Small antennas and radiation resistance

My 2004 Dayton Hamvention Power Point presentation on Small Verticals can be downloaded here... DAYTON 2004.

The main points when dealing with small antennas are:

There is no magic bullet or magic cure to make a small antenna act like a large one. It all comes down to current distribution over linear distance.

Small antennas require extraordinary care to obtain high efficiency.

How do we make a small antenna as efficient as possible?

	First, we make current as uniform as possible over the length of the antenna.
	Second, we use low loss loading such as optimum form (size, length, and diameter) loading coils.
	Third, we make the antenna as large and straight as possible in a line. We don't fold, bend, zigzag, or curve the antenna especially in the high current areas.
	We keep the high voltage points (the open ends) away form other things (like lossy earth), and the high current areas away from other large lossy conductors.
	Most important, we keep current as high as possible throughout the length of the antenna by using as much capacitance as possible at the antenna ends.

What this does is maximize radiation resistance (while at the same time minimizing loss). The text below explains how radiation resistance and loss interact.

Radiation Resistance

Radiation resistance is probably the most abused and misused term in antennas. The reason it is so often misused is the lack of clear definition. When a term has several nebulous meanings and uses, it is only natural that misuses will appear. The lack of a firm well-accepted definition allows meanings to slip from one application into another, where a totally erroneous conclusion can be drawn from what otherwise would be a good formula!

Common Uses

There are two commonly used "correct" meanings of radiation resistance and one totally incorrect use. The "correct" uses are:

	The resistive part of an antenna's feedpoint impedance that is caused by radiation from the antenna
	The total EM power radiated in all directions divided by the square of net current causing the radiation

Neither of the above definitions include loss resistances of any type! The moment loss resistance is included, we have the third commonly used (but totally useless) definition. This definition, which includes losses, must be considered incorrect because it is comprised of resistances that have nothing to do with radiation. The misused definition is:

The real (or resistive) part of an antenna's feedpoint impedance including loss related resistances.

The correct name for the third "radiation resistance is actually the antenna feedpoint resistance, not radiation resistance!

Of the above good definitions, the first definition is the most commonly abused through mistake. The second definition is an IRE definition (albeit a good one that never caught on). In every case I've seen, it is the second good definition that always provides the most direct and useful answer.

Examples of Misuse

Folded Monopoles

Folded monopoles probably provide the best examples of misuse of the term radiation resistance. Quite often, in discussions of folded monopoles, claims are made that multiple drops increase the radiation resistance and lower losses. The justification for this incorrect claim is the folding raises radiation resistance, and % eff = 100 * Rrad/(Rrad + Rloss) .

What folded monopole fanatics forget is that all losses must be normalized to the point where radiation resistance is taken, otherwise the efficiency formula won't mean a thing!

Let's look at what actually happens in a folded element, and use it to understand how the poor definition of radiation resistance causes the misunderstanding.

Consider the unipole above. Lets assume we short the open terminals, and feed it as a normal Marconi vertical with a feedpoint at the point where we measure I3. I3 is ALWAYS the vector sum or in-phase combination of currents I1 and I2. With continuity through each leg, I1 and I2 share all of the ground current. This happens regardless of where the feedpoint is located in the lower portions of the antenna.

With 1/4wl height and a reasonable element diameter, the radiation resistance (fed as a traditional monopole) would be about 36-ohms.

Assume ground loss, normalized to the point where we measure I3, could be represented by 14 ohms. Applying 500 watts would make current I3 equal 3.16 amperes. Power loss in ground resistance would be I^2R, or 3.16^2 times 14, about 140 watts. Feedpoint resistance would be 50 ohms. Feedpoint power, as a check, would be 3.16^2 times 50 ohms or 500 watts. With equal diameter legs, that current would divide and 1.58 amperes would flow in each upper leg.

Let's use the formula %eff = 100*Rrad/(Rrad+Rloss). We have 36/36+14 = .72 so the result is 72% efficiency, 28% loss. 28% loss times 500 watts is 140 watts in ground losses. This matches the other method just above.

Opening the terminals and feeding as a folded unipole, half of the radiator current is in I1 while the other half is in I2. Current is halved to 1.58 amperes at the feedpoint and power remains the same. The feedpoint resistance now becomes 200 ohms. We can confirm this with I squared R, or 1.58^2 *200=500 watts. It all works out great so far!

Now let's MIS-use the same efficiency formula, like Orr does in his Handbook and others do in various places. We would have 200/200+14 = .9346 or 93.46 % efficiency.

We know we still have 3.16 amperes flowing as I3, and we know ground resistance is still 14 ohms (normalized to the point where I3 is measured). I-squared-R losses are 3.16^2 * 14 = 140 watts! We have exactly the same power loss.

Let's transform the ground loss value that was normalized at 14-ohms where I3 is measured to the feedpoint by the same impedance multiplication as the feed resistance, or 1:4. We'd now think ground resistance would be 4*14 = 56 ohms. 56 ohms of the feedpoint resistance is loss. Trying that same efficiency formula, we get:

144/144+56 = .72, or 72% efficiency!!! Now everything checks out fine.

The Common Mistake

Orr and others have used the first definition of radiation resistance, the portion of the terminal resistance of the feedpoint responsible for radiation. Unfortunately they failed to normalize ground losses to the same point where the radiation resistance was taken!

We can not use a formula that is based on everything being normalized to one point, unless we actually do that for every term in the formula!

There is no change in efficiency when the NET radiator current remains the same, and when ground current remains the same. It is pathological engineering to think otherwise.

Using The Second Definition

If we use the second IRE definition of radiation resistance, where the effective current causing radiation is compared to power radiated, we find nothing changes. A folded dipole or monopole has the same radiation resistance as a regular dipole or monopole the same size, and a small loop has the same radiation resistance regardless of turns.

The magic vanishes along with the incorrect definitions and perceptions.

You can read about this in textbooks. The "Antenna Engineering Handbook" by Jasik in 3-13, 19-3, and in other sections uses correct definitions and descriptions.

Quad's and other Loops

We find the same efficiency misconceptions in articles about small loops and large quads. Authors sometimes assume, incorrectly, radiation resistance changes in a favorable proportion to loss resistance as we make the feed impedance increase. What we really are doing is placing the feedpoint in series with a smaller portion of NET current causing radiation.

With a large full-size quad element the pattern under some conditions will slightly change, but efficiency remains basically the same. With a small loop antenna, losses can actually increase with more turns!

Terminated Folded Elements

Another abuse of radiation resistance is found in terminated antennas. Some manufacturers and authors claim a resistance can be inserted in series with one leg of a folded monopole or folded dipole, and the other leg fed. The usual arm-waving claim is the antenna isn't really resistor loaded, and that efficiency is very good because radiation resistance is high.

That claim is absolute nonsense!

A large terminated Rhombic is well-known to have poor efficiency. Rhombic gain is actually low compared to other antennas having the same sin/sin x antenna pattern, because Rhombic efficiency is generally less than 50%. At least half of the power is consumed in termination and ground losses below the antenna. The actual gain may be reasonably high compared to a dipole, but not to other efficient antennas with the same half-power beam width.

The typical manufacturing buzz-word is that terminated monopole and dipole antennas are "traveling wave antennas" and by some magic (that even large terminated Rhombic antennas can't achieve) have broad bandwidth and high efficiency.

A Rhombic focuses energy (that is not transformed into heat) into a narrow beam that has considerable gain, but if it sprayed the radiation around in a non-focused pattern, a regular dipole would win hands down. Throw a resistor on that dipole to smooth SWR variations, or on a vertical, and efficiency suffers.

I listened to a station on 75 meters 600 miles away testing a Sommer T-25 vertical. He was 30 over nine using a dipole, and dropped to S6 with the vertical. The European he was working reported a similar change. By removing the termination resistor and base-loading the same vertical, a local Ham gained almost 25dB on 80 meters!

When we abuse or misuse radiation resistance, we can invent all kinds of magical antennas. We can have CFA's, E-H antennas, terminated dipoles, small magnetic loops, and verticals with all sorts of magical claims. Few, if any, of the claims are ever correct. Any time we see a claim that efficiency changes a large amount because of feed method change, it should be a red flag.

Increasing Radiation Resistance

Radiation resistance, at least under the useful IRE definition, can be defined by the following formula:

which would translate to:

Where He is the effective height center of accelerating charges that cause radiation. In other words, He is the effective height, expressed in fractions of a wavelength, of the distributed common-mode current in the structure.

(Common-mode current is the vector sum of all currents, or the effective in-phase current at any point, or the current we would measure if we placed a giant clamp-on current probe around ALL of the conductors at that any given height.)

He and must both be in the same units, either given as degrees or decimal fractions of a wavelength.

As an example, a uniform current single conductor antenna has an actual physical height of 15.19 feet on 1.8 MHz, where one wavelength is 546.67 feet, the effective height is:

15.19/546.67= 0.0278 wl

Since charges are distributed evenly throughout the structure the full height is used. The effective height is .027 wl, the same as the physical height. The height in electrical degrees is .0278 * 360 = 10 degrees

We have a radiation resistance of:

We can express this graphically in a chart, such as one found in the Antenna Engineering Handbook by Jasik:

Finding 10-degree height on the graph above, and following that line until we reach the crossing for unity current ratio, we see the ~1.27 ohm radiation resistance is in agreement.

Notice that the number of vertical conductors does NOT enter into the equation! This is the absolute maximum possible radiation resistance we can obtain for a given radiator height.

Non-uniform Current

Radiation resistance is purely a function of the effective current distribution and height of the radiator, and is limited by height (spatial length)! Current throughout the antenna will not remain uniform if we reduce the size of the flat-top or hat.

Current will become zero at the very top with no hat, and 100% base loading. In this case, with no change in height, radiation resistance will be approximately 1/4th the value of the uniform current example. The result is exactly like a 50% reduction in effective element height.

If we follow the 10-degree line to the intersection point with 0 top current, we find radiation resistance to be around .32 ohms. 1.27 ohms, the radiation resistance for uniform current, becomes 1.27/4 or .3175 ohms.

If we stay on the uniform current line, we find that .3175 ohms would be the radiation resistance of a 5-degree monopole with uniform current.

Efficiency

It often helps to look at the extremes, so we can get a feel for the effect of changes.

Let's look at the poor ground extreme and assume we have system losses, normalized to the current maximum, that are many times the radiation resistance. This would be the case for a short 160 or 80 meter mobile antenna.

In such a system radiation resistance would dominate any change that would affect efficiency. Current distribution would mean everything to efficiency.

Assume we have a base loading coil, either good or poor, and a thin mobile whip above the coil. Efficiency would increase by a factor of approximately four times by installing a capacitance hat with several times the distributed capacitance of antenna conductors below the hat.

Moving the coil would have little or no effect on efficiency.

A six-foot antenna with a large hat would be electrically equal to a 12-foot antenna without a hat.

This is why very poor inductors used on antennas in mobile shootouts, with large hats, equal or beat very large high-Q coils in similar height antennas that do not have large hats. One case in mind was a Hamstick lash-up in a mobile. The Hamstick, a notoriously poor efficiency antenna for 75-meters, soundly trounced Bugcatcher antennas when a large hat was added to the Hamstick.

Moving the coil up on the antenna has the effect of making current below the coil uniform, but without a hat current above the coil is a triangular taper that reaches zero at the element tip. The effective height of the area above the coil is 50% of actual height.

If we add a large hat at the bottom of the whip, current in the whip is actually reduced! At the same time, we change nothing below the coil. The effect of adding a large hat below the whip is to reduce the effective height of the antenna, when considered as a percentage of physical height. Radiation resistance and efficiency is generally reduced by adding a hat just above a coil, even if the hat allows us to use a smaller coil!

Adding a large hat at either end of a coil also reduces coil Q, since a large portion of the hat capacitance directly shunts the inductor.

Conclusion

We can reach the following conclusions:

	Radiation resistance, or at least the useful definition of radiation resistance, is limited by spatial area (or height in the case of a vertical) any antenna occupies.
	Radiation resistance is maximized by making current as large as possible over the entire spatial area of the antenna.
	Surrounding objects generally reduce radiation resistance and efficiency, even when they are NOT resonant, because they reduce effective height! This includes dielectrics that increase capacitance of the antenna to ground, since any increase in capacitance appearing well below the top of an antenna reduces effective height.
	Radiation comes from charge acceleration, nothing else. The longer the linear spatial distance we move charges in, the fewer charges we need to move at any point for the same amount of EM radiation. This is just another way of saying radiation resistance is higher in physically longer structures, especially when they carry uniform current.
	Any antenna (including Linear Loading, Helical Loading, Folded Monopoles, Fractal shapes, CFA, E-H, and so on) claiming to increase radiation resistance beyond the limits outline above is based on misunderstandings or untrue distortions of basic antenna principles.

This page has been visited Hit Counter times since June 12, 2004