Mike (WA7ARK) recently posted details of an interesting experiment: Measuring currents in an unbalanced dipole.
Above is a diagram of his experiment, and several points at which he measured the magnitude of current with his RF current probe.
Let’s look closely at his measurements at points B, C, D, E and F, all very close in terms of wavelength.
Essentially, all of them except D measured approximately 1A, and D was close to 0A.
Think about this, why is it so (as Prof Julius Sumner Miller used ask?)
Above is my diagram of the region where measurements B-F were made.
The diagram assumes fully developed skin effect and TEM mode propagation on the coax, and that the length of the section analysed is very much less than wavelength (ie there is insignificant phase change with location).
Since this is part of a standing wave antenna the net or common mode current in this region is determined by the wider antenna context. This region is one where the standing wave current is approximately uniform over the section depicted.
So, you might not be surprised to find that the current flowing on the outer surface of both sections of coax shield is I1, as is the current flowing on the wire to the right of the end of the coax.
The trickier part might be the currents in the small region where the coax is broken out to two wires and then back to coax. Let’s call the current on the inner conductor at that point I1 and on the link between the shields Ix, both flowing to the right.
There are two constraints that play here:
- current on the inner conductor will be approximately uniform (I1); and
- common mode current along the length in the diagram will be approximately uniform (I1).
So, with those constraints we can say that in the shield gap \(I_1+I_x=I_1\) so \(I_x=0\).
None of this is in conflict with discussion of currents on transmission lines in previous articles.
What about further along the line?
The analysis above is correct for location of the gap very much less than wavelength as the magnitude and phase of the relevant currents are equal… hence the appearance if I1 in so many places.
For greater offset, Icommon (I12) falls away due to approximately sinusoidal distribution of current on the nominal half wave dipole, the phase of Icommon (I21) is approximately uniform along the dipole leg. The phase of the current on the inner conductor leads that at the shield end (and Icommon).
The exact solution depends on factors like whether there are standing waves on the coax interior, its velocity factor, dipole current distribution and more.
That said, a ‘back of the envelope’ solution of 30° physical offset of the shield gap, vf=0.67, is: I1=1.00∠45, Icommon=I12=0.866∠0, gives |Ilink|=|I2|=0.725A (by the Law of Cosines).
Above is a phasor diagram at the linked shield gap, it applies only to the two wire section within the ‘gap’.
Looking at that diagram, as the distance from the linked shield gap to end of shield is reduced, |I12| approaches |I1|, the phase of I1/I12 approaches zero, |I2| approaches zero. The scenario Mike measured would have phase of I1/I12 around 5° and |I2| very small, unbelievably small perhaps, but there is the explanation of why it is so small.
The solution from Resolve measurement of I1, I2 and I12 into Ic and Id:
