A 'current' balun forces equal currents at the balun's location (usually the feedpoint) by inserting sufficient common-mode impedance on the braid outer. Clearly, the higher the impedance the better, but no one seems to discuss how much is sufficient. Here I attempt to answer that question by considering radiation pattern distortion.
The problem with asking how much is necessary to solve an RFI problem (be that 'RF in the shack', or feedline radiation of mains noise into the antenna) is that it depends on many other uncontrolled factors. In that instance you may have better luck concentrating on common-mode filtering of your mains supply and adding feedline chokes as they exit the house. Nevertheless, reducing feedline radiation will help with all these aspects.
Consider a 1/4-wave wire connected to one half of the dipole at the feedpoint, i.e. the 'we didn't fit a balun' situation, but this time add an inductor to mimic a choke (current) balun. This represents the worst case situation.
The figure shows the current distribution when the inductance is zero.
The figure below shows the current distribution with 10k series inductive reactance. Feedline current has now been substantially suppressed.
Current in the vertical feedline causes vertically polarised radation, which may be measured separately in 4NEC2. This will tend to 'fill-in' the nulls of the ends of the dipole when the total field is measured. Let's sweep the inductor value and record the vertically polarised radiation, as we did in InducedFeedlineRadiation:
An empirical model is also shown, given by:
With R set to 50 Ohms.
The choke forms a low-pass filter acting against the surge impedance of the radiating feeder.
We might expect that the starting point with no balun sees two lots of current in one half of the dipole, one lot in the other half, and one lot in the feeder. That would mean the vertically polarised feeder radiation would be approximately 9.5dB down on the horizontally polarised radiation, which itself is reduced by 3.5dB due to the radiation of the feeder. Given that 4NEC2 predicted 2.6dBi radiation from the ideal dipole without feeder radiation (theoretically it should be 2.2dB), we might therefore expect this starting point to be about -12dBi. It’s higher than this, suggesting that the feeder collects more of the displacement current than the other half of the dipole, which isn’t surprising since the capacitance between them will be greater (they're closer together).
When the isolation in dB of a current choking balun is measured (e.g. by measuring S21 of the common-mode with a VNA), 6dB may thus be subtracted from this result to give the approximate dBi value. Another 2.2dB may be subtracted to account for the isotropic gain of a dipole, which then gives a figure for the depth of the side rejection. The dBi gain figure will obviously change for antennas with gain.
So how much choking impedance is enough? To answer this we need to ask ourselves how much side rejection we want. Even VHF yagis don't do much better than about 30dB front-to-side ratio, and they will have substantial forward gain, so we'll use that figure. If we're using a dipole, subtract the 2.2dB isotropic gain to get 27.8dB and on the plot above read across to find that you need about 600 ohms. This is very close to the general rule of thumb to aim for ten times the 50 Ohm feedpoint impedance.
I think people fuss too much trying to get several kOhms of choking impedance. Provided the antenna is being fed at a current maxima, the feedpoint impedance will be low and getting more than 500 Ohms is sufficient. Antennas where the choke needs to be located at a high impedance voltage maxima (e.g. End Fed Half-Wave or End-Connected Windom) will require a correspondingly higher choke impedance.