Does twisting a two wire open line reduce radiation

The question is often asked in online fora, and the answers offered are almost always one of:

No, it makes absolutely no difference; or
Yes, it eliminates feed line radiation.

The first answer is the most popular.

Are they both be correct? Well no, appealing as short answers are, neither is correct as written.

Differential and common mode

A pair of conductors in proximity of some other conductors or conducting surface (such as the natural ground) can operate in two modes simultaneously, differential mode and common mode.

Differential mode is where energy is transferred due to fields between the two conductors forming the pair, and common mode is where energy is transferred due to fields between the two conductors forming the pair together and another conductor or conducting surface.

The currents flowing in the two conductors at any point can be decomposed into the differential and common mode currents.

Differential current Id is the component that is equal but opposite in direction, it is half the difference in the two complex line currents I1 and I2.

Common mode current Ic is the component of the line currents common to both conductors, it is half the sum of I1 and I2.

Id=(I1-I2)/2
Ic=(I1+I2)/2
I1=Ic+Id
I2=Ic-Id

So, for example, if I1=2A and I2=-1A, Id=(2--1)/2=1.5A, Ic=(2-1)/2=0.5A.

A line that is operating with perfect balance has only differential current, ie common mode current is zero. It is unlikely that a feed line in a practical antenna system is perfectly balanced, but with due care, it can have very low common mode current, 20dB or more less than the differential component.

Differential component

In the case of differential current:

at distant points at right angles to the plane of the conductors, the current moment due to the current in one conductor is fully cancelled by the current in the other conductor;
at distant points in the plane of the conductors, the magnitude of the current moments are approximately equal, but there is a small phase delay due to the separation of the conductors, and the current moments do not fully cancel;
at other distant points, as with those in the plane of the conductors, the cancellation is not complete, bit it is also proportional to the cosine of the angle subtended by the points and the normal to the plane of the conductors.

Fig 1:

Fig 1 shows the relative net current moment at a great distance normal to a short line in the plane of the conductors for a range of line spacing in wavelengths. It can be seen that the net current moment (and therefore radiation) is very low at small spacing but is much greater at spacing above 0.01λ. So, for practical purposes for HF, a line with spacing of 150mm will have worse case net current moment of less than -20dB in the plane of the conductors, and even less in other directions.

Twisting a two wire line will reduce the net current moment due to differential current if the twist rate relative to wavelength (twists / wavelength) is high. With sufficiently high twist rate and even geometry, even for larger line spacing, the relative current moment can be very small.

Twisting a uniform two wire line reduces radiation due to differential mode current. On receive, Twisting a uniform two wire line reduces the differential current induced directly in the feed line due to external noise and signals.

Common mode component

In the case of common mode current:

at distant points at right angles to the plane of the conductors, the current moment due to the current in one conductor is fully reinforced by the current in the other conductor (ie doubled);
at distant points in the plane of the conductors, the magnitude of the current moments are approximately equal, but there is a small phase delay due to the separation of the conductors, and the current moments do not fully reinforce;
at other distant points, as with those in the plane of the conductors, the cancellation is not complete, bit it is also proportional to the cosine of the angle subtended by the points and the normal to the plane of the conductors.

Fig 1:

Fig 2 shows the relative net current moment at a great distance normal to a short line in the plane of the conductors for a range of line spacing in wavelengths. It can be seen that the net current moment (and therefore radiation) is highest with small spacing, and reduces only slightly for larger spacing. It in not uncommon that the common mode component of current is greater than -20dB relative to the differential component, and in such cases can be a greater contribution to feed line radiation than that described in the previous section.

Twisting a two wire line will not reduce the total net current moment due to common mode current. The net current moment averaged in all directions will be exactly the same.

Twisting a uniform two wire line does not reduce average radiation due to common mode current. On receive, Twisting a uniform two wire line has little effect on the common mode current induced directly in the feed line due to external noise and signals. Common mode current on the feed line is quite likely to inject differential current at the end of the feed line.

Summary

Smaller spacing reduce feed line radiation and direct feed line pickup due to differential current component.

Spacing has only a small effect on radiation or pickup due to common mode current component.

If you have a feed line that is very well balanced, twisting the line can help to reduce feed line radiation, or noise pickup directly by the feed line. If there is substantial common mode current, any benefit to differential induction from twisting the feed line is likely to be masked by the common mode current. On the other hand, if common mode current is high, there will be little benefit from twisting the line.

To be fully effective, the feed line twist rate needs to be high.

Links / References

Changes

Version	Date	Description
1.01	23/09/2011	Initial.
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