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Practical Antenna Theory

(Part 1)
by AD5XJ, Ken Standard
ARRL Technical Specialist

To begin this introduction it should be said that there is no attempt here to educate the reader on basic electronics or the mechanical aspects of antenna building and feedline construction. Learning how to put on a coax connector or stand–off ladder line, are subjects best left to personal discussions in a one–to–one level meeting with a local Elmer. It is assumed, for this text, that the reader has at least a basic understanding of electronics and electronic theory of AC circuits, requisite for any serious study of antennas, (see chapter 4 of the 21st edition of The Amateur Handbook© for basic knowledge) and has viewed with more than passing interest, basic antenna system practice. The reader is provided some basic knowledge of how radio frequencies behave on a radio frequency radiator and feed line, and discussion progresses to the more complex subject of impedance and directional antennas. This is not a reference text. It is a broad sketch of the very detailed and complex subject of antennas and feedlines and the theory that is underlying their design. The reader is allowed to explore at leisure, the details in trusted, locally available sources and the reference material listed at the end. There is a lot of material here and the text is expansive. You are encouraged to go slowly through it all and not skip to the end or skip subjects that become tedious.

The text is presented in a logically progressive manner. That is to say it is logical to the author and hopefully to the reader. Knowledge gained in earlier chapters is used to build on more complex theory in successive chapters. Each chapter is a very brief thumbnail treatment of some tediously complex subject matter. Diagrams and graphs are used to visually illustrate the theory discussed in the text. This is not to make light of the complex nature of antennas or feedlines. It is an attempt to provide essential information for the non–technically proficient ham who has a serious interest in antenna and feedline theory and operation. Of course there are other text on the subjects covered, too numerous to list in entirety. The sources provided are reliable and credible text that are dedicated and oriented to the serious study of antennas and feedline theory in mind for the radio amateur.

This text should provide the basics for making common choices and decisions in the average (if there is such a thing) ham shack or antenna farm. An effective methodology to study this kind of material would be to use the presented subject as a “springboard” to learning. That is to say, the material presented is designed to stimulate the reader to do the proper research for a full and detailed understanding of the presented subject. There is no attempt to be absolutely and strictly parallel to current and acceptable textbook theory on antennas and feedline. This is not meant to say the information is not accurate. The simplification of any complex subject allows for the elimination of important or meaningful details. It is left to the reader and student to research these details from the material references at the end of the book, from trusted online sources or from reliable and vetted local sources. The references at the end are a very good starting point for in-depth study. The Internet is also a good source of information. However, caution should be exercised when using online information as a reference due to much misinformation and mis–use of fact also being available. Not every Internet source has a thorough understanding of the subjects nor has it necessarily suffered the vetting process of the more reliable texts referenced.

“The theory of transmission lines and antennae similar in nature to transmission line is often treated in simple form as a series of spatially diverse lumped constants that are then mathematically treated with Kirchoff’s law. However, theoretical assumptions applied to static circuits are not easily transferred to transmission lines or antennas.

Static circuit theory is based on the assumption:

  1. That there are spatially diverse components with electric or magnetic fields. Electric fields are generated generally by capacitance and magnetic fields are generated by inductance.
  2. That currents are equal in magnitudes and phase within each respective component.

These assumptions are not rigid in the respect that one must assume that the time needed to process the currents is shorter than the time of one period (cycle). These assumptions do not directly translate to a dynamic application of a complex structure such as an antenna over real ground. Every element in an antenna or feedline is a carrier of electrical and magnetic properties and thus an influential part of the antenna or feedline in its overall characteristics. In order to simplify and illustrate the complex and highly interactive nature of antennae and feedline components, discussion is reduced to equivalence in the form of common lumped values and static circuits (as can be evidenced by the illustrations in chapter one) where the limitations above are acknowledged. But if we cannot apply such rules to the line as a whole, we can apply these rules to small elements within the whole that can be considered a sum of these processes (an antenna trap for instance). One such application is the method of moments calculations used by popular antenna modeling software programs (EZNEC, NEC4Win, MMANA and MMANA–GAL, etc.). In this method an element of an antenna is treated as a wire that has been arbitrarily segmented. Each segment is used to calculate important features such as current, impedances, phase, and phase angle of current in the middle of each segment. The overall characteristics of the model are an amalgam of each segment calculated individually (the moment) accounting for transitions of diameter of elements (e.g. tapering of tubing), lump constants and proximity to ground. Such programs do a very good job of approximating antenna characteristics without relying on empirical modeling in the real world. They are however not so good at approximating irregular components and matching mechanisms that are not of the straightforward type. The common coaxial linear choke (aka. The bazooka choke), and coaxial stub tuning, are but two examples of simple physical elements that are difficult to model accurately.”
—paraphrased from Reflections see referenced text at end.

