Antenna Q Factor

You’ve probably heard the term “Q factor” tossed around in describing antennas, but maybe you haven’t quite yet picked up on exactly what it means from a practical standpoint. Let’s see if we can get at Q, or quality factor, as it relates to antenna circuits and amateur radio operations without reviewing any college level physics or higher math. When we’re done, you’ll have an intuitive understanding of Q that likely far exceeds that of the average ham!

In the grander picture beyond ham radio, the quality factor is a value that describes some characteristics of an oscillating or resonating system. In radio we’re mostly interested in electric circuits that do the oscillating, and an antenna circuit is of particular interest as oscillating circuits go. We’ll get to the practical upshot of an antenna’s Q factor shortly, but we can get a good sense of Q factor by thinking about some other kinds of oscillators, like a simple pendulum – a hefty weight hanging on the end of a long string, able to swing back and forth. Stick with me and we’ll get back to antennas with your exclamation of “Ahhhhhhh! I get it!” in just a moment.

Q factor defines the damping of a resonator. The pendulum in water is damped more than the same pendulum swinging in air.

 

Q-factor_bowling_ball

Q factor defines the damping of a resonator. The pendulum in water is damped more than the same pendulum swinging in air.

Damping: Q factor defines the damping of a resonator. You may think of damping as how long it takes for an oscillator’s action to die out. Suppose with a single push you swing a lengthy and weighty pendulum that’s hanging in air from a high anchor point. Imagine a bowling ball strung up from the ceiling by a nylon cord. You push the ball up and then release it, and you count 200 back-and-forth swinging cycles until the bowling ball is perfectly still again. This pendulum oscillator is not damped very much, but the resistance of the air against the ball and perhaps a little friction at the anchor point delete a fraction of the initial energy you supplied with each cycle until the pendulum is again unmoving. The energy is lost slowly.

Suddenly, the plumbing fails dramatically and the room fills with water. Fortunately, you’re a good swimmer and you displace the bowling ball again to the exact same location as before and then release it. You count only a handful of back-and-forth swinging cycles before the bowling ball is stationary in its watery surrounding. The pendulum oscillator is now highly damped by the water’s resistance. It loses the imparted energy very rapidly.

Resonance: Suppose you want to keep the pendulum oscillating with its natural frequency of resonance. You have to add just enough energy each cycle to overcome the energy lost to the resistance. With the bowling ball suspended in air you could easily make up for the lost energy each cycle by providing just a tiny little push at a convenient spot in the swinging cycle, perhaps just as the ball peaks in height and begins downward along its arced path. It’s easy to maintain resonant oscillations this way. But in the water you would have to issue a rather forceful shove each cycle to make up for all the energy lost in a single back-and-forth swing! Reinforcing resonance ain’t so easy with a highly damped oscillator!

Q Defined: Q factor is defined as the ratio of the energy stored in the oscillator to the energy that must be imparted per cycle to keep the oscillator swinging consistently. That is, the energy of the initial lift and shove of the bowling ball compared to the energy of just one of your regular reinforcing shoves to keep the ball swinging to the exact same height (amplitude) each cycle. The energy you add with a shove each cycle is exactly the same as the energy lost to resistance each cycle. So, in an equation form it looks like this:

Q = 2π x Energy Stored / Energy Lost Per Cycle

(The 2π term is a mathematical convenience that keeps things simple, so we won’t worry with it.)

From this simple equation you can see that our bowling ball suspended in air is a high Q oscillator – the energy lost per cycle is quite small compared to the energy stored from that initial shove, so Q will be a relatively high value. On the other hand, the bowling ball pendulum in water is a very low Q oscillator since gobs of energy are lost per cycle as compared with the initial stored energy, resulting in a lower comparative value for Q.

Now, enough of this bowling ball absurdity and back to some serious antenna talk!

Loading coil and capacitance hat. Compliments Hi-Q-Antennas.
Q-factor_loading_coil

Loading coil and capacitance hat. Compliments Hi-Q-Antennas.

Back to Antennas: Energized antennas are oscillators too. Current surges back and forth in radiating elements and, just like a bowling ball dangling from your ceiling and flying back-and-forth, there is a natural resonant frequency for an antenna. When you trim an antenna’s length you are adjusting the resonant frequency by changing the distance that current has to flow from end to end of the element, and hence, the time required for it to do so!

The time required for current to surge back and forth along the element’s length can also be impacted by inserting components like coils (inductors) or capacitors. It’s sort of like cheating; inserting the components to make the antenna act like a much longer antenna than its true physical length. You may hear terms such as “loading coils” and “capacitance hats,” or a “loaded antenna,” simply meaning that such tricks have been used to fool the antenna into thinking it’s a bigger boy than its diminutive height or length indicates!

“So,” you now ask, “why are some antennas still really long if we can just load them up with coils and hats and keep them shorter?” Good question, and the answer is Q.

Q and SWR Bandwidth: Q factor has no units – no ohms or henry or amps or anything – just a number. And there’s more than one way to calculate Q for an antenna. We can’t practically use the equation listed earlier, but magical mathematical transformations provide us the following more practical definition of Q when applied to oscillators that have relatively high Q values (>>1), like most antennas:

Q = ƒc ÷ (ƒ2 – ƒ1)

…where ƒc is the frequency of resonance (the center frequency to which the antenna is trimmed), and …ƒ1 and ƒ2 are the frequencies above and below the center frequency to which the antenna will operate, or achieve and acceptable value of SWR. (Properly, this is where the frequency results in 3 dB of power loss compared to the center frequency power transfer, but you can also use the frequencies where SWR increases to 2:1 as a practical comparison measure between antenna systems.)

You’re probably starting to feel that “Ahhhhhh!” well up in your throat.

You see now, as in the SWR curve diagram below, that an antenna that operates well over a broad band of frequencies (ƒ2 – ƒ1) is going to result in a relatively low Q value. An antenna that operates well across only a very narrow range of frequencies is going to generate a relatively high Q value. Thinking back to our bowling ball pendulums, the high Q antenna (bowling ball in air) is going to oscillate very efficiently and requires only a little reinforcing energy from the transmitter when it is functioning near its resonant frequency. But if you tune away from the resonant frequency only slightly you are going to see rapidly rising SWR and reduced efficiency. That freely swinging bowling ball doesn’t like to be stopped or changed from its natural swinging frequency! Don’t try and reverse its path before it’s ready to do so!

On the other hand, while a low Q antenna is somewhat more damped and may require slightly more reinforcing energy, it can oscillate well across a much broader range of frequencies. Note, the bowling ball in water is an over-the-top extreme illustration of low Q. However, you can imagine that because the bowling ball loses energy so rapidly in the water, it would not be difficult to get it to move back-and-forth at frequencies other than its natural resonant frequency, given the force to drive it. Just shove it back and forth with a little greater effort at any rate you wish! It won’t be stubborn or knock you over with a high store of energy like the air pendulum.

Comparison SWR curves for a Low Q and a High Q antenna system. The 2:1 SWR bandwidth is used for comparison computations using associated frequencies.

 

Q-factor_swr_curves

Comparison SWR curves for a Low Q and a High Q antenna system. The 2:1 SWR bandwidth is used for comparison computations using associated frequencies.

Q, Physically Shortened, and Full Length Antennas: Again, our bowling ball illustrations are extreme cases, and with antennas the difference between high Q and low Q is not quite so starkly exhibited, but the effects are important! Here’s why, and here’s why every antenna is not loaded up with coils and hats to keep it short and convenient.

When an antenna is physically shortened for the desired operating frequency and a loading coil is added to help it resonate at that desired frequency anyway, the Q factor is increased. You may consider that the inductive coil’s effect is to reduce damping in the antenna circuit at the desired operating frequency. Generally, the greater the antenna loading the higher the Q factor, and thus, the narrower the SWR bandwidth of the antenna. But greater loading (higher Q) also allows physically shorter antennas for a given frequency.

The advantage of the low Q antenna is its efficient operation across a broad bandwidth, so a full length antenna is simple and effective and large, and great for home shack use. A full length half-wave dipole is an example, or a ¼-wave vertical with ground plane. For the HF bands these antennas may be many dozens of feet long, so mounting one atop the family van probably is not an option.

The advantage of a high Q antenna is its shortened length, so you’ll often see these mounted on vehicles for mobile HF operations. A loading coil and perhaps a disk, spoke, or swirly capacitance hat is the telltale sign of a vertical high-Q loaded antenna. They get the job done at or very near the resonant frequency of the loaded antenna.

Finally, you ask: “What good is a high Q antenna if you’re limited to only one amateur band and perhaps only a very narrow range of frequencies in that one band?” Yea, that would be sort of a drag, huh? Driving cross-country never able to leave 14.313 MHz. Never fear, there are common solutions!

Many high-Q mobile antenna manufacturers implement mechanized antennas that change the antenna’s resonant frequency itself! Although the SWR bandwidth is very narrow, the tuned operating frequency is made to always be the centered resonant frequency by changing the size of the loading coil as you tune from frequency to frequency, or band to band. Think of that sharp, V-shaped high Q SWR curve in the diagram above moving quickly up and down the band as you tune, or jumping to another band altogether to slide along with your tuning whim!

Usually this is implemented by using a movable tap on a large loading coil so that the number of turns used by the antenna changes commensurately with the desired operating frequency. The amount of loading is changed in this way depending on the operating frequency selected, thereby altering the antenna’s center resonant frequency. It’s a clever solution, if substantially more complex than a static wire or vertical radiator. Sometimes you’ll hear these referred to generically as “screwdriver antennas” due to a seminal design that employed an electric screwdriver motor component to move the tap up and down the coil. But several varieties are found on the amateur market by a variety of names.

High Q, low Q, and 10Q for reading! 10Q very much! I hope this helps you understand the world of loaded antennas a little better through the nature of Q. Good luck, 73, and may the Q be with you!

~ WØSTU