The Private Life of Coaxial Cable

This is a common theme from several of my talks over the years about Ferrite Chokes and Baluns. By expanding the topic into a blog format, I hope to be able to explain it in more detail, and add some FAQs as time goes on.

This well-known image originated with Walt Maxwell W2DU, the author of many articles about transmission lines. It brings out several important points.

  • The inside of a coaxial cable truly is “private” – completely screened from the outside world. This is one of the rare statements that can be handed to absolute beginners as a simple fact, and still remains valid all the way through to graduate-level EM physics.
  • The private interior of coax is due to the skin effect which means that, at RF, current flows only on the surfaces of conductors.

    There are many confusing illustrations in textbooks that make some people imagine the skin effect only applies to electrical conductors of some particular shape and size, or in some particular type of circuit. That isn’t true! The best and most generalized derivation of the skin effect I have been able to find is reproduced here. All the high-level EM physics and maths leads to a simple and very powerful conclusion:
    Whenever and wherever an RF current is flowing (regardless of the circuit configuration, regardless of the reason) the skin effect will always be present.
    RF current will be forced to flow very close to the outer surface of the conductor, and there is no net current flow into or through the thickness of the material. 
    Because we know the skin effect will always be present, we can use that as a starting point when tracing RF current pathways on complex shapes such as coaxial cables and shielded loops. Suddenly, the whole topic of shielding (and what you need to do to make it work correctly) will begin to make sense!
    There is one condition, though: you have to hold onto that idea consistently. Many of the myths in RF engineering arise because people aren’t being logically consistent. They imagine they can switch these basic ideas on-and-off to suit their own preconceived notions… and physics just ain’t like that.  
  • The skin effect in coaxial cables means that the outside surface of the shield is a completely separate conductor from the inside surface.
    The outside surface of the shield is part of the outside world. This is where the so-called “common-mode” currents flow.
  • Let’s look again at that diagram. It shows the open end of a coaxial cable carrying three separate RF currents (I1, I2 and I3). The cable is connected to two wires coming from the antenna and carrying currents I4 and I5.

Private Life of Coax

  • Inside the coax, current I1 flows on the outside surface of the centre conductor, and current I2 flows on the inside surface of the shield. Because the centre conductor is entirely surrounded by the shield, electromagnetic coupling is very tight and this forces I1 and I2 to be exactly equal and opposite. Even a very short length of coax is sufficient to enforce this to a very high degree of accuracy.
    So:
    • Due to the way coax is constructed, the inside of the coax will only support energy transfer in the differential, transmission-line mode.
    • Inside the coax, the common-mode current is zero.
  • Now look at the currents I4 and I5 close to the feedpoint of the antenna. In the real world, there is no such thing as a perfectly balanced antenna. Here are a couple of slides to make that point:

Because a perfectly balanced antenna is such an UN-natural phenomenon, I4 and I5 will almost always be UNequal. 

  • When we connect the antenna to the coaxial feedline, the current I4 becomes re-labeled as I1 flowing on the centre conductor, but it’s still the same current.

    Now if I4 and I5 happened to be exactly equal, I5 would flow entirely into the inside surface of the shield to become I2, and everything would be fine. But I4 and I5 never are the same, so what happens to the difference?
  • Point X on the diagram is where I5 from the antenna can divide into two parts, shared between I2 and I3. I2 is the part the flows into the inside surface of the shield, and as we have already seen, this must be numerically equal to I1.

    The difference between I4 and I5 becomes I3, flowing on the outside surface of the shield. Note that this happens only at the open end of the coax, where the inside and outside of the shield meet together. Everywhere else along the coax, I2 and I3 each create their own skin effects on opposite surfaces of the shield, that keep those two currents physically separated.

Those are a lot of observations to keep in mind, but they all lead to one simple conclusion.

Summary

  • Because the currents I4 and I5 in the antenna are never quite equal, they can be mathematically resolved into a differential-mode component and a separate common-mode component.

  • However, a coaxial feedline will physically do the same thing! At RF, where the skin effect creates a third conductor on the outside of the shield, the pure differential-mode component of the incoming two-wire connection will automatically be routed into the private, shielded interior of the coax to become I1 and I2. Meanwhile the common-mode component is routed separately onto the third conductor, the outside of the shield, to become I3.

And that’s the private life of coax.

 

FAQs

Ooh, we’ve got lots of those… if you follow this blog, I will add to and answer these from time to time.

FAQ1. “I don’t feel comfortable about using the term ‘common-mode’ in relation to coax.”

The classical concepts of common mode and differential mode were based on twin-wire transmission lines, which can support the two different modes on the same two conductors. However, this was long before coax was invented, and coax doesn’t work like that.

The difference is that, at RF frequencies, the skin effect creates a third conductor on the outside of the shield, so the coax becomes a three-conductor transmission line which will carries its common-mode current separately on the outside of the shield. Seen from that viewpoint, it is perfectly justifiable that engineers call I3 “the common-mode current”… because that’s exactly what it is! 

 

 

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