You should do your own 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.


SWR And What It Is Not

One of the most often discussed topics in Ham Radio, and definitely the most misunderstood, is SWR. If we were to take what is heard on the air as gospel, we would always be in pursuit of the elusive 1.00:1 SWR. Reasoning behind this pursuit is as varied as ham radio itself. But one thing is obvious when compared with the appropriate literature available from many sources, including the ARRL. Having a low SWR is no more an indication of antenna system performance than a high SWR is a guarantee of power being wasted. If you have only one source of technical information on antennas, make it the ARRL Antenna Book! We will refer to it quite a few times over the next few articles and the text on the presented subject in the ARRL Antenna Book is thorough and illuminating.

In this series of articles we will learn some basics, some theory, and dispel a few myths that are generally perpetuated in the Ham Radio community. We want to take a practical, informed approach to antenna system problem solving, rather than “best guess” a solution, or folow the proliferation of common ham radio myths. You will become armed with the knowledge needed to solve those previously “difficult” antenna system problems on your own.

The first thing to learn about the RF that flows in our coax is that it has unique characteristics. Yes it is an alternating current much like the 120 VAC coming from the outlet you plug your power supply into, albeit at a much higher frequency. However, the primary difference is the reason for RF presenting characteristics that are quite unlike 60 Hz AC – frequency. These characteristics are present regardless of the type of cable or service line used as transmission line. You may use open wire twin lead as transmission line rather than coaxial cable. The use of the term “coax” in this study will be a general use term often interchanged for “transmission line” regardless of type or construction. Literally speaking, “coax” is an abbreviation for “coaxial” – referring to the construction of the physical cable as being, two concentric conductors on the same longitudinal axis.

We can describe, in general terms, RF characteristics by behavior. Pay close attention to these terms as they will be used throughout.

Skin Effect

This is a term that describes the complex theory that RF does not travel inside of a conductor as does DC from a battery or 60 cycle AC from the wall outlet. Instead, RF is believed to follow the outside surface of a conductor (hence the term skin effect). As we will see later, this is significant in terms of how fast RF is allowed to flow down the transmission line.

right hand rule
Fig C–The “right–hand rule” relates the direction of current flow to the magnetic field it produces. Picture courtesy ARRL Handbook.

Why is there skin effect?

When a time–varying current flows in a conductor, a time–varying magnetic field will be created around the conductor. A simple example is in Fig. C shown. A current flowing in the wire creates a magnetic field around the wire as indicated. The direction of the magnetic field in relation to the current obeys the “right–hand rule”...that is, if the thumb of your right hand extends in the direction of positive current flow as shown [i.e. negative to positive voltage], the magnetic field will curl around the wire in the same direction as your fingers.

Just as a current creates a magnetic field, a time–varying field, from some external or internal source [e.g. RF current], will induce a time–varying current in a conductor. This is called an “eddy” current and higher frequencies yield greater amplitude eddy currents in a given conductor. The direction of the eddy current is such that its magnetic field opposes the inducing field.

eddy currents
Fig D – Eddy currents in wire produce the skin effect. The through current (A) produces a magnetic field (B) that induces eddy currents (C). The eddy currents offset through current near the wire center and add to through current near the wire surface

We can see how these currents and fields create skin effect by examining [the next figue]. This is a section of a round wire carrying a current from one end to the other. This current is labeled “A”. It is simply the net current flowing through the wire. This current creates a magnetic field both inside and outside the wire as indicated by the dashed lines “B”. This field, in turn, creates an eddy current “C” as shown.

Notice that near the center of the wire, the eddy current opposes the desired current, but on the outer part of the wire, the eddy current aids the desired current. If we look at a cross–section of the wire, we see that the current density near the center is reduced, but near the outside, the current density is increased. As frequency increases, less current flows on the inside of the wire and more flows near the outside surface. Of course, the net current stays the same, but it is crowded into a smaller and smaller portion of the wire’s cross-sectional area.

The result is that the apparent resistance of the wire increases because we are using only a small portion the available copper area to carry current. This means that the loss for a given current will be higher. In copper at HF, the current is crowded into a layer of 2 mils, or less, in thickness. The rest of wire only provides mechanical support for the thin outer layer that conducts!

There is another way to look at skin effect. If you have a large sheet of conductor and you irradiate it with a electromagnetic wave perpendicular to the surface, the wave will penetrate the surface for some small distance. The amplitude of the wave decreases exponentially and the depth at which the amplitude has decreased to 1/e ≈ 37% (e ≈ 2.718, the base of natural logarithms) is referred to as the penetration or skin depth (δ). Increasing frequency decreases δ.
— Rudy Severns,N6LF in a paper titled Conductors for HF antennas.

Traveling Incident Wave

This term is used to describe RF waves traveling up the coax to the antenna or load. Notice the term describes only the initial power traveling in the same direction, toward the antenna. This will be significant as we define other terms. Traveling wave simply indicates that an alternating cycle of power or voltage is moving with time along the transmission line. For mathematical simplicity, traveling waves are usually discussed for a specific frequency, as is SWR.

Traveling Reflected (Return) Wave

This term is used to describe the un–absorbed RF waves that flow on the coax away from the antenna (or load) to the source.

Velocity Factor

This term encapsuates or describes the delay RF energy encounters as a traveling wave. It is caused by the material used as dielectric in the transmission line. Some materials slow the traveling wave significantly, while some dielectric materials do not. All dielectrics are measured against the standard of air (sea level and 50% humidity) as a value of 1.00 or 100%. Generally speaking, the larger the velocity factor (i.e. numbers approaching 100% or 1.00) the closer the resemblance to open–wire feedline – which has a velocity factor range of .98 to 1.00 (virtually no delay of propagation). Do not confuse open–wire twin lead transmission line with the sibling version, twin–lead “window” or “ladder” line. Ladder line has a much higher velocity factor (i.e. lower numbers) than open–wire line.

When RF must flow on the coax and encounters a dielectric material such as polyurethane (PE) the rate of travel (propagation velocity) along the conductor is slower. How much slower is indicated by the velocity factor expressed in comparison with the velocity of an air dielectric (e.g. .66 or .87 as in round coax). More on this subject later.

Standing Wave and Standing Wave Ratios (SWR, VSWR, etc)


Standing waves are believed to be the result of the encounter between forward traveling waves and return traveling waves. This being said, it is also true that there is no standing wave if there is no forward power. The assumption is always made that the frequency of the incident and return waves remains the same as does the length of the antenna and transmission line. This encounter is best illustrated by the figure seen here.

Notice that where the traveling wave peaks approach the same polarity, so does the magnitude of the standing wave (even though the waves are traveling in opposite directions). The polarity of the standing wave magnitude is determined by the magnitude of the additive waves (i.e. two positive magnitudes produce a positive standing wave magnitude and two negative magnitudes produce negative standing wave magnitudes).

When the comparisons are of the voltage magnitudes, we speak of VSWR or voltage standing wave ratio. There are other comparisons that are similar, but are rarely used in ham radio. These will not be discussed here.

So now that we have defined some of the more common terms we use when talking about transmission line and antennas, let’s look at what causes SWR.

Causes of SWR

The most common cause of SWR on the coax is a mismatch of characteristic impedance. This choice of words is important in understanding SWR. A transmission line is not a simple resistive value as we would think of it in passive components in the rig we use. Nor is it a simple inductive or capacitive reactance. Not only that, but it should not be characterized as a “length of shielded wire”. Transmission lines are actually complex networks containing the equivalent of all the three basic electrical components: resistance, capacitance, and inductance. Because of this fact, transmission lines must be analyzed by reducing the complex terms into terms of an RLC network.

The two conductors that make up a transmission line (the two parallel wires of open–feed line or the shield and center conductor of a coaxial line) are arranged in such a way that the electrical field of one conductor is offset or nullified by the opposite electric field of the other conductor. The two conductors in such close proximity exhibit a complex set of characteristics that we call impedance. The illustration shown here is from the ARRL Antenna Book chapter on transmission lines.

Courtesy ARRL Antenna Book© 20th Edition

Characterisc Impedance

This complex characteristic impedance discussed is expressed in writing it like this:

R +jX

It is expressed this way to show the complex nature of transmission lines (or antennas). The “R” term represents the resistive or often called the real part of the characteristic while the “+” or “- jX” indicates the reactive or imaginary part of the characteristic. It is possible to have a zero value for the reactive term, in which case the only important value is “R”. This is mostly theoretical but is rarely a practical value.

Both antennas and transmission lines exhibit this complex character. In fact, some phyical structures mimic transmission lines in just this way. The theory underlying antennas and transmission line characteristics is explained very well in The ARRL Handbook© and in The ARRL Antenna Book©. It is well worth the reading to fully understand this complex subject. This discussion is merely food for thought.

A mismatch may occur in either part (or both) of the characteristic impedances of the source or load (i.e. feedline or antenna). This mismatch gives rise to inefficiencies in the transfer of power from the delivery vehicle (your feedline) to the consumer destination (your antenna). When the load is not able to consume all the power delivered, the undelivered portion is returned to the source. This returned and undelivered power is the reflected traveling wave defined earlier.

Impedance mismatches occur for various reasons. The most common are: transmission line impedance and antenna feedpoint impedance mismatch, open feedline circuit or shorted feedline circuit.

You may encounter any or all of these conditions as your ham radio experience grows longer.

Causes of SWR

Should we be concerned when a VSWR can be measured on our coax? That depends. That is not a smart Alec answer, it is just the facts. Remember we discovered that your feedline and antenna are complex in character. So too, are the conditions under which we may become concerned about VSWR. To simplify the answer somewhat, let’s look at a common situation.


Hypothetical Example

You are installing a 2 meter mobile rig in your car. The antenna is installed and you ran RG58/U cable to the rig and you follow the manufacturer’s instructions to the letter. The VSWR you measure is 1:1.00. Perfect right? Why then does it not “hear” or “talk” very well?

We are assuming the manufacturer’s instructions include proper grounding instructions, which you follow. Is this 1.00:1 VSWR a problem? It is not supposed to be...right?

Myth #1

Here is where we can dispel myth #1 – That you will burn out the final transistors in your rig due to a 1.5:1 or even a 2:1 VSWR. Most modern VHF rigs will handle a very wide SWR range without damage. This relatively minor VSWR will NOT harm most modern rigs on the market today. Higher VSWR situations may make RF power transmission very inefficient for the transmitter. The inefficiencies cause the final transistors to work harder to produce power – and yes (if the SWR is high enough, as in a short, and the rig is in transmit mode long enough, there could be thermal break down in the finals. But notice, this is due to the loss of efficiency, NOT reflected RF.

How about performance? Why does this 1.00:1 VSWR not affect performance?

Good performance is a result of removing as many inefficiencies as possible from the antenna system. Remember we discussed how impedance mismatches give rise to inefficiencies in the transfer of power to the antenna. That power must go somewhere.

It does not get transferred to the rig finals: goodbye Myth #1.

That thing called I2R loss

Power that is unused by the antenna will continue to travel on the transmission line back and forth from source to antenna until it is absorbed (or dissipated) by the actual (read it “real”) resistance of the transmission line wire in what is known as I2R losses. This amounts to an attenuation that can dissipate as much as 2–3 watts out of 50 watts leaving your transmitter (given the RG58 coax in our scenario) from only a 3:1 VSWR or lower.

Courtesy ARRL Antenna Book© 20th Edition

More importantly, a 2.0:1 VSWR will attenuate incoming signals as well. The graph shown illustrates the amount of loss due to attenuation (the I2R losses) by one type of coaxial feedline. It also makes clear that investment in high quality feed line could pay you back with very good weak signal performance.

On point of our discussion, the graph illustrates plainly that high SWR readings (i.e. above 3.0:1) at lower HF frequencies, are not as detrimental as some would have us to believe. The higher the frequency the more effect the transmission line may have on attenuation.

Feedline Loss

Since we are considering only the antenna system (leaving the rig or tuner out of it for now) we must consider the loss of efficiency to be due to the difference in characteristic impedance of the transmission line and the impedance of the antenna at the feed point. This difference could be due to an improper selection of coax type (RG59 instead of RG58 or vice verse). A mismatch could also be due to an improperly tuned antenna. Tuning an antenna usually involves changing the characteristic impedance at the feedpoint by changing the length or adjusting a matching network that is part of the antenna. We will look at proper selection of feedline type and antenna feed point matching later.

Now let’s change the scenario to 440 Mhz. The major factor in this scenario, (even if the antenna is perfectly matched) is the attenuation by the RG58/U coax. It is a whopping 10 db per 100 feet! That is an increase of more than 20 over the 2 meter scenario. Compare that to only 1.5 db at 3.5 Mhz.

This is a scenario where 2.0:1 is significantly high due to the amount of power that would be dissipated in the coax due to SWR induced I2R losses. Accordingly, signals being received could be attenuated to the point of unreadable, simply being lost in the coax.

So is it worth hours of cutting and measuring for that .5 SWR decrease in terms of signal received? Only you can make that decision based on what you may have learned here and your particular situation. But, given the information learned so far, you should think long and hard before spending tons of time for nominal improvements in lower SWR readings.

More to come:
Does a matchbox remove SWR?
Does my matchbox tune my antenna, or my radio, or both? What is radiating coax?
Proper selection of feed line type.
Antenna matching techniques.



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