Archive for the ‘Theory’ Category

Understanding Mountain Radio Signal Paths

2011/12/11 1 comment

VHF/UHF radio propagation in mountainous terrain can be difficult and sometimes may seem impossible. As you know, higher frequencies travel primarily line-of-sight. Unlike HF, they do not reflect off the ionosphere, so their range can be rather limited (although knowledgeable DXer’s know special tricks, like meteor scatter.)

However, all is not lost. It is possible to make sense out of using higher frequencies in mountain communities, and at the November WARS (Willits Amateur Radio Society) seminar Tim Hanna, WB9NJS, described some of his experimentation and research on this topic.

Tim got interested in mountain VHF propagation after being surprised that he could communicate over 2M FM from his home QTH in Willits to Wayne, W6WMV, in Finely (south of Clear Lake.) The signal path is a good distance and there are two significant mountains in the way; regardless, Tim was still able to communicate quite well.

In his presentation Tim reviewed the ways radio signals change direction:

  • Reflection: wave changes direction by bouncing off other objects (a metal fence post for example).
  • Refraction: wave changes direction due to variations in the air (or other medium). Examples are cold and hot spots where the density of the air differs.
  • Diffraction: wave changes direction by passing over sharply defined edges — often called the “knife edge effect”.

Next, Tim introduced a handy mapping tool for analyzing signal paths. The software is from DeLorme and makes it fairly easy to go from a flat map of the path to an elevation profile view that helps you see the obstacles that are in the way.

Since Tim uses an 8 element 2M beam, he first determined the bearing of the best signal to Wayne. This could then be plotted on the DeLorme map:

Once that was done, an elevation profile could be generated:

Looking at this profile, you might begin to wonder how Tim’s signal was able to reach Wayne in Finely. There are a two peaks that should block the signal. Tim speculated that perhaps knife edge diffraction was helping his signal bend over one or more peaks.

Tim also noticed another possibility. It could be that signals were being reflected off Mount Konocti behind Wayne. If so, the signal map becomes:

To plot such an elevation profile, the profile is “unfolded” to show it by distance. It becomes:

To understand this profile, note that that tall peak on the right isn’t blocking the signal, it’s reflecting the signal. That’s how reflection is shown on a profile plot.

So, this signal path seems more likely. Although there may be a knife edge effect at the peak closer to Tim, the reflection of the signal from Mount Konocti behind Wayne makes sense. The middle peak becomes less of a factor because it’s no longer in the way.

Tim went on to show several other signal paths for unusual radio contacts he’s made from his QTH on the west side of Willits. Some are not such direct paths as the one to Wayne in Finely, but looking at the elevation profiles helps you understand how such paths are even possible. For example, he’s able to communicate with K6FTY who lives a considerable distance to the north. The trick again is to use a directional antenna to reflect the signal off various high-elevation peaks.

Thanks again to Tim Hanna for his educational WARS presentation. It’s good information for those of us who live in the mountainous terrain of Mendocino and Lake Counties. If you find you can’t make a VHF/UHF QSO directly, you now know that you can try reflecting or diffracting your signal off various peaks to increase the likelihood of your success.


Examples of Signal Strength Related to Power

The Answer to Antenna Puzzle #2 was based on the idea that signal strength is related to power by squares.

If you remember the power formula from ohm’s law, you know that:

power = voltage squared / resistance

and signal strength is most often measured in voltage per unit length (for example micro-volts per meter.)

To show this relationship, here are a few photos of signal strength measured on the 10M band at four different power levels. This was done by connecting an oscilloscope to a nearby monitor antenna, then snapping a photo of the screen.

Each image is twice the power of the previous image.

For 10 watts we see 0.39 volts (peak-to-peak):

10 watt signal

For 20 watts we see 0.542 volts. Notice that we don’t see twice the 0.39 volts, what we see is the square root of two times the square of 0.39.  So, thats:

0.39 squared = 0.152
0.152 x 2 = 0.304
square root of 0.304 = 0.551 (roughly)

20 watt signal

For 40 watts we see about 0.846 volts. (Notice that it’s not precisely what we expected. That’s because I don’t have precise control over the radio’s power output. It’s just approximate.)

40 watt signal

For 80 watts we see 1.192 volts:

80 watt signal

So, when you go from 10 watts to 80 watts you don’t see your signal strength increase by a factor of 8, you only see it increase by about 3!  (Kind of seems like a rip-off, doesn’t it?)

That’s worth keeping in mind if you ever need to measure the signal strength of your antenna or figure out strange antenna puzzles posted to miscellaneous ham radio sites on the web.

How Does a Yagi Antenna Work?

2011/04/25 4 comments

It seems like a simple enough question, right?

Three weeks ago at the McARCS meeting in Mendocino, a few of us built cheap Yagi-Uda antennas for 2M. I wrote about the experience in Snipping the Yagi. There’s nothing like building an antenna to make you curious as to how and why they actually work. Yagi-Uda antennas provide excellent gain and directiveness, and the more directors you add, the more they provide!

I remember once reading that the Yagi design was invented back in 1929, but that their theory of operation was not understood until 1975. That being said, good luck finding a decent description of how they work! I’ve searched online and also looked through a number of radio textbooks, but so far I’ve come up empty for an adequate description of the Yagi’s mechanism. There are plenty of descriptions covering its design and properties, but very little about the theory behind it.

While over on the coast, I chatted with Derek, KE6EBZ, who uses a nice 2M Yagi beam that he built from an old TV antenna. We agreed that the function of the reflector seemed like that of a mirror — not difficult to imagine. But, the directors were more of a puzzle. Derek suggested that the shorter lengths of the director elements helped focus the wave in the forward direction.

As Cindy and I drove home later that afternoon… I thought more about Derek’s suggestion. I’d seen that kind of focus pattern before — 30 years ago while building a laser diffraction lab at UC Davis. Essentially, if you paint a big dark circle on a window, light diffracts around it much like a lens. It’s called a zone plate, and… if you continue the pattern of dark and clear in concentric circles around it, it will become even more focused. It becomes a Fresnel lens.

So, is that how Yagi directors works? They form a sort of Fresnel lens? I don’t know. Seems like something to study a bit deeper.

Such a lens might account for the directivity of a Yagi, but where does its high gain come from? Its gain can go beyond 18 dBd. Producing that much gain from parasitic (non-driven) elements seems difficult to comprehend, especially if you think of the directors as focusing only the radiative EM field (the far field) and only in a single dimension.

Recently it dawned on me that many of a Yagi’s directors fall within the near field of the driven element. That means they have mutually inductive and capacitive coupling to the driven element, more than just an effect due to re-radiation of the far field. So, in terms of magnetic induction, the first director works a lot like a transformer. That means that the director can actually pull more energy from the driven element — energy that cannot be tapped from the radiative field alone. Something similar could also be said about its capacitive coupling of the E field to pull energy. So, the directors can pull more power from the feed point… which really helps explain where the high gain comes from. Very cool.

Of course, this also means that the phasing of the whole mechanism must be very precise. The induced and coupled energies must perfectly match the phase of the radiated wave as it passes by. Wow, isn’t that elegant. You could almost think of a Yagi as a medium of propagation… with the wave travelling through it. (Of course, that means the wave velocity is changed while it does so… interesting to consider… hmmm, could be something to this.)

Well, I suppose everyone already knows this, and I’m just the last guy on the block to figure it out. The elmers reading this article are yawning and commenting, “yes of course that’s how it works, dummy.” But, it does get me thinking… what happens in the subsequent directors as the near and far fields pass by… and how far backwards can the induction and coupling have an effect?

Obviously, the mechanism of a Yagi is fairly complex. It sure would be nice to learn more about it. You’ve really got to wonder why such a elegant antenna has so little published about how it actually works.

If you’ve come across in-depth descriptions of Yagi theory, please post a comment here for all to read! Many thanks.

Answer #2: Power vs. Signal Strength

2011/04/24 2 comments

Antenna Puzzle #2 asked why 3 db of gain is obvious for two identical dipoles for reception (3 db): Simple dipole array (receive) But… it’s not so obvious for transmission!

This is a wonderful question because it shows how power and field strength differ, even though they are directly related.

An insight into the answer comes if you ask the question: if you double the power to your dipole, how much does the field strength increase? The answer is that power is related to E-field strength squared.  If your power is 100 watts, and you double it to 200 watts, your field strength does not double. That’s because the square root of 100 is 10, and the square root of 200 is 14.14. So, doubling your power only increased your field strength by about 40%.

With that in mind, you can now analyze the dipoles above for transmission. Here’s a diagram that shows the proportional values (not actual values):

How power and field strength relate.

So, here’s what’s happening:

  1. 100W is divided in half, so 50W for each dipole.
  2. 50W radiates as a field that is proportional to the square root of 50, thus 7.07.
  3. At the receive antenna, the two fields combine, 7.07 + 7.07 = 14.14.
  4. The power received is the square of the field strength: 14.14 squared = 200.

So, you must add the field strength of each dipole, not power.  (And of course, the above is written to show the proportions, not actual values. The actual received power is substantially less due to distance and antenna pattern.)

You can now see that the power gain of the system is double (3 db, just like before), even though the power was been split between the two dipoles!  Another way to write this is:

pwr-recv = (sqrt(pwr-xmit / 2) * 2) ^ 2

If you enter that into your favorite calculator, slide-rule, or programming language, you’ll see that the pwr-recv result is always double the pwr-xmit input.

So, the principle of antenna reciprocity is safe and sound. The gain is the same for both receive and transmit.

For greater detail see: Signal Strength Relationship to Radiated Power.

Categories: Antennas, Theory Tags: ,

Antenna Puzzle #2

2011/04/09 2 comments

Here’s a simple but interesting antenna puzzle to think about…

Let’s say you use a wire dipole for the 20M band. You decide you want to boost your gain by adding a second dipole (end-to-end, i.e. colinear) and combine their feeds (in phase, of course.)

The two antennas receive the incoming signal (depicted in green below) which gets combined to double its strength at the receiver. Here’s the diagram:

Simple dipole array (receive)

So, this simple array provides 3 dBd of gain. It makes sense because each antenna is receiving an independent field of energy from the distant station.

Now, you use the same setup to transmit 20 watts on CW. Of course, your power gets divided in half between the two dipoles. Each antenna gets 10 watts.

Simple dipole array (transmit)

But, wait… if you simply put that 20 watts into a single dipole wouldn’t that be the same thing as two antennas at 10 watts?

The principle of antenna reciprocity dictates that an antenna must behave the same for both receive and transmit. It has the same gain, directivity, and pattern. So where’s your 3 dB of gain on transmit?

Perhaps you’ll answer that the two antenna fields significantly overlap. But, even if they add together perfectly, won’t the distant station still see the same signal as one antenna at 20 watts? Where’s the 3 dB? (The output should be equivalent to 40 watts.)

So, there you go, a puzzle. What’s your solution? Post it here as a comment.

Answer now posted here: Power vs Signal Strength 

Simplicity Defined

I’ve written before about “keeping it simple”. You know, the KISS principle.

It’s an old idea, but these days it’s even more ignored than ever. Whether it be modern computing, modern government, modern medicine, or modern law… all have become overly complex.

Of course, “simple” does not seem so easy to define, and in fact, simple designs are often much more difficult to achieve or produce.

This morning at about 2AM it occurred to me how to define “simple”.

It’s important to first understand that simplicity is relative to the layer you’re looking at. For example, if I talk about a diode, or even just a tree for that matter, the concept formed in your mind is quite simple. Yet, if you drop down a layer or two, you find vast complexity.

What I’ve concluded is that the concept of “simple” requires both layered abstraction and clean expression.

I’ve written about it on my other blog. See Definition of Simple for the story.

I think having a solid grasp of the definition of simple is critical these days.  So many of our systems, including government, management, medicine, law, banking… are collapsing under the weight of their own complexities.

Sure, there are people/experts who do understand many of the complexities, but that’s not enough… because there are many others who must deal with those complexities, but who do not understand, and will make the wrong choices and decisions as a result. That’s how governments, companies, markets, engineering marvels, and entire societies collapse. Best to be avoided.

Best to keep things as simple as possible. But, of course, you need to know the definition of simple in order to do that.

Categories: Theory Tags:

Antenna Basics – Charge

Ok, I finally got some time to begin my short series of articles about antenna theory.

So you know… I like the KISS principle. Keep things simple. I’m not going to make this complicated. As an electrical engineer I can tell you that there are hundreds of books on this subject that dive in to a range of details and complexities… often to such an extreme that few readers understand.

I prefer first principles. These are the fundamental ideas upon which a theory is based. For antennas, these principles were studied beginning in the 1880’s by scientists like Heinrich Hertz, and those ideas are still quite relevant today.

An Experiment

A simple experiment provides a great starting point for discussion. You can actually build this and try it out (but that’s not really necessary to understand the theory behind it. )

Parts list:

  1. A ten inch sphere made of thin copper or other conductive metal.
  2. Ten feet of copper wire and a few insulators to hang it.
  3. An AM radio.
  4. A high voltage DC source, such as a Van de Graaff generator.

Hang the wire and the sphere near each other, using insulators. Here’s a crude diagram (and not drawn to scale):

Uncharged sphere and wire

Using the voltage source, charge the sphere to negative 10,000 volts (or any high voltage, it does not matter.)

Turn on your AM radio, it can be positioned anywhere in the room, and tune it to a clear frequency.

Now, using an insulated rod, touch the wire to the sphere.

You’ll hear a snap or click sound on the radio. Interesting!

Congratulations. You’ve just built the most basic radio transmitter and antenna possible. Experiments of this sort were first performed by Heinrich Hertz (yes, as in megaHertz) in 1887 to prove the existence of electromagnetic waves.

The Explanation

Physics and radio books just love to dive into the details of voltages, currents, fluxes, and fields. However, it’s good to recognize that those are all derivatives of a fundamental concept: charge. If you think in terms of charge, it’s easier to understand how those other terms relate.

  • Think of a charge as an electrically unbalanced atom. It has either too many or too few electrons to balance out the protons of its nucleus. When it has too many, it’s negatively charged. When too few, it’s positively charged.
  • Different materials can become charged using various methods. What that means is that their atoms have either too few or too many electrons.
  • Charge can be distributed evenly or unevenly within a material. Part of a material may be negative while another part is positive.
  • Charge can flow from one point to another. In some materials, such as metals, charges flow quite freely (they conduct.) In fact, they act a lot like a fluid or gas, flowing and sloshing around with very little friction. This fact is really important.
  • Charges repel and attract with tremendous force. How much force? Physicist Richard Feynman provides the best example: if you stand one arm’s length from another person, and both of you are charged with one percent more electrons than protons, the force of repulsion between you would be enough to lift the entire weight of the earth. That’s correct. Just one percent of your electrons. It gives you a sense of the magnitude of the force we’re dealing with here, doesn’t it?
  • This extreme force causes charges to move. For example, if we add a few extra electrons to a thin metal sphere, the repulsive force causes all of the electrons to flow and distribute themselves across the sphere. This is true for all metal objects, not just spheres.

In the experiment above, here’s what happened in terms of charge:

  1. You charged the sphere by adding extra electrons to it.
  2. The sphere is made of metal, and its electrons move freely.
  3. Because of their extreme repulsive forces, the electrons spread out evenly over the surface of the sphere. I’ll call it electron pressure. That’s a good way to think of it: a force or tension between all of the extra electrons.
  4. The wire has no charge and when touched to the sphere the electron pressure begins to push electrons down the wire.
  5. Electrons flow down the wire until the electron pressure within the wire becomes equal to that of the sphere.
  6. As the electrons are accelerated (begin to move in a specific direction, down the wire) they produce electromagnetic radiation: radio waves.
  7. These waves radiate outward, and the AM radio detects these waves, making the click sound.

Here’s the diagram again, showing the charge beginning to flow down the wire:

charge flowing down wire

The charge moves down the wire very quickly. The extra electrons also push the electrons that are already within the wire, just like a hose that’s full of water when pressured from a facet.  Yes, it’s a lot like a wave of water pressure moving through a hose.

After a short period of time the charge has moved halfway down the wire.

charging wire

Then, after another short period of time the electrons reach the end of the wire:

charged wire

The electrons no longer have anywhere to go and they distribute themselves evenly across the wire, and radio waves are no longer being produced.

Essentially, this experiment produced a single burst of radio waves which are heard on the AM receiver.

(Ok, those of you who are experts will recognize that I’ve simplified this explanation quite a lot… but I think the first order effects far outweigh the other details for the purposes of this description. I’ll cover some of that in articles to follow.)


This experiment provides a launching point to get you thinking about the process. I think it’s quite interesting how very simple this experiment is, showing how fundamental this process is in nature. It’s all around us and is happening all the time.

Notice that I’ve not said much about voltage, current, fluxes, fields, frequencies, or phases.  But then, the process shown here isn’t really that useful, it just sends a single click.

In the next article, I’ll cover what happens if we charge and discharge this wire at regular intervals… that is, at a specific frequency.  In addition, there’s a deeper paradox lurking here: no matter where you tune your AM radio, you’ll hear the click sound. The wave emitted by this process is extremely broad in frequency. You might say it has no frequency, or more accurately, it has all the frequencies.

Also, for the sake of this introduction I’ve glossed over various important points that need to be discussed. For example, what causes the radio wave to be emitted from the wire?  That part will get even more interesting.
Categories: Antennas, Theory Tags: