# Capacitive hats on wire dipoles?

Capacitive hats seem to be advertised as an option for mobile vertical antennas. One mentioned advantage is the they can widen the SWR bandwidth, making the antenna easier to tune.

What might be the effect of using capacitive hats, not on a mobile vertical, but symmetrically on both ends of a wire dipole, or a shortened dipole?

Since wind loading isn't as much of an issue on non-mobile wire antennas, it seems almost any size capacitive hat might be possible by using arbitrarily large sheets of conductive wire screen material (hung or inside toy hoops, etc.). How might varying the size of the capacitive hats (from tin-can lid to patio door size) change the antenna's characteristics? (SWR, SWR bandwidth, radiation resistance, pattern, and etc.)

Added: Other than an increase in wind loading, is there any downside? Why shouldn't every dipole have a little conductive disk (or more) at the end?

• One of the most thoroughly researched subjects in ham radio antennas. See ARRL Antenna Book section on Short Vertical Antennas for the answers to all of these questions, and so much more. A seminal paper in the amateur literature is Sevick, QST, March 1973, "The W2FMI Ground-Mounted Short Vertical". – Brian K1LI Sep 18 '18 at 1:33
• Good question. I hope you hold out for a good answer which can provide some data. Although much has been written on capacitive top loading versus inductive base loading, a comparison to the full half-wave alternative is not something I've seen. – Phil Frost - W8II Sep 18 '18 at 2:21
• @BrianK1LI Most of the wire in Jerry Sevick's very short vertical was in the capacitive hat itself! Years ago, I had a 40m SSB QSO with him using that antenna; between that and listening to him contact others, I can attest that it worked very well indeed. Capacitive top-loading is quite common on short verticals used on 160m (the T antenna or inverted-L), and --as unbelievable as it may seem-- they can work almost as well as full-size 120' vericals. I find this idea applied to dipoles fascinating. – Mike Waters Sep 18 '18 at 19:28
• Here is a PDF of the QST article that @BrianK1LI and myself commented about. Why shouldn't two of these back-to-back, parallel with the earth, of a suitable height, and fed in the center work as well or better than this vertical? And no ground radials, counterpoise, etc. are required! – Mike Waters Sep 18 '18 at 21:36
• @MikeWaters : Some of the answers to this: ham.stackexchange.com/questions/9826/… might imply that a low dipole (even with dual hats?) might not radiate as a well vertical over a solid ground plane. Wonder if the bottom hat might change that somewhat... – hotpaw2 Sep 18 '18 at 23:22

A capacitance hat used on a shortened antenna ($\le$ 1/8 λ for verticals and $\le$ 1/4 λ for dipoles) converts a largely triangular current distribution with the maximum current at the feedpoint, to a more uniform current distribution or alternatively, it lessens the peak current in the antenna element. This has the effect of:

1.) Raising the Rr (radiation resistance) of the antenna and thus improves the efficiency of the antenna.

2.) It helps to neutralize the inherent capacitive reactance of the shortened antenna and thus generally makes matching the antenna to the feedline an easier task.

Like all shortened antennas, the bandwidth of the antenna is typically less than a "full size" version of the antenna. But the hat will generally broaden the bandwidth compared to other methods of matching the antenna.

The concept of capacity hats on dipoles is not new. Here is a picture of a commercial dipole from DX Engineering. Note the clearly visible wire hats:

Here is a photo from DJ0IP showing his 40 meter cap hat dipole below his spider beam:

The classic modeling approach is to treat the antenna (or in the case of a dipole, each leg) as an open ended transmission line in order to calculate the impedance magnitude of the antenna (or the leg). The degree of wavelength of the antenna (or leg) is also computed. These values allow the reactance that is required to make up the "missing degrees" of the antenna element. Finally, the capacitive reactance required in the capacitance hat is computed. The following universal reactance curve for an open or shorted transmission line is used to compute the reactance required based on the missing degrees:

source: QST, September 1978, Designing a Vertical Antenna by Walter Schulz K3OQF

Inspection of the above diagram shows that if the element is a full 90° (1/4 wavelength) in length, then the transmission line effect will transform the infinite impedance of the open end to a near zero impedance (with near zero reactance) on the opposite end. For any electrical length in-between, the ratio of capacitive reactance to impedance is depicted. If the antenna is of simple wire construction, an impedance calculator such as https://chemandy.com/calculators/round-wire-impedance-calculator.htm may prove sufficient to determine the initial impedance magnitude of the wire. The commonly used formula for calculating impedance magnitude is:

$$Z_{MAG}=60(ln\left(\frac{2L}{r}\right) -1) \tag 1$$

where L is the length of the antenna or the leg of a dipole and r is the radius of the conductor, both in the same units.

The capacitance of the capacitive hat can be approximated from:

$$C_{pF}\approx0.89D \tag 2$$

where D is the diameter of the capacitance hat in inches.

Equation 2 is a reasonable approximation for circular capacitance hats constructed with plates, meshes or skeletal elements (e.g. spokes with a circumferential wire). It is important that the radius of the capacitance hat be <0.1 wavelengths so that the hat does not become a radiating element rather than strictly a capacitor at the end(s) of the antenna.

The capacitive reactance of the hat in ohms is given by the standard capacitive reactance formula:

$$X_C=\frac{1}{2\pi fC} \tag 3$$

where f is the frequency in hertz and C is the capacitance in farads.

• Thank you for adding "It is important that the radius of the capacitance hat be <0.1 wavelengths so that the hat does not become a radiating element rather than strictly a capacitor at the end(s) of the antenna." If the radius was too large, I would think that excessive power would be dissipated in the antenna (and perhaps even in the air dielectric, but I doubt that!). What would actually happen? – Mike Waters Sep 19 '18 at 0:15
• Jerry's article indicates that once the main element is shortened beyond a certain point, a loading coil must be added between it and the capacitive hat. (His 40m antenna was just six feet high!) I assume the same would be true for a very short dipole. – Mike Waters Sep 19 '18 at 0:51
• @MikeWaters I wouldn't expect much power dissipation in the air dielectric except if there is high moisture content or pollutants. – Glenn W9IQ Sep 19 '18 at 12:11
• @MikeWaters Regarding the addition of a loading coil for a very short antenna, I suspect this has more to do with the problem that you cannot obtain sufficient capacitance with any practical size hat to make up the needed degrees so an inductor is also required. – Glenn W9IQ Sep 19 '18 at 12:55
• @MikeWaters I'd guess the most significant impact of a "too large" capacitive hat is it would no longer meet the definition of "dipole" or "capacitive hat". In particular, assuming constant current throughout the hat ceases to be an acceptable simplification, and so the model of the antenna must become more complicated than a simple dipole if the results are to remain accurate. – Phil Frost - W8II Sep 19 '18 at 20:56

Capacitive end loading has the effect of electrically "lengthening" a dipole (i.e. tunes it to a lower frequency). Similar to mid-loading with an inductor but with 3 notable differences:

Potential downsides, other than mechanical issues such as wind loading: There are none.

Why shouldn't every dipole have a little conductive disk (or more) at the end?

For dipoles already tuned to the proper frequency, I would answer "they do not need it". For other cases... it gets difficult to describe so please see the flow chart below.

Summary: Best case would be a full size, half-wavelength, tuned dipole. But if there is a wire length restriction for whatever reason, adding a set of "cap hats" is truly a no-brainer.

In the case of a normal dipole that does not "need" capacitive end loading, there may still be a case for adding small "tin can lids" to the end --and, of course, shortening the wire a little to keep the tuned frequency constant. I cannot cite the reference, but it seemed to state that adding slight capacitive end loading like this gave a slight increase in radiation resistance. For "fussy" people such as me, this is enough to encourage adding cap hats to all of my otherwise-perfect dipoles. Unfortunately, I cannot cite that reference, did not memorize the optimal cap hat size, have not verified independently, and do not know how to measure radiation resistance.

• You say there are 'no potential downsides' and 'it is a "compromise antenna". Respectully, that sounds like a contradiction. What do you believe to be the differences, and to what extent? I do not feel qualified to fully answer that. – Mike Waters Sep 18 '18 at 23:04
• By "compromise antenna" I only mean that the antenna is not a full size dipole. If it were a full size dipole there would be (mostly) no reason to add capacitance ends. But since we are talking about a somewhat short dipole, the options are (1) cap hats, (2) inductance loading, or (3) an antenna tuner. Of that selection, there are no disadvantages of a cap hat compared to the other choices. – Chris K8NVH Sep 19 '18 at 1:01
• There are 2 additional effects, I hesitate to add in the answer because (1) I cannot find the reference and (2) the effects are small enough that I doubt they affect the decision process. The first is that <i>small<\I> cap hats add a little more radiation resistance than was removed due to the wire shrinking (a good thing). Second is that the pattern changes slightly; the cap hats steer the pattern a little more in the radial direction (usually a good thing). – Chris K8NVH Sep 19 '18 at 1:11
• It's not a compromise antenna, compared to a full size dipole, unless there is a measurable downside. A dipole, with the addition of a pair of small capacitive hats, can be nearly full-sized, so should not be considered a highly shortened compromise antenna (unless there is a downside). – hotpaw2 Sep 19 '18 at 15:28
• @hotpaw2 Fair enough, maybe there is a better word? What I am trying to express is there is a decision to be made: "should I make the wires a little longer?" vs "should I make the cap hat a little bigger?" In general "wire a little longer" gives better results. (This MIGHT not be true when within, say, 95% of perfect wire length, but I do not believe that is the situation being discussed and the difference is subtle anyhow.) I will look harder for that other reference and edit this answer for preciseness. Suggestions for replacing "compromise antenna" are encouraged and welcomed :-) – Chris K8NVH Sep 19 '18 at 16:21

To elaborate, the free-space, far-field directivity of a linear, 1/2-wavelength-long, center-fed, perfect dipole varies from that of an "infinitesimal," linear, center-fed, perfect dipole only by about 0.4dB.

However the gain of each of those configurations depends on the ratio of radiation resistance to the sum of radiation resistance with all other heat-dissipating, ohmic losses present in the antenna system.

Those other losses typically are larger for Z-matched antenna systems using loading coils, traps, and/or "capacitance hats" with electrically short radiating conductors — which system gain may be reduced by many decibels from that when using a "full sized," unloaded radiator.

[Reference: Antennas, 3rd Edition, Kraus/Marhefka, pp 23-26].

• Interesting, because a few other sources seem to suggest that small capacitive hats (on near full-sized dipoles) lower resistive loses, and/or increase radiation resistance, compared to an ideal wire dipole. Is there perhaps a cross-over point? – hotpaw2 Sep 19 '18 at 15:18

I installed a 40m dipole, having just enough space in my yard. I cut it to length as per the formula, so resonance should have been close… I used 12 gauge insulated wire. As a test, I installed 4 x 18” wire radials on each end to see the effect. Using an antenna analyzer, I was surprised to see that resonance was down around 6.200 mhz. I replaced the 4 wire radials I improvised, with a larger 3 leaf clover shaped cap hats, made with steel wire, fastened the cap hat to the wire using split nut connectors and soldered the ends of the dipole to the cap hat. The dipole resonated somewhere in the upper 5 mhz range. I then shortened the wire from the middle to bring it close to resonance on 40m. At the moment, the antenna resonates around 7.350 mhz , SWR is 1.2/1.3 @ R=50 ohms. After I trim it a bit, the dipole should be about right. On my first contact with a person I had spoken to before, he was surprised that I was now coming in 25+ over…. The overall length on my dipole, with the hats, is now roughly 50'ish ft. The size and shape of the cap hats will determine the final length of your dipole. With out over thinking capacitor hats, size, shape or equations, etc… just try it. I would say that in no way does using capacitor hats become a compromise to the signal in any way, if anything, it will likely greatly improve the efficiency of the dipole you have.

Best regards, Rene VE6DAY