There is rarely anything more misunderstood or misrepresented in the world of ham radio than the venerable antenna tuner. The myths and rumors that swirl around these remarkable but simple devices abound. Here we wish to examine what it is exactly that they do and how they do it. We are going to take a look deep into the mysteries of the antenna tuner and try to settle them once and for all.

As always … there will be times where I could do more math, go deeper into derivations and so forth. This article is meant to be accessible to all levels of people so please keep that in mind while reading.

Oh … and one more thing. I’m going to assume you have at-least a passing knowledge of Ohm’s law and power. If you don’t … then time to look stuff up!

Oh … and one more one more thing. Semantics is a big problem when we talk about systems that can get a bit complex. There is a huge difference between talking about an antenna and the antenna system for instance. I will try to be as clear as possible and point these things out where appropriate.

Lets start at the beginning shall we?

The Transceiver

This is my transceiver. There are many like it, but this is mine. It’s what puts the fire in the wire and drives my voice around the world. Like many, it is capable of putting out 100 watts. Key word there is capable … because it will deliver 100 watts when the load (antenna/antenna system) looks like 50Ω. The entire transceiver was designed around the idea of driving a 50Ω load, in fact if it drives a different load, then it cannot deliver 100w.

So how do we begin analyzing this? Lets take a look at the most simple of cases, the DC equivalent of what happens. This is what is known as the Thevenin equivalent. The Vsource and Rsource represents the voltage that the transceiver puts out when transmitting and the internal resistance that can be seen from the outside of the transceiver looking in. This is a way to represent what could be a very complex system, in a very simple fashion, that is also correct from a circuit analysis point of view. The Rload represents any load we have on the antenna port of the transceiver, could be a dummy load, could be a light bulb, could be anything, but we shall assume right now it’s the antenna.

And I do mean … just the antenna. No coax, no connectors, no balun, nothing else. This is an important point. Yes this is a bit impractical but we are just trying to analyze the simplest case here. If we add anything else to our system it will make things more complex and in the end muddle what we are trying to learn here. I will discuss these things towards the end of this article. For now just imagine the transceiver itself is sitting up in the air directly wired to the antenna.

In the perfect case, our transceiver is capable of delivering 100 watts of power to our load (antenna). This happens when the load (antenna) itself is 50Ω. So just for fun (if you can call it that) lets do a bit of math and figure out what the voltage around the load is and the voltage generated by the source.

We know from power and Ohms law that \(P=VI\) and \(I=V/R\) so we can express our power equation in terms of voltage as \(P=V^2/R\)

So if \(P=100W\) and \(R=50\Omega\)

Then we can solve for the Voltage across the load and determine that \(V_{load} = \sqrt{PR} ~= 70.711V\).

Since Rsource and Rload are the same (50Ω) we can say the \(V_{source} = 2*V_{load} = 141.42V\).

So for the rest of this article, we are going to set \(V_{source} = 141.42V\) and \(R_{source} = 50\Omega\) since this will allow our load to absorb 100 Watts if it’s 50Ω.

YAY … we have our model of a 100 watt transceiver ready. This model will allow us to analyze things in both DC (for our simple examples) and AC (for when we start dealing with RF signals).

Maximum Power Transfer – P. 1

This entire article is really about maximum power transfer. Hopefully by the end of it you will understand why. Although I would be willing to bet you already know most of it. After all, why do we put anything between our transceivers and antennas? To get THE MOST POWER!. So lets keep looking at our simple little model. We have already figured out that our source voltage should be around 141V, our source resistance is 50Ω, and if our load (antenna) resistance is also 50Ω then it absorbs 100 Watts of power.

There is a very simple theorem in electrical engineering about maximum power transfer. It simply goes, for the source to deliver the maximum power possible to the load, the load resistance should be equal to the source resistance. In other words, the transceiver will deliver the most power when the load (antenna) is matched to the source at 50Ω. If you stop and think about it with ohms law, it makes sense. If we start making Rload smaller, the current in the system will increase but the voltage across the load will decrease. In fact the voltage across it will decrease faster than the current will increase. Thus leading to less power being absorbed by the load. Conversely, if we increase the load resistance, the voltage across it will increase and the current through it will decrease. In this case the current will decrease faster than the voltage will increase. Again leading to less power being absorbed by the load. We can show this mathematically with Ohm’s law and the power equation.

\(I_{load} = V_{source}/[50+R_{load}]\) and \( P=I^2R_{load}\)

thus if we use the values we calculated before, we can plot what the power absorbed by the load is as a function of it’s resistance. It looks like:

Now it’s very easy to see that at 50Ω we get the most power in our load. Any other resistance will lead to decreased power.

AC Analysis – Done Dirt Cheap

Now we move into the meat and potatos (or potatoes if Dan Quayle is reading this) of our analysis. Some of you may be curious why I did all that analysis in DC when AC is what we are really after. Well the truth is almost everything about DC analysis will carry over to AC, but it is here we start adding more complexity.

What complexity you ask? Reactance … that is considering we often have capacitance and inductance to deal with once we move into the AC domain. In fact it makes analyzing power even more complex. Adding capacitance or inductance to a circuit does some odd things. The most important of all is the fact that it shifts the current out of phase with the voltage. In other words is possible at a point in time to have voltage across something without any current, or current through something without any voltage! This leads to something very interesting … Wattless power. Ideal capacitors and inductors do not absorb power … they store it … then release it later. This is what causes the current and voltages to be out of phase with each other. Because they can be out of phase, we have to adjust our definition of power a wee bit.

Definition time!

Active power: Real power being absorbed in a system due to resistances

Reactive power: Power being temporarily stored in an inductor or capacitor then released back into the system

Complex power: The total of Active and Reactive power

Apparent power: The magnitude of the Complex power

It is the interplay between Active and Reactive power that determines how much real power can ever be delivered to a component in a circuit. Introducing a capacitor or inductor into a circuit can limit the current flow in that circuit even though it will never absorb any power itself. Which is bad, we don’t want anything interfering with out ability to get power out to our antenna! As an example, lets re-run the power vs load resistance example done earlier but this time adding a certain amount of reactance. In this case, 43jΩ of reactance was added into our circuit.

Because this reactance limited the current flow, some of the possible power was stored in an inductance rather than being delivered to our load. The more reactance in a circuit, the less power will be available to our load. In this case only about 85 watts of power maximum was available. Now imagine a circuit with even bigger reactances … ouch. In fact if we fixed our load resistance to 50Ω and varied the reactance we can easily see the effects on the power available to a 50Ω load.

You can easily see how any capacitance or inductance that is bigger than even a small fraction of 50Ω really limits the amount of power available to the 50Ω load.

So what has been learned so far? We want the resistance of our load to match the resistance of our source (50Ω) and we don’t want any reactance in our circuit to limit current flow.

At which point our intrepid hero learns the antenna is actually a three headed monster to deal with.

Oh my. Sounds a bit scary doesn’t it?

Well it can be, but in this case it is important to understand what is actually happening in the antenna itself. Especially since we are taking a look at it in a circuit theory viewpoint. Frankly if we all just used separate, single-band antennas each cut for the frequencies we are using, we wouldn’t need any of this. A properly cut antenna has a real impedance of close to 50Ω and negligible reactance. It is what we call … matched. However, if we start trying to use it away from the frequency it was designed for, two things start happening. First, reactance starts to grow .. which as we learned limits available Active power. Second, and this gets a little interesting, the resistance the antenna provides becomes a combination of radiation resistance and loss resistance.

At the resonant frequency the antenna is cut for, the antenna itself looks very simple as a circuit. It’s more or less about a 50Ω resistor in which the power absorbed is radiated into the air. Generally speaking the model for an antenna looks like:

In this model there are three things for us to consider. The first being the C and L or any capacitance or inductance the antenna may have. If you’ve ever used an antenna analyzer that reports the impedance of the antenna, this is given by either a + or – j value. It’s the reactance the antenna has. The Rloss represents any Ohmic losses in the antenna. That is … any power absorbed that is converted to heat instead of radiation. Rradiation is the important one. It represents the resistance that power will be converted into radiation! And that is what we want most of all, to get that power out as radiation instead of heat.

So lets just assume we have a dipole, perhaps cut for the 40m band or about 20m in total length. At around 7.1 MHz the model becomes simple. At the resonant frequency, the C and L become zero (Which is what resonance actually means, the reactance or imaginary part of the Impedance is zero), the Rloss is almost zero, and the Rradiation will be close to about 70Ω (because that is how a dipole works). Now 70Ω isn’t 50Ω but it’s still in a decent range where the power transferred is still about 90W (for a 100W/50Ω system).

Now if that antenna was analyzed at other frequencies .. away from that resonant point .. the values for these components would change. The reactance of the antenna would grow, Rradiation may shrink, and Rloss may grow. It is possible to calculate these values for any ideal dipole in free-space, but it is not trivial. Here is the impedance of this sample antenna as a function of frequency.

You can see the resistance bouncing up and down as a function of frequency (all the way up close to infinity at twice the resonant frequency) and you can see the reactance bouncing between very high capacitance (negative numbers) and high inductance (positive numbers). Notice how the reactance goes through zero at odd multiples of resonance … 7.1 MHz .. 21.3 MHz .. over and over. Of course the resistance shown in this plot is the total resistance .. the combination of Rloss and Rradiation. The follow plot shows a comparison between the two as a function of frequency.

Now lets throw another term at you, Antenna Efficiency. The efficiency of an antenna is really just the ratio between the radiation resistance and the total real input resistance. That is what percentage of the real input resistance is used to convert the RF energy to radiation. Around the resonant frequencies the efficiency is near 1.0 (100%), close to double the resonant frequency it goes down to 0.0 (0%). At least in the ideal case.

I’ve been around the world and I..I..I can’t find my tuner

Those astute readers have probably noticed by now the one thing I haven’t actually talked about is the antenna tuner itself. I wanted to lay down all this ground work to get down to one … simple … thing.

The antenna tuner doesn’t tune an antenna.

What everyone colloquially calls an antenna tuner is actually called a Transmatch. What does it do you ask? It creates a matching network to your antenna (if connected directly to the antenna) or the antenna system (if you are like many people and have coax or ladder line running to the antenna from the tuner).

By adding a combination of inductors and capacitors across the antenna it accomplishes two separate but equally important things.

It cancels any reactance the antenna or antenna system may have. Remember – reactance is bad. It transforms the real part of the input impedance of the antenna into 50Ω – which allows for maximum power transfer into the antenna.

For example, this circuit shamelessly stolen from wikipedia illustrates an example of what a simple antenna tuner can do.

In this case the load (antenna) is simply a 1000Ω real resistance. By adding the proper capacitance in parallel and inductance in series, the equivalent impedance presented to our transceiver is transformed to 50Ω. Since it it now 50Ω we can do simple circuit analysis to determine the current through (or voltage across) the 1000Ω load resistance. So we can easily calculate how much power is absorbed by it. The same techniques can be applied when the load also has a reactive component as well. Likewise we can also split the resistance into loss and radiation and determine how much power actually gets radiated.

By cancelling the reactance of the antenna and transforming its impedance to 50Ω, the antenna tuner allows the antenna to work over a wider frequency range than an antenna without it. It DOES NOT nor will it ever allow a bad antenna to work as good as an antenna cut for the right frequency. It will allow it to work better than without an antenna tuner. In fact with some simple circuit solving we can see this.

In this plot we have several different situations considered. The blue line represents the simplest of cases. We connect our antenna directly to our transceiver and see how much power gets absorbed by the antenna. This of course assumes that the transceiver will work no matter what is hooked up to it (don’t try this at home kids .. it’s purely theoretical).You see that the antenna only seems to really work with any decent efficiency at it’s resonant or odd multiple of it’s resonant frequency.

The red line takes the blue line one step further, it splits the real part of the antennas impedance into loss and radiation and only displays what is actually being radiated. It should be no surprise that it is even worse than before. The further off resonance the antenna is used at, the greater the portion of available power is wasted as heat (and other ohmic losses).

The orange line is our last case, the case in which we have an antenna tuner to perform the matching of the antenna to our 50Ω system. My little program calculated the input impedance of the antenna at each frequency and then determined what combination of capacitors and inductors (and also their values) were required to perform the matching. In case you are looking at the area below 6 MHz and wondering why it looks different, that is the point where the real part of the antennas input impedance drops below 50Ω so a different configuration of matching was needed.

Also the green areas are approximate frequencies of the amateur bands.

The effect of the matching system is very noticeable on quite a number of the bands. On the 12m band you can have 60W radiated instead of 5W, on the 80m band you have 8W radiated instead of 0.4W.

Now I know someone will mention how they use their 40m dipole/G5RV/flagpole/mothers dentures on 80m and have no problem making contacts. Well, antennas are only one part of the equation. The atmosphere can take care of the rest. In fact I’ve accidentally made contacts on 40m with no antenna or coax hooked up to my tuner. I don’t recommend it though.

What about coax loss you may ask? Well I wanted to keep things as simple as possible and this is certainly a best case scenario. Anything else you want to add in will only make things worse. So as long as you understand the best case scenario, you should be able to get a firm grasp on what happens when you make it worse.

Next time I’ll tackle feedline losses and other things in our antenna systems!