Coaxial Balun

This Balun, (adapter from Balanced Line to Unbalanced Line and vice versa), use one section of ¼ wavelength and one of ¾ wavelength in coaxial cable.
This device requires that the electrical length of both sections include the ¼ wavelength coaxial transformer.
The unbalanced impedance value has exactly the same value of the coaxial cable. For this reasons the name is just 1:1 balun but the purpose of this device is to match any impedance value.
The length difference between the ¼ wavelength and the ¾ wavelength sections provides the necessary 180° degrees electrical phase-shift, as required, for ex. from the open dipole radiator.
Since the narrow bandwidth, this balun is well suited for the monobander antenna only, therefore is particularly indicated to couple the radiator of the VHF/UHF Yagi-Uda antenna, but is possible to use successfully in the HF also.
Remember to take account of the electrical length of the coaxial cable, the speed factor (ex. 0,659 for the RG58, but it depends on the own cable speed factor). So please, use your own particular cable specifications.
Instead of the 1:1 Balun, is possible to couple the 50 or 75 Ohm unbalanced Line or with any unbalanced line to any balanced Impedance value. To do it, is enough to replace the two ¼ wavelength pair’s transformer with two sections, always of coaxial line, at calculated value. This is better understood from the figure given like immediate explanation as the 1:1 Balun example.

As shown in the balun image, the 1:1 balun is done by the

[ ¼ W L * V c ] coax cable section of Z c impedance;
and the
[ ¾ W L * V c ] coax cable section of Z c impedance;
which is refolded three times in order to obtain the same physical length of the shortest section, this is not the electrical requirement, then it is for practical layout convenience only.

WL is the Wave Length; WL = ( constant light speed / frequency )
Vc is the Velocity constant or propagation speed factor in the coax cable; i.e. the electrical length.

The mathematical simplified formulae for the calculation is simply:

Z c = s q r t ( Z o * Z i ) { Z c is the Impedance value in the coaxial cable }
Z o = ( Z c * Z c ) / Z i { Z o is the resistive impedance at antenna balanced value }
Z i = ( Z c * Z c ) / Z o { Z i is the final unbalanced value seen at the Rx/Tx coaxial line }