Practical Antenna Theory

(Part 4)
by AD5XJ, Ken Standard
ARRL Technical Specialist

This series of articles deal with the more technical aspects of antennas and the practical theory behind their use. You will find this guide to be a pragmatic approach to antenna theory. The views expressed here are the author’s and are not meant to be the definitive text on the subject. You should also be armed with the knowledge that there may be changes from time to time where technology advances and the author deems it approprate to update the text.

You should do your won research and fill in where there are “learning gaps”.

Much of the material in this series is derived from publications by the ARRL. Namely,

The ARRL Handbook ®


The ARRL Antenna Book ®.

You should consider those publications reference material in this cursory study of a very complex subject. The most recent editions are available from the ARRL Store online and can be seen at many hamfests, but may vary in quality from used to mint conditon, over many past versions. Any should be considered a valuable addition to your reference library on antennas.

I hope you enjoy this. Please email me if you have questions or would like to see a particular subject enhanced.

Antenna Theory 101

From our discussion last time, you should have been able to take away simple but conservative operating rules to improve your chances of being heard on the air and enjoy long service life from your antenna and transmitting equipment. We discussed the role of antenna system components like the balun and the role it plays in getting our signal heard.

In this article we will look at the theory behind antennas. Let me warn you ahead of time – this is not light reading. But with a little effort, study of the presented material will provide valuable information and understanding of the subject. The stated goal of this series is to arm you with the knowledge and understanding that will enable you to do things for yourself rather than always relying on antenna manufacturers to supply what you need and to make troubleshooting problems easier.

The Vertical Antenna exposed

Let’s start by illustrating a common antenna and the theory involved with it. The first diagram shown is a discrete component equivalence diagram. In other words the diagram shows in discrete terms the factors that influence RF as it travels on your vertical antenna.

We said from the beginning that transmission lines and antennas have complex characteristics. This diagram illustrates the reason for the complex nature of an antenna of any type or size.

By definition, there is series inductance along the length of the antenna conductor that will influence RF current in the conductor of the antenna element. Inductance increases in value with the length of the element. You may remember from studying basic electronic theory, inductors tend to oppose the flow of currents in a conductor. This is true of the antenna as a conductor of radio frequency currents as well.

The vertical antenna as a discrete model – ©ARRL Antenna Book

Because of the proximity to ground, the antenna element will also have a capacitive component as well. Electronic theory defines a capacitor as two conductors placed near each other and carrying electrical opposite charges and that oppose changes in voltage. That surely fits our vertical antenna (the ground being a conductor, however poor, and the other being the vertical antenna element). But also notice that only part of the antenna is very close to the ground. The base section of the antenna will (by definition) have more capacitive effect than the tip. Also by definition, the base will have less inductive quality than the entire length of the element. This is to say that the reactive component values at different points along the length of the antenna element will have different values even though the frequency and length may not change.

It may be apparent from the illustration that the series inductance and the shunt capacitance form a parallel LC circuit. It is, in fact, a parallel tuned circuit at the frequency we wish to transmit and receive on. We now have to deal with the concept of resonance.

Antennas at resonance

Basic electronic theory explained resonance of LC circuits to mean that the reactance of one component is exactly the same but opposite as the reactance of the other component in the circuit. This equal but opposite action cancels the reactive values. In this case, for our antenna to be resonant, the series inductance of the element conductor and the shunt capacitance of the element proximity to ground would be equal and opposite. Here we are talking about capacitive reactance in ohms and inductive reactance in ohms not capacitance or inductance values specifically. We must be very clear on the difference between the two to properly understand the implications of antenna resonance and the rest of antenna theory.

We can illustrate this in a couple of ways. First lets recall the way we express the feed point impedance of the antenna. We learned that it is written as:

R +jX

In this expression, a reactive component carries a “+” or “-” expression to indicate inductive or capacitive reactance values. The minus sign expresses the capacitive reactance value and the plus the inductive reactance. A resonant antenna would have no reactive component because they are equal and opposite at the resonant frequency – canceling each other. Therefore the only part of the expression that has meaning is the “real” value.

Graphing Resonance


This illustration involves looking at reactance in a more dynamic way. That is, we must see the effect that frequency has on reactance near resonance.

In the illustration provided, the real, capacitive, and inductive reactance of a resonant antenna, are plotted against frequency. At the frequency where capacitive reactance becomes zero and inductive reactance becomes zero simultaneously, the antenna becomes resonant. At this frequency only the real (The “R” scale on the chart) value of the characteristic impedance plays a part in antenna performance.

At frequencies above and below resonance, the impedance at the antenna feed point becomes more complex. At lower frequencies, the antenna is more capacitive and at higher frequencies than resonance, it appears more inductive (illustrated by the reactance curve making a positive then negative excursion each side of the resonate frequency).

It is this dynamic and complex nature of the antenna that is at the root of most SWR readings measured on the coax. In our SWR plot, the resonant frequency has a convenient real value of 50 ohms. However, off–resonance real values are much lower with an added reactive value. One could expect the SWR to be more than 2:1 long before going off scale in either direction.

So how do we apply all this knowledge to normal practice? In the case of vertical antennas, we can see from the material presented that, the length of the antenna is a major determining factor in any antenna being self–resonant (a term indicating no other components like external capacitors or loading coils are needed to resonate).


Antenna length is measured in terms of how far RF will travel during one RF cycle (called a wavelength). Remember, this length will depend on frequency more than any other factor. The higher the frequency, the shorter the wavelength, and the shorter the resonant antenna.

When the resonant antenna is long enough to allow a complete wavelength to reach the end of the antenna exactly, it is called a full–wavelength antenna. Resonant lengths may occur at certain fractional wavelengths as well. The most common fractional wavelength antenna is the ¼ wave. Quarter–wave means that the antenna length allows only 90º of the full cycle to flow on the antenna. That’s OK because we know that resonant circuits only need a small excitation to sustain maximum current. We will examine current along our fractional wavelength antenna later.


Dipoles, on the other hand, are usually ½ to one full wavelength long. The feed point connection is usually somewhere near the center (recall our mention of the Windom dipole). Scientists and experimenters often use the ½ wavelength, center–fed, horizontal dipole as a reference for gain and feed point characteristics. In free space, the ½ wave dipole exhibits predictable impedance and radiation pattern characteristics that are practically and mathematically convenient. To that end, the reference is often used by designation “dbi”. The “i” indicates a comparison to the ½ wavelength dipole in free space (scientists call this an isotropic dipole – “i” for isotropic). Actually, it does not matter whether the isotropic dipole is horizontal or vertical, seeing that there is no influence from ground in free space.

The illustration below shows the current magnitude of RF as it flows on a ¼ wave vertical antenna. The curve traced on the right side of the diagram shows a non–linear current curve almost all the way to the tip. This type of curve is called a cosine curve, because it follows a mathematical calculation based on the sinusoidal nature of RF. More importantly to us, there is a dramatic fall off of current as RF reaches the tip of the vertical radiator. Ideally, we would like to have the maximum current flow all the way to the end in order to produce a maximum radiated signal. Practically speaking, that is an unrealistic goal. We can, however, dramatically increase current flow in most of the antenna length. To accomplish this, we can place reactive components in series with the antenna element, part of the way from the base to the tip (most conveniently 50–60% of the length).


By doing so, we alter the normal current flow along the element to resemble the next diagram below. This type of antenna is called center–loaded. The illustration depicts current flow in the center–loaded antenna. The center load is provided by the coil inductor, placed about 50–60% of the length from the base. This is a very short antenna – only 30º (1/12 wavelength). You can see from the current flow trace at the right of the diagram, there is a more or less linear current flow all the way to the coil near the center. The inductive load altered the current flow in the antenna element to provide maximum current for more than half the length of the element. Allowing the maximum current to flow for more of the length of the antenna produces the possibility of more radiated signal. As can be seen, the current flow in the top half of the antenna falls off in a more or less linear fashion becoming zero at the tip. This diagram is true for fractional wavelength vertical antennas only. The same indications would be true for any non–resonant fractional wavelength antenna less than a wavelength. However, the longer the antenna element overall, the more distance the maximum current flow is allowed – thus more radiated signal. It is logical to assume that a 5/8 wave center–loaded antenna will outperform a 3/8 wave center–loaded antenna in signal strength (given all other factors are the same e. g. power, environment, ground plane, etc.). In this case “bigger is better” (size always matters where antennas are concerned).

Shortened Antenna Performance

Can shortened antennas perform adequately on the air? By all means. But to do so, all sources of inefficiency must be minimized. The greatest source of signal loss in shortened antennas is what is called I2R loss. This is power that is dissipated in passive components (like coils) as heat. This kind of loss is due to incorrect diameter and length choices the antenna maker employs and the size of the conductor used to make the inductor. Smaller wire will have higher series DC resistance and more I2R loss than larger wire or tubing. A good rule of thumb for ham radio antenna inductors is “short, fat and made with big wire” is good. Whereas “long skinny and made with small wire” is not.

Image courtesy Texas Bug Catcher web site.

Consider the time honored “Bug Catcher” mobile antenna. It is an extremely short vertical for mobile use, but one that has been a good performer because of the wise use of the design guidelines given here. On the opposite extreme is the “hamstick” style antenna. Moderate success has been enjoyed using the “hamstick” or “outbacker” style antenna despite the design inefficiencies. Somewhere in the middle of the extremes is a compromise design that proves to be both convenient and efficient. The “Hustler” style large diameter resonators on a mobile vertical prove to be quite efficient and are more practical than the much bulkier “Bug Catcher” style antenna for HF. Using the Hustler method of antenna construction, a single, or multiple band vertical can be constructed by choosing screw–together radiating and resonating components in combination to construct a useful shortened vertical for mobile or stationary use.

In practical form, the vertical antenna has a maximum efficiency of no more than 30% or 3.25 dbi. When considering the vertical for base station use, look for design and construction techniques as described for our example. Do not be persuaded by advertising hype that expounds the virtues of some new “whiz–bang” design that will allow you to work all bands with 1:1 SWR. To coin a phrase “It ain’t gonna happen”.

Base Station Antennas

Base station verticals have three basic types:

  1. The single or multi–band monopole. This type uses one vertical radiator to transmit on all rated frequencies and depends on earth ground as a reflector or counterpoise (not an accurate term but a common one). This type of antenna may require ground wires to improve the effect of ground radiation at lower HF frequencies in some soil conditions. If good construction is used, as with the 5BTV (a multi–band trap loaded vertical) or Butternut HF6V (a base loaded multi–band vertical), it can be a very useful DX or non–directional HF base antenna.
  2. The vertical dipole or vertical offset–fed dipole. This type of vertical antenna is unique in that it has the feedpoint somewhere near the center of the vertical element. The top half being one conductor and the bottom half being the other. The advantage here is there is no need for a radial system. The antenna contains it’s own counterpoise radiator as part of the antenna construction. Feedpoint impedances are usually higher than ground–mounted verticals and are an easier match in some cases. This does not necessarily translate to better radiation.
  3. The vertical dipole with complex loading. In this style of antenna, the feed point is again elevated to somewhere near the center and external reactive elements are added to cause parts of the vertical to be resonant at different frequencies by providing proximity loading. You may notice this in the form of wires or cylindrical (trombone) capacitors at certain points on the antenna elements.

Verticals that exhibit an overall length of more than ¼ wavelength at the lowest operating frequency will perform better overall. Shortened antennas are a compromise at best and at worst are a total waste of your hard earned cash.

I would be remiss if I did not mention the importance of the ground in the efficiency of vertical antennas. I will provide a more thorough discussion in a future article.

Let’s now review the information supplied previously in our descriptions of the complex nature of antennae and apply that information to a common and very popular antenna design. The same type of antenna for VHF may look completely different than one designed for HF frequencies. To illustrate this, we will look at a popular VHF design – The “J–Pole”.

The “J–pole” antenna has become the most popular of VHF antennas in fixed and portable configurations. It’s popularity stems mainly from simple construction and easy tuning.

We will take a look at this unorthodox design and attempt to condense the theory behind the operation.

J–Pole made from copper pipe.

The pictorial is of one version of the “j” pole made from copper pipe. This is a common building material available from home improvement supply stores and hardware stores everywhere. The only skill needed to assemble this antenna is involved in soldering the fittings together to be rugged and long lasting. Low lead content solder should be used for durability and safety. Measurement of the dimensions are not super critical (although best results are obtained where tolerances do not exceed ¼ inch).

The largest part of the antenna is the ¾ wavelength main element. At the base of this element is a matching network consisting of a tuned quarter wave open stub. The antenna is fed by tapping a point that is part of the way up from the closed end of the stub. The exact point will depend on the actual measurements of the components and the installed environment. The adjustable feed point matching provides a convenient and simple match for an otherwise difficult to match ¾ wave vertical. Vertical monopole antennas of this length are inherently very low impedance (on the order of 1 to 2 ohms). To match our common 50 ohm coax, we needed to have a tuned matching network that would allow us to have a correct impedance at the feed point.

The “J–pole” provides this insertion point with the use of a matching network called a transmission line transformer. Transmission line transformers are created by using tuned elements at the desired frequencies and matching the needed impedance, but tapping into the tuned element at a point that matches the coax – this is roughly equivalent to a tap on a wire transformer at the desired number of turns to match the input impedance.


The illustration shown is a depiction of the same matching network on a dipole antenna. The dipole is a full wavelength dipole with each side being ½ wavelength. The match in the middle is a ¼ wavelength stub (shorted at one end).

Keeping this view in mind, mentally remove one of the dipole elements and stand the other up vertically. Voiala! We have a “J–pole”. In any vertically oriented monopole antenna that is base fed, the opposite element is the ground. In the case of our “J–pole”, one of the coax connections (the shield) is connected to ground.

It should be obvious by now that the “J–pole” is active over the entire structure – none of which is insulated from the rest. Some vertically mounted antenna have insulating base mounts. The “J–pole” does not. This means that wherever it is mounted, care must be taken to offer a proper ground to the mounting, as this will greatly effect the performance and tuning of the antenna system. he proper mounting point of the “J–pole” is on the bottom of the long side. This is the shield side of your coax. The center conductor will attach to the same place on the opposite side of the stub loading as in this photo.


73 for now.



Rev. 1.01 2018-01-10 AD5XJ