Does a balun transformer cut the signal in half?
The balun transformer looks like a voltage divider using inductors instead of resisters. How could the signal not be reduced by half?
A balun transformer converts a balanced impedance to unbalanced impedance. Some baluns also change the impedance. For example a balun converts balanced 300 ohm ( twin lead ) to unbalanced (75 ohm coax). This reduces the voltage from the twin lead by a factor of one half so the 75ohm coax sees a voltage of 1/2 that on the twin lead. The current in the coax is doubled from that of the twin lead. There is no power loss in an ideal balun.
In short a balun is not a resistive divider, it is used to match impedances and insure that impedances are properly terminated. It uses coupled inductors.
A 300 to 75 ohm balun connects directly connects one leg of the 300 ohm twin lead to the center of 75 ohm coax. The other twin lead line connects to two series coupled inductors, The center of the coupled inductors is grounded, the shield of the 75 ohm coax is connected to this ground. The second inductor connects to the twin lead line connected to the center of the 75 ohm coax. The net result is the 1 to 1 autotransformer halves the voltage and doubles the current. I suggest you draw this out, it will help you understand baluns
BALUN COAXIAL TIPO “COLLINS”