 Mhz signal.

Answer 1

This is a low power circuit ,an oldie but a goodie .It performs fine by todays standards. The transformers must handle 10.7 MHz so in this case they do not have to be broadband .The author may have had some broadband 50 ohm transformer designs on hand which would be OK for say 1.8 to 30 MHz which would be very good at 10.7MHz.Otherwise the number of turns is ballparked to give a shunt impedance of say 10 times the system impedance of 50 ohms nominal so 500 ohms wont upset things .

Answer 2

The trifilar construction is the important part, which makes these transmission-line transformers. The signal flows in/out of each transformer along a parallel structure (pairs of wires, or one with respect to the others around it), with controlled impedance given by the geometry of those wires (number, diameter and spacing). The same is true of each winding to its surroundings, and the parallel-series combination allows establishing a new impedance. Or inverting phase, as is needed for a balun.

These are Ruthroff type 1:2 baluns, meaning the delay between transmission lines and ports is not matched, and the balance will suffer at some upper cutoff frequency.

The lower cutoff frequency is defined by the core and turns. At middle frequencies, the ferrite's permeability drops off as core losses take over, and this determines the insertion losses due to shunt resistance.

Turns and core size also determines maximum signal level (core saturation), though core losses are generally the limiting factor above 100kHz or so.

As for core geometry, wider is generally better (higher Ae (core effective area) compared to winding length and area), as this reduces turns and maximizes bandwidth (upper cutoff depends on winding length). At shortwave frequencies, this isn't very important, and toroids are more than adequate.