The Weird Antenna Wire End Effect

I have been giving some thought to antenna wires recently. I was particularly interested in the reason for them being shorter than we would expect if we simply calculate their length by dividing signal propagation speed by the frequency of the signal.

The length (L) of a half wave wire can be calculated using the simple formula: c/2f=L where c is the propagation speed of an electromagnetic wave in free space. The rounded value of c is 984 million feet per second, so a half wave wire at 3.5MHz will be 984/(2×3.5)=140 feet.

If we cut and trim a half wave wire for the 80m band we find the resonant length is shorter than the value calculated above. This is because a half wave wire is electrically longer than its physical length due to something called the “End Effect”. This is the capacitive coupling of an unterminated wire end to ground.

An 80m half-wave is also a full wave on 40m (A in figure 1). On 40m it is comprised of an inner half wave wire (B in figure 1) and an outer half wave wire (C+D in figure 1). The inner half wave wire is terminated by the outer half wave wire and is therefore unaffected by the End Effect.

The outer half wave wire is unterminated so it is shortened by about 3% due to the antenna End Effect. Wire insulation, velocity factor etc result in a total shortening of about 5%.

The shortened length is calculated by the formula 468/f. This means that the inner half wave wire (which should be defined by the formula 492/f) is too short by an amount 468/492=95%.

So a half wave wire that is tuned for resonance on 80m will NOT be resonant on 40m despite a precise harmonic relationship between the two bands. The bottom of the 40m band (in North America) is 7.0MHz which is exactly twice the frequency of the bottom of the 80m band – 3.5MHz.

There is also a precise harmonic relationship between the 80m band, the 40m band and the 20m band. The bottom end of the 20m band – 14.0MHz – is exactly twice the frequency of the bottom of the 40m band and exactly four times the frequency of the bottom of the 80m band. But a half wave wire cut for resonance on 80m will similarly NOT be resonant on 20m.

If we refer to figure 2 we can see why. The portion of the wire “B” is now a full wave on 20m and it is terminated by the half wave sections “C” and “D”. So B is too short by the same 5%.

Now suppose we take a half wave wire and turn it vertically. We now have a half wave vertical antenna. Does the End Effect still apply? Does it apply if the “other half” of the dipole is virtual (i.e. a ground-mounted quarter wave vertical)?

We still have an unterminated wire end at the top of the antenna (it could be a metal whip). We still use the same 5% shortening factor in calculating its length. Let’s take it one step further. The End Effect is caused by a capacitive coupling between an unterminated wire end and the ground. The capacitive shortening effect is only about 3%, but could we increase the capacitive coupling to make the shortening even greater?

The answer is a definite yes. We can create a larger capacitive coupling to ground using something called a “capacitance hat“. A capacitance hat, also known as a capacity hat, or top hat can be used to significantly shorten a vertical radiator.

A capacitance hat is made with radial spokes or a circular conductor (or similar arrangements). The diameter of the hat is roughly equal to the amount by which the radiating element can be shortened.

This is illustrated in figure 3. A half wave wire that is erected as an inverted-V has a quarter-wave vertical section (B) and a quarter wave horizontal section (A). If the quarter wave horizontal section is arranged so that it lies centered on top of the quarter wave vertical section, we now have a quarter wave vertical antenna (D) with a capacitance hat (C) that will theoretically be resonant at the same frequency as the half-wave inverted-V antenna.

In practical terms, a single wire capacitance hat may not be very efficient, so several such wires forming a circular arrangement around the plane of the vertical element may be required.

If we stand on our heads and take another look, a quarter wave vertical antenna with a quarter wave capacitance hat is an upside down version of a quarter wave vertical antenna with a quarter wave radial field.

The main difference is the vertical with the “cap hat” is resonant at twice the frequency of its upside down cousin. Could we build a dual-band antenna and change bands by turning it upside down? Impractical perhaps but it kinda makes sense in an upside down sorta way.

These are my thoughts on the topic and, since this is not a scientific treatise, feel free to debate or disagree.