(Steyer nd) describes the DK7ZB balun / match for VHF and UHF Yagis.
To understand how the “DK7ZB-Match” works look at the left picture. Inside the coax cable we have two currents I1 and I2 with the same amount but with a phase shift of 180°.
No. At any point along the coaxial line, a current I on the outer surface of the inner conductor causes an equal current in the opposite direction on the inner surface of the outer conductor.
As the currents are shown with the designated directions, I2=I1, not I2=I1<180.
A consequent simplification is that I4=I2-I3=I1-I3.
There is an issue with the current arrow I3 in the lower right of the diagram. It might imply that the only current in the conductors is I3, but the current between the nearby node and lower end of the shield is I3-I1.
If the structure was much much shorter than the wavelength, there would be negligible phase change in currents along the structure, so I1 would be uniform along the centre conductor, I2 uniform along the inside surface of the outer conductor, and I3 uniform along the outer surface of the outer conductor.
The diagram notation does show that I3 (which is equal to the dipole drive imbalance) is uniform along the structure, and that I3 flows to ground.
DK7ZB goes on:
If we connect a dipole or the radiator of a Yagi direct to the coax, a part of I2 is not running to the arm 2 but down the outer part of the coax shield. Therefore I1 and I4 are not in balance and the dipole is fed asymmetric.
But how can we suppress the common-mode current I3? A simple solution is to ground the outer shield in a distance of lambda/4 at the peak of the current.
So, the length of the structure is in fact a quarter wavelength electrically, or close to it to achieve the choking effect. I3 will be in the form of a standing wave with current maximum at the lower (‘grounded’) end, and current minimum at the upper end.
It happens also that his usual configuration of this balun is that there is a standing wave on the inside of the coax, and so I1 and I2 are not uniform along the conductor, and whilst it is relevant to the designed impedance transformation, it is inconsequential to reduction of dipole current imbalance.
DK7ZB continues with the development of his variation of a Pawsey balun:
But now we get a new interesting problem: For the transformation 28/50 Ohm we need a quarterwave piece of coax with an impedance of 37,5 Ohm (2×75 Ohm parallel). The velocity of the wave inside the coax is lower than outside (VF = 0,667 for PE).
The outside of the shield has air (and a litle bit of insulation) in the surrounding and VF = 0,97. For grounding the common mode currents this piece should have a length of 50 cm, with a VF = 0,667 and a length of 34,5 cm this piece of coax is to short. By making a loop of this two cables as shown in the picture down we get an additional inductivity and we come closer to an electrical length of lambda/4. Ideal is coax cable with foam-PE and a VF = 0,82
Above is DK7ZB’s implementation of his balun with the loop and
I copied the above implementation and measured the common mode impedance Zcm.
Above is the Zcm measurement. There is a quite narrow self resonance where Zcm is quite high for about 10MHz bandwidth centred on 125MHz, but at 144MHz Zcm=83-j260Ω which is too low to qualify as a good common mode choke.
Like all narrowband / tuned common mode chokes, tuning to the desired frequency band is essential to their effective operation.
Like most published balun designs, this one is published without measurements to demonstrate its operation or effectiveness